We apply Theorem 1 noting that Ψ AM (u, v, p) = (u+v)/2 is continuous in all its arguments, and that the Bayes optimal classifier for P AM is of the requisite thresholded form.

while there has been considerable amount of work on consistency of algorithms for univariate performance measures [16,[20][21][22], theoretical results on non-decomposable measures have been limited to characterizing the Bayes optimal classifier for F-measure [15,23,24], and some consistency results for F-measure for certain idealized versions of the empirical plug-in and decision theoretic methods that have access to the true class probability [15].


This soft clustering is often desired, as it encodes uncertainties on datato-cluster assignments.

many algorithms are either similarity-based or model-based.


These switching experiments typically reveal transient responses to the switch that have rather long time scales, and it is tempting to identify these long time scales as the time scales of adaptation.

to address this, we look directly at the input/output relation as the standard deviation u(t) varies in time.


In Fig 2 , we report two values, W k 2 − (I − W k 1 A) 2 and θ k , obtained by the baseline LISTA model (4) trained under the noiseless setting.

the training is modeled as: Many empirical results, e.g., [3][4][5][6][7], show that a trained K-layer LISTA (with K usually set to 10 ∼ 20) or its variants can generalize more than well to unseen samples (x , b ) from the same P(x, b) and recover x from b to the same accuracy within one or two order-of-magnitude fewer iterations than the original ISTA.


For any prior distribution over MDPs, the optimal exploration strategy is available through dynamic programming in the Bayesian belief state space.

according to their metric, averaged across the 14 games they consider, we improve upon both base DQN (0.29) and their best method (0.37) to obtain 0.62 via bootstrapped DQN.


Given an image of a face, the network learns to infer properties such as pose and lighting.


Given such a set of clusters, we show that Gibbs sampling is essentially a message passing algorithm over the cluster graph formed by connecting clusters that have atoms that are in the Markov blanket of each other.

an alternative approach is random scan Gibbs sampling which often converges faster than systematic scan Gibbs sampling).


• Optionally: If we have additional meta-information z, then the above mentioned networks could be conditioned to obtain the conditioning mapping φ(x m |z).

their extensions to handle the case when the inputs or outputs are permutation invariant sets rather than fixed dimensional vectors is not trivial and researchers have only recently started to investigate them [5][6][7][8].


CRF [22,19]) as recurrent works to effect on final convolution predictions.

figure 3 shows the qualitative comparison with the baseline "Deeplabv2 [6]".


Thus, the task of optimal coordination in a team Markov game boils down to having all the agents play an optimal Nash equilibrium in state games.

with GLIE exploration, at every time step p , each joint action occurs with positive probability.


The q u are independent of topics and offer greater modeling flexibility, but they are less interpretable than the η u in CTPF.

it is about probabilistic modeling and statistical algorithms.


For both languages, we extracted the following emission features: indicators for the words, their prefixes and suffixes of length 3, the previous and next words and the word shape according to the Stanford NLP pipeline 2,3 .

in the English case, we found that the performance plateaued for any label matrix with rank greater than 20 and we see an improvement of 0.5% accuracy.


We interpret the presence of a pair (x, x 0 ) in the support of D as the preference of x 0 over x.

we used L1-norm for slack variables and allowed the constraint cache and the tolerance for termination criterion to grow in order to control the algorithm's convergence, especially for larger values of the regularization constant.


Indeed, the work of [4] assumes the Bouquet Model where distributions are restricted to be isotropic Gaussians whereas the work of [5] assumes a more stringent model of sub-orthonormal matrices, something that even Gaussian designs do not satisfy.

even after allowing the L 1 algorithm to run for 500 iterations, it was unable to reach the desired residual error of 10 −4 .


D = 0), or used spike history mapped to a set of 4 basis functions formed by othogonalising decaying exponentials with time constants 0.1, 10, 20, 40ms (similar to those used in [1]).

it is important to note that the Gaussian model has free parameters for the singleneuron variability, whereas the conditional variance of the Poisson model is constrained to equal the mean.


(ii) Nodes i ∈ V , compute their beliefs as follows: (iii) Estimate max.

in Section 5 we develop two iterative message-passing algorithms.


The computational cost shows the expected trend, with Gamma being least costly, followed by Spec, Pears, and finally Boot (this trend is only visible for the larger m = 500 datasets).

obtaining a consistent finite sample estimate of this threshold -that is, an estimate that converges to the true threshold in the infinite sample limit -is a significant challenge.


The generator uses the loss E Z∼P Z D(G(Z)).

for example, if we assume that d is not bounded from below and consider two points x, y ∈ M that are sufficiently close then a penalty term of the Lipschitz quotient as in (12) imposes a condition on the differential around x and y in the direction (x − y) only, i.e.


We propose a non-parametric Bayesian framework for modeling collections of such data.

as the discrete Poisson distribution is characterized by a rate parameter λ, the Poisson process 1 is characterized by a rate function λ(t); it has the property that over any given time interval T , the number of events occurring within that time is Poisson with rate given by λ = T λ(t).


Semidefinite optimization can be described as the problem of optimizing a linear function of a symmetric matrix subject to linear equality constraints and the condition that the matrix be positive semi-definite.

as expected the maximal-alignment kernels' spectral transformation is zigzagged, diffusion and Gaussian field's are very smooth, while order constrained kernels' are in between.


Similar phenomena have also been demonstrated in Fig.

a higher-order TSBN, TSBN-4, performs much better than the first-order TSBN does, suggesting that using high-order messages can help TSBN better pass useful information.


When t = m we obtain that x (i) 1:m ∼ q(x 1:m ).

a global maximum of ( 1) is called a U − M maximal clique of graph G. When both sets U and M are clear from the context, we simply call the solution a maximal clique.


We now detail the network structure used for our experiments that incorporates this structure.

we now assume that we have available to us the matrix of pairwise similarities between features S j,k computed as above.


Intuitively, we need the hashed space to contain no more than P solutions because that is a base case where we know how to produce uniform samples via enumeration.

conditioned on σ surviving, the mean and variance of the size of the surviving set |S i | are independent of σ because of 3-wise independence.


These prior and penalty weights have been incorporated successfully into offline procedures [3,6,11].

appendix B discusses how to use "abstaining" to provide a smooth restart from alpha-death, whereas Appendix C contains a numerical simulation demonstrating the use of decaying memory.


SVM s∪t is a linear SVM trained on the union of the target and source examples.

the situation where the test data is drawn from a distribution that is related, but not identical, to the distribution of the training data has been widely studied in the field of machine learning and it is traditionally addressed using so-called "domain adaptation" methods.


This connection to generative models is very powerful, and can easily be extended to include missing data-one of the large advantages of generative models in machine learning.

the expectation error ) over both the distribution of x and the distribution of nearest neighbor x N N for a given x: We then replace the posteriors p(C|x) and p(C|x N N ) as p c (x)/(p 1 (x) + p 2 (x)) and p c (x N N )/(p 1 (x N N ) + p 2 (x N N )) respectively, and approximate the expectation of the posterior x at a fixed distance d N from test point x using pc (x)/(p 1 (x) + p2 (x)).


Furthermore, it is rather unrealistic to assume that a Bayes decision function can be represented by the algorithm.

these results are purely asymptotic, i.e.


On one hand, from the table, we can see that our framework TLRisk greatly outperforms the baseline methods Image Only and Search+Image, no matter which dissimilarity function is applied.

first of all, the loss function L(θ C , θ Xt , r = 1) can be formulated using distance functions between the two models θ C and θ Xt , so that Since the sizes of Θ C and Θ Xt are exponential in general, we cannot calculate Equation (3) straightforwardly.


Then try to utilize Definition 1 to bound the remainder terms.

thus it has a very intuitive interpretation.


In simulation we divided X into 100 bins, and initial spikes N 1 = 1000.

if the overall neural activity is weak at time k, then the global inhibition regulating M is decreased to allow more spikes at time k + 1.


Thresholds were drawn according to W 2 (' 0) § © 6 We generated ) networks, and compared results of standard loopy belief propagation to results obtained by fractional belief propagation where the scale parameters were obtained by Algorithm 2.

in section 8 we end with the conclusion.


We will always integrate out H ′ t and will work directly with the distribution probability P ′ (H (j) = 1), and 0 otherwise.

to sample from a TRBM P , we need to perform a directed pass, sampling from each RBM on every timestep.


1 e ⌦(n 1/2 ) for all i 2 [m]: Now, let F 0 be the collection of all functions f j for which f j (S i ) = 1/2 + |S i |/(2n) on all sets {S i } m i=1 .

the algorithm cannot learn any information about which function in F 0 generates the samples.


The solution is well known when λ = 0 since it corresponds exactly to the rescaled Chebyshev polynomial [Golub and Varga, 1961], but as far as we know there is no known result about its regularized version, thus making the "finite-step" version hard to analyze.

if we wait at least O(N ) updates, then the extrapolation method is of the same order of complexity as the optimization algorithm.


We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse Gaussian processes.

as discussed in section 3.4, depending on the characteristics of the dynamical system, other smoothing methods could be more appropriate [20].


Instead, we formulate a complexity measure that captures the diversity of the observed tasks.

the main technical difficulty is to control the propagation of errors.


hMetis returns within seconds, however the assignments were not competitive.

in many applications, the data is of rich structure that can be represented by a hypergraph, where the data items are represented by vertices and the associations among items are represented by hyperedges.


In finite state-action problems, it has been shown that Q-learning converges to the optimal action-value function [5,10].

a stationary Markov policy π(•|x) is the distribution over the control actions given the current state x.


Furthermore, we would like to classify every sample that is distant from radiologist mark as negative, this is easily accomplished by considering each negative candidate as a bag.

in Section 2 we show that CAD data is better modeled in the multiple instance learning (MIL) framework, and subsequently present a novel convex-hull-based MIL algorithm.


For each pair of descriptors, a simple search that uses O(α 2 ) time is sufficient to determine whether the pair has more than β tags in common.

in practice this formulation was found to be restrictive and sometimes the explanations contain inconsistencies or were incomplete.


We modeled the power consumption by assigning a cost of 0 for executing the stay action at the recharging station, and a cost of 1 otherwise.

the Bellman backup operator for CPOMDP generates pairs of α-vectors (α R , α C ), each vector corresponding to the expected total reward and cost, respectively.


we say that a topic j is dominant for a word w, if (i) w has a unique largest probability in the topics, and (ii) its largest probability is in topic j.


In , the convergence rate for a time-varying topology was proved when the maximum of the subgradient is assumed to be bounded.

eCD-PSGD is more robust to more aggressive quantization, as extremely low precision quantization can cause DCD-PSGD to diverge, since DCD-PSGD has strict constraint on quantization.


I consider the usual Bayesian setup of supervised learning: A training set DN = {(Xi, y; ) Ii = 1 ... , N} (x E Rd and y E R) is known and the output for the new input x is predicted by the function f(x) which is sampled from the prior distribution of model outputs.

for the simulations, I use analytical GP learning (scaling like CJ (N 3 )) [4] and a TAP mean field algorithm for Bayesian NN.


Since the first betting round is a small portion of the entire game, storing a value for each state in a table required just 42 MB.

while DeepStack defeated a set of non-elite human professionals in HUNL, it never defeated prior top AIs despite using over one million core hours to train the agent, suggesting its approach may not be sufficiently efficient in domains like poker.


Traditionally partially-specified data X is characterized as incomplete data containing missing values [19,40], i.e., some sequence elements are replaced by an unknown word symbol <unk>.

for example, we can allow for missing subsequences of unknown or bounded length, negative information, and observed constraints in the form of conjunctions of disjunctions or partial orderings.


Since in the experimental section we do not exploit the solution to this problem for reasons that we will explain later, here we just sketch such procedure.

we revise the theoretical approach presented in [13] by: i) giving a simpler and direct solution to the problem of devising an exact closed-form solution (full rank case) for the weights of a linear autoencoder network for sequences, highlighting the relationship between the proposed solution and PCA of the input data; ii) introducing a new formulation of the autoencoder learning problem able to return an optimal solution also in the case of a number of hidden units which is less than the rank of the full data matrix; iii) proposing a procedure for approximate learning of the autoencoder network weights under the scenario of very large sequence datasets.


Simple bounds to this quantity, like H , besides being hard to compute due to the presence of the supremum, are extremely conservative since the Rényi divergence is raised to the horizon H. We suggest the replacement of the Rényi divergence with an estimate )) defined only in terms of the policy Rényi divergence (see Appendix E.2 for details).

a prime example of this alternating procedure is Proximal Policy Optimization (PPO) [44], that has displayed remarkable performance on continuous control tasks.


We report the results of our experiments in Figure 1.

we want the learner to select TPQs for which the responses will be most useful toward the goal of learning the target policy.


Definition 1 (Self-Expressiveness Property (SEP)).

this is an important scenario because real data such as those in Hopkins155 and Extended YaleB often suffer from both problems, as illustrated in [8, Figure 9 & 10].


On this attractive-only Ising potential, the Swendsen-Wang method [12] mixes rapidly, and so we use the resulting samples to estimate the ground truth.

the central result on rapid mixing is given by the following Theorem, due to Dyer et al.


In two typical cases using 500 and 5000 training points full GP runs in 0.24 seconds (for 500 training points) and in 34 seconds (for 5000 training points), VDMGP runs in 0.35 and 3.1 seconds while SPGP-DR runs in 0.01 and 0.10 seconds.

2 Available at http://theoval.cmp.uea.ac.uk/ ˜gcc/competition/ Temp: 106 dimensions 7117/3558 training/testing data, SO2: 27 dimensions 15304/7652 training/testing data.


[32] proposed stochastic rotated quantization of gradients, and reduced gradient precision to 4 bits for MNIST and CIFAR dataset.

in this work, we compare TernGrad with 32-bit gradients, considering 32-bit is the default precision in modern deep learning frameworks.


Third, their method has quadratic dependence on the problem condition number unless extra acceleration technique is combined, while our method depends only linearly on condition number as shown in Section 4,.

due to space limitation, we only present part of the results here, more experiments can be found in supplementary materials.


Pham and Pagh then showed that TENSORSKETCH can also be used for statistical learning with the polynomial kernel [16].

we say an n × k matrix V with orthonormal columns spans a rank-k Before proving the correctness of the algorithm, we start with two key lemmas.


All the information regarding data point correlations is captured in the KL term and the connection with the observations comes through the variational distribution.

more precisely, k x determines the properties of each temporal latent function x q (t).


The other part has to do with making them potentially conditional on action and observation.

the target functions z i are only part of specifying the question network.


Active stereo techniques supply their own light [4].

the output of this system is a set of pre-aligned laser range measurements and camera images.


Then, we observe that opt(L) ≥ opt(L ′ ) = opt I ′ (L ′ ).

as an example for calculating the validity, the state-capital cue distinguishes the first and the third pair but is correct only on the latter.


For an input image I and a given pair of kernels, we can measure the data log-likelihood by associating each window with the maximum likelihood kernel: We search for a blurring model p k0 such that, when combined with the model p 1 (derivatives of the unblurred image), will maximize the log-likelihood of the observed derivatives: One problem we need to address in defining the likelihoods is the fact that uniform areas, or areas with pure horizontal edges (the aperture problem) don't contain any information about the blur.

yet, the histogram structure of different images is not identical, and we found that trying to deblur one image using the statistics of a different image doesn't work that well.


[2018] provided a general approach to compute finite sample analysis in the case of linear multiple time scales stochastic approximation problems.

motivated by the recent papers by Nemirovski et al.


to classify the recipes we used 10-fold crossevaluation with 5 repetitions, picking 80 random recipes per-class for each repetition.


We only need to do simple matrix multiplications to approximate the integral at each point, but do not have to solve matrix inversion problems.

the parallelism of the vector field is used to measure the linearity of the target prediction function.


For the VF dataset, witnesses   consistently achieve higher than 93% accuracy whereas face descriptor has lower than 86% for 3 attributes.

note that the larger values the non-witness neurons have, the more substantial reduction they undertake.


There is a clear divide with improved performance from the Schatten-∞ based methods.

letting Ũdiag(s) ṼT X represent the rank-k+ 1 approximate SVD, then the approximate #-operator corresponds to the low-rank approximation and the reweighted remainder, We note that the #-operator is also defined for the ∞ norm, however, for notational clarity, we will denote this as x and leave the # notation for the Schatten-∞ case.


Given a domain X and covariance function K(•, •) ∈ X × X → R, a Gaussian process (GP) over the space of real-valued functions of X specifies the joint distribution at any finite set X ⊂ X : where the f = {f n } N n=1 are (latent) values associated with each x n ∈ X, and K ff is the Gram matrix, the evaluation of the covariance function at all pairs (x i , x j ).

this is in contrast to the IVM, in which sites excluded from the active set have parameters clamped to zero, and where those included are not iterated to convergence, such that the necessary fixed point conditions do not hold.


Note that the original algorithm in [11] is designed for batch mode active learning.

the evaluation function L(D l , D u , x s ) essentially consists of two components: L s,s − det(L a,a )/L s,s and Minimizing the first component is equivalent to minimizing L s,s because L a,a is independent from the selected instance x s . Since L = (K +λI) −1 , we have to choose an instance with small L s,s , we select the instance with large self-similarity K s,s .


These data were collected using a free association task, where participants were given a cue word and asked to generate a single associate of the cue.

consistent with the principle of least collaborative effort, we make a second prediction that speaker and hearer will collaborate and share the communicative burden equally.


Acknowledgements -Thanks to Paul Hoyer, Jarmo Hurri, Bruno Olshausen, Liam Paninski, Phil Sallee, Eero Simoncelli, and Harri Valpola for discussions and comments.

although it is clear that the variability degrades performance on many perceptual tasks of the laboratory, it might well be that it plays an important function in everyday sensory tasks.


Thus there is a computational price to be paid for the optimization of a true segmentation error.

the connected components of this thresholded affinity graph are the segments of the image.


MHE can be regarded as a complement that can be applied on top of these methods.

we consider to use arccos( ŵ i ŵj ) to replace ŵi − ŵj in hyperspherical energies.


The above definition implies, for µ(X) ≤ µ, the following inequalities.

for points with large contribution, where −Y i Z i β 0, the objective function increases by a term almost linear in −Y i Z i β.


Assumptions 3 and 4 are the key technical conditions under which we can generalize the analyses in [2,3,4] to the general GLM case.

we note that this analysis might be of independent interest even outside the context of modeling and recovering graphical models.


The model is constructed according to the principle of separation of time scales: processes that operate in the 100-1000 ms range are modeled as accurately as possible, those that vary on a much shorter time scale are assumed to instantaneously achieve their steady-state values, and those that occur over longer time scales, such as slow inactivation, are assumed constant.

dopamine release results in the amplification of key ion currents, leading to the emergence of bistability, which not only modulates the peak firing rate but also introduces a temporal and state dependence of the model's response, thus improving the detectability of temporally correlated inputs.


If the z i were supplied to the reservoir, each sub-vector would on average have the same impact on the reservoir neuron activations.

in this paper, the decoder is a phoneme recognizer just accommodating a bigram phoneme language model.


Learning similarities is also of particular importance for posture analysis [8] and video parsing [17].

to overcome this issue we relax the binary constraints and force instead the continuous solution to the boundaries of the feasible range by maximizing the additional term λ 3 X − 0.5 2 F using the Frobenius norm.


We randomize the procedure in the following manner: (i) C ∼ W(p, I p×p ), (ii) x i ∼ N (0, C), (iii) q ∼ B(1, 1) for the first and q ∼ B(1, 4) for the second cases, (iv) I(j ∈ A) ∼ Bernoulli(q) for j = 1, . . . , p where I(.)

[12] choose to further mix over a and a global λ while fixing the values of b and φ.


One is the full classifier that Bob owns, the second is the privacy-preserving classifier that Bob owns and the last is the on-line classifier that Alice constructs.

the theoretical construct was still too demanding to be of practical use.


Throughout the paper we use linear SVMs.

the results in Table 2 show that the generalization ability can significantly be increased by RCE.


While this approach takes into account structural correlations, the marginal probabilities are generally dense and different from each other.

the main challenge is how to compute the Jacobian of Π Ω .


While we cannot prove that the algorithms converge to the minimum, in all the applications we have tried, they perform very well.

the interesting thing about this experiment is the fact that no filter ever is allowed to see global information, except through S. even though W is blind to anything larger than a 16 × 16 patch, through the inhibition of S, the model is able to learn the placement of facial structures and long edges.


We do not apply any other special preprocessing to the data.

we report report results that use beam size 10, but using beam size 2 only lowers the F1 score of LSTM+A on the development set by 0.2, and using beam size 1 lowers it by 0.5.


Our discrete log-concavity tester improves on previous work in terms of both sample and time complexity.

this will turn out to be crucial for our applications.


Although perceptual spaces were adopted in [18], only very simple hypotheses (rectangles over the position of dots) were used.

we present an algorithm for learning visual concepts directly from images, using probabilistic predictions generated by visual classifiers as the input to a Bayesian generalization model.


To circumvent these issues we explicitly incorporate the prior knowledge that a neuron only reads out from one particular location in space and model each neuron with a spatial transformer layer [19] with a single grid point reading from v ijk .

we optimized the objective using ADAM [43] and a two stage training schedule with step size 0.005 and 0.001, respectively.


The flexibility of the framework of RKHS embeddings of signed measures allows us to consider variables that are themselves multidimensional.

tests of total and pairwise independence are insufficient, however, since they do not rule out all third order factorizations of the joint distribution.


We propose a new probabilistic model for analyzing dynamic evolutions of relational data, such as additions, deletions and split & merge, of relation clusters like communities in social networks.

a large amount of relational data in the real world is time-varying.


First, the coherent support of a region, commonly assumed to be of a single label, serves as a good prior for many labeling tasks.

solving (3) with this Y is generally NP-hard.


In these networks, the temporal and structural behaviors are clearly separated.

this work focuses on upper bounding the influence σ A (T ) for any given time T and characterizing the critical times at which phase transitions occur between sub-critical and supercritical behaviors.


Since our current architectures solve complicated temporal tasks they must have some capacity for temporal relational reasoning.

inspecting the perplexity broken down by word frequency in supplementary table 3, we see the RMC improved the modeling of frequent words, and this is where the drop in overall perplexity is obtained.


The condition ŷj , ĝj > 0 holds as long as the negative gradient ĝj is pointing towards the minimum of the loss (w.r.t.

in fact, there are now a number of works that provide alternatives to BatchNorm [1,3,13,31], but none of them seem to bring us any closer to understanding this issue.


We set the "width" parameter in the Gaussian kernel to be the mean of all pair-wise training data distances, a standard heuristic.

a similarity function K : X × X → R is said to be an ( , B)-good similarity for a learning problem with respect to a loss function L : R → R + where > 0 if for some transfer function f : R → R and some weighing function w : One can see that taking the loss functions as L(x) = 1 x<C f γ gives us Equation 3 which defines a good similarity under the 0−1 loss function.


30th Conference on Neural Information Processing Systems (NIPS 2016), Barcelona, Spain.

it makes more sense to assign different sampling probabilities for different features and make the features compete with each other.


A good indication that this is not the case is that (2) is NP-hard, even in the noiseless case when ) for rank(X ⇤ )  k [20] (if we don't require RIP, we can have each A i be non-zero on a single entry in which case (2) becomes a matrix completion problem, for which hardness has been shown even under fairly favorable conditions [13]) 3 .

for any stationary point U this implies Now using the isometry property of A i gives us the following result.


Another related line of work is about spatial pyramids in object classification, in particular the pyramid matching kernel [24].

the main bottleneck of our method is still the first CNN layer.


There have been some examples of deployed active learning with human feedback; for human perception [11,17], interactive search and citation screening [18,19], and in particular by research groups from industry, for web content personalization and contextual advertising [20,21].

for example, serving many (near) simultaneous 'getQuery' requests is straightforward; one can simply enlarge the pool of workers by launching additional slave machines and point them towards the web request queue, just like typical web-apps are scaled.


Theorem 1 For any τ, α ∈ (0, 1), every policy tree π ∈ Π b0,D,K satisfies with probability at least 1−τ , where Vπ (b 0 ) is the estimated value of π under any set of K randomly sampled scenarios for belief b 0 .

regularization does not appear beneficial to this problem, possibly because it is mostly deterministic, except for the sensing action.


Recent research has combined (iii) and (iv) within a single model [6], and methods have been developed recently to address (v) while performing (iv) [5].

in [6] model selection was performed (for the number of features and number of neurons) and a maximum likelihood (ML) "point" estimate was constituted for the model parameters; since a fixed number of clusters are inferred in [6], the model does not directly allow for the "appearance"/"disappearance" of neurons, or for any temporal dependence to the spike statistics.


The subgraph B contains in contrast the difficult, combinatorial subproblem and is assigned to a combinatorial solver.

a reparametrization, that is reparametrized potentials θφ , will be called optimal, if the corresponding φ is the solution of the dual problem (3).


The reason we chose ReLU activation was that many/most of the new neural networks are incorporating it.

note that the accuracy of different adversarial attacks varies, which is expected since the various strengths of different attack method.


We therefore introduce a second partition matroid constraint M U = (E, I U ), which limits to p the number of samples selected by each model.

the procedure reduces and by a multiplicative factor (1 µ) in line 6, linearly decreases k by k and additively increases p by p , in Line 7.


Layer-wise coordination modifies the structure of Transformer from two aspects: First, each layer in the decoder attends to the corresponding layer in the encoder.

the overall structure of our model with layer-wise coordination is shown in Figure 1.


More specifically, batchnorm was applied to each of the 50 minibatches; each example was normalized using 32 examples, but the resulting gradients were aggregated over 50 minibatches.

unlike batchnorm, our method ensures that that all layers are trained on internal representations that will be actually used during inference.


We begin by demonstrating that indeed a few public users suffice for making accurate recommendations.

( 3) is solved on the basis of public users only.


A compact statistical measure of the degree of self-similarity of a stochastic process is the Hurst parameter [4].

its arrival intensity varies considerably over many time scales.


Finally, our approach draws from concepts in the Gaussian process optimization and decision-making literature [1,2] to propose a Bayesian decision-theoretic PE approach.

here the required expected value of information computations can be derived in closed-form to facilitate the selection of informative queries and determine the highest utility item from the available item set as quickly as possible.


Note that β = 2 0 = 1 reverts back to the standard active learning oracle, since epiphany always happens immediately.

this case is the simplest but captures the essence of the algorithm we propose in this section.


Specifically, given v, u and I, we predict the change in u that will lead to the maximum log p(u|x, v).

the main advantage of our model is that it can learn on large images of faces without localization label information (no manual cropping required).


We also give a bound for arbitrary π, and show corresponding lower bounds in both the uniform and non-uniform cases.

the toy example above is a 1-d linear separator.


We propose "Adept," an adaptive stimulus selection method that can optimize population objective functions.

to examine how Adept performs in the presence of noise, we first recorded a "ground-truth", spike-sorted dataset in which 2,000 natural images were presented (100 ms flashes, 5 to 30 repeats per image randomly presented throughout the session).


[24] provide an iterative algorithm for solving problem (10) that can handle arbitrarily large number of unknowns in every constraint.

the KL divergence can admit very small values of Pr(x|θ 2 ) since it is concerned with the summation shown in equation ( 4) (and not the worst case).


The fidelity ratings on the other hand are fairly uniform across all models, except for #3.3, which also has the poorest musicality rating.

for the three subnetworks of the ADA (see Figure 1), we adopt the WaveNet [43] architecture, because it allows us to specify their RFs exactly.


As is typical in supervised learning, in multiset prediction a model , then evaluated on a separate test set {(x i , Y i )} n i=1 using evaluation metrics m(•, •) that compare the predicted and target multisets, i.e.

this is analogous to the experiments on MNIST Multi, where the performance gap increased when moving from four to ten digits.


Theorem 6 (Sample-based weak regret transfer bound from bipartite ranking to binary classification).

another implication of the above result is a justification for the use of the AUC as a surrogate performance measure when learning in cost-sensitive classification settings where the misclassification costs are unknown during training time [23].


The chosen action influences the observable state of the environment in a stochastic fashion and imposes some loss on the learner.

aim to solve the optimization problem q t+1 = arg min q∈∆(M ) q, ˆ t subject to the constraint D (q q t ) ≤ ε for some ε > 0.


The goal of general rcA is to obtain a linear M x N demixing matrix W to recover the independent components c with a minimal knowledge of A and c, normally M = N. Then, the recovered components u are given by u = Wx.

iCA only defines the directions of independent components.


Second, starting from the negative sample with the highest score, it iteratively finds the optimal interleaving rank for each of the |N | negative samples.

we propose a more efficient algorithm to maximize δ j (•), which exploits the special structure of this discrete function.


From the definition of H − , we can choose f : For Part 3, first note that, for any φ, ψ is continuous on [0, 1] and ψ(0) = 0 by Lemma 4, part 6, and hence θ i → 0 implies ψ(θ i ) → 0.


The attention mechanism (see Section 2.2) adds more "computational capacity" to this model.

exact algorithms for the problems we are dealing with are more costly.


Still, these are not the distributions that typically define probabilistic topic models: the probability of a word given a topic.

for intrinsic scores (I), we use the trained corpus itself as the reference corpus.


It is worth mentioning that models based on multinomial or Poisson likelihoods such as LDA [3], HDP [27], FTM [29] and PFA [32], also enjoy this property.

in [32], h kn is provided with a beta-Bernoulli process prior by letting π kn = π k ∼ Beta(cǫ, c(1 − ǫ)), meaning that every document has on average the same probability of seeing a particular topic as active, based on corpus-wide popularity.


In our algorithm, we set the parameter = 0.24 and the confidence level α = 0.05.

in addition, we use λ = 1.5 log(d)/n for NLL as recommended in [23] and use the same tuning parameter for Direct_clime.


These separator variables S in the junction tree are p q junction tree of q Figure 1: Approximating a complete graph p by a tree q.

q tries to preserve the marginals and pairwise marginals of p: Expectation propagation is a general framework for approximating distributions of the form (1) by approximating the factors one by one.


Finally, we also thank Karl Moritz Hermann, John Hale, Richard Evans, David Saxton, and Angeliki Lazaridou for valuable comments and discussion.

to our knowledge, no tasks of this kind explicitly require counting beyond the range observed during training.


Our results are not affected if these parameters are changed by a factor of 2-3.


We experimentally validated that SING was able to embed music notes into a small dimension vector space where the pitch, instrument and velocity were disentangled when trained with this spectral loss, as well as synthesizing pairs of instruments and pitches that were not present in the training set.

next are two 1x1 convolutions with 4096 channels and ReLU as an activation function.


In order to address this shortcoming, in recent years several authors have proposed to learn object classifiers from weakly-labeled Internet images, such as photos retrieved by keyword-based image search engines.

for each class k, we train a binary SVM on the data obtained by merging D t k with D s k , where the data in the latter set is assumed to contain only positive examples, i.e., no outliers.


For example, a human labelling of a short segment of the song could be automatically extrapolated to the remainder of the song, using energy spikes in the audio signal to fine-tune the placement of beats.

the particle filter version produces 16 correct answers, two double-speed, two half-speed, two syncopated, and the same three 'switching' tracks.


Our work expands on the membership query model, and our abstention and noise models are related to a variant of the Tsybakov noise condition.

in this section, we start with the one dimensional case (d = 1) to demonstrate the main idea.


This lower bound follows from the minimax lower bound proofs for regression in the next section.

let ∂D denote the boundary of D and define the set of boundary points as , where C o = 6 √ dκ 0 , then for all p ∈ P X , all pairs of points x 1 , x 2 ∈ supp(p) \ B and all D ∈ D, with probability > 1 − 1/m, for large enough m ≥ m 0 , where m 0 depends only on the fixed parameters of the class P XY (γ).


The infinite sum is truncated, analogous to the truncated stick-breaking representation of the Dirichlet process [9].

we consider binary vote matrices from the United States Senate and House of Representatives, from the first congress in 1789 to the present.


A Markov chain is defined using these affinities by setting the transition probability 3 4 (' ) from vertex 5) to vertex to be proportional to the edge affinity, 0 6 (' ) .

as ¡ ¨ § © , the Markov chain approaches the stationary distribution x , ¢ ¥ x e . Assuming the graph is connected with edges having non-zero weights, it is convenient to interpret the Markovian relaxation process as perturbations to the stationary distribution, ) , where B ¥ § is associated with the stationary distribution x and x ) ¥ 2c B w x ) .


Our contribution is in proving that kernel quadratures can be consistent even when the integrand does not belong to the assumed RKHS, i.e., when the integrand is less smooth than assumed.

then the points are defined as X i = {iz/n} ∈ [0, 1] d for i = 1, . . . , n. Here z is selected so that the resulting worst case error (2) becomes as small as possible.


Stepsizes for LAG-WK, LAG-PS, and GD are chosen as α = 1/L; to optimize performance and guarantee stability, α = 1/(M L) is used in Cyc-IAG and Num-IAG.

the original idea of LAG comes from a simple rewriting of the GD iteration (2) as Let us view ∇L m (θ k )−∇L m (θ k−1 ) as a refinement to ∇L m (θ k−1 ), and recall that obtaining this refinement requires a round of communication between the server and the worker m. to save communication, we can skip the server's communication with the worker m if this refinement is small compared to the old gradient; that is, m ≥ 0, if communicating with some workers will bring only small gradient refinements, we skip those communications (contained in set M k c ) and end up with where M k and M k c are the sets of workers that do and do not communicate with the server, respectively.


Essentially, if this number is less than some Φ-dependent constant κ, the BP/OMP solution is proven to be equivalent to the minimum ℓ 0 -norm solution.

we will henceforth refer to w SBL as the solution of this algorithm when initialized at Γ = I M and ŵ = Φ † t. 1 In [9] (which extends work in [10]), we have argued why w SBL should be considered a viable candidate for solving (1).


In general, it is difficult to quantify this reduction except in a few special cases.

to show that the potential reduction in local minima derived above translates into concrete results, we conducted a simulation study using randomized basis vectors distributed isometrically in t-space.


GenMiR++ returns a score value in [0, 1] for each potential interaction.

we represent each group as a latent feature and define interactions between entities within each group.


We find the global mixtures and edge structure that maximizes the probability of the observed {z in } labels.

we focus on the practical application of detecting and analyzing cars in cluttered, unconstrained images.


The ellipsoidal shape defined in (2) has the disadvantage of restricting the shape of possible regions in the colour space.

both have an internal 64-bit RISC processor with clock speeds of 192MHz and 384MHz, respectively.


The large number of images collected by ImageNet allows us to train classifiers from images to the leaf node labels, which we will describe shortly.

this research has largely focused on a fairly narrow task: assigning a label (or sometimes multiple labels) to a single image at a time.


This suggests that clutter perception is best described at the proto-object level, a level intermediate to that of objects and features.

we also introduced a new and validated clutter perception dataset consisting of a variety of scene types and object categories.


If we could divide individuals into groups according to their mechanisms-or disease subtypes (see e.g.

we learn these parameters using expectation maximization (EM) to find a local maximum of the observed-data log-likelihood.


we decide update direction by the linear system (7) while monitoring inequalities ( 8) and ( 9).


Image Source Recovery We repeated the same test using 100 photos from [18].

we derived tensorial moments for a number of models, provided an efficient inference algorithm, concentration of measure theorems and reconstruction guarantees.


Definition 1 (Oblivious Subspace Embedding).

then we can rewrite model (1) in a compact form where is a vector of all 1s, ⌦ is the Kronecker product, and is the Khatri-Rao product.


It appears that quantizing convolutional layers too aggressively (e.g., 2-bit precision) can lead to accuracy loss if trained for the same period of time as the full precision variant.

then there is a random stopping time R supported on {1, . . . , N } so that QSGD with quantization level s, constant stepsizes η = O(1/L) and access to stochastic gradients of f with Moreover, the communication cost is the same as in Theorem 3.4.


We can conclude that the overall performance of PRPCA is comparable with that of link-content MF.

note that in relational data, there exist both content and link observations.


Then, in each round t, the base learner A receives not only the example x t , but also an o↵set y 0 t 2 R d for the prediction, and produces a prediction A(x t ) 2 R d , after which it receives the loss function `t and su↵ers loss `t(y 0 t + ↵A(x t )).

as for competing with span(F), since linear loss functions are 0-smooth, we obtain the following easy corollary of Theorem 1: ] be a given parameter, and set B = ⌘N D. Algorithm 1 is an online learning algorithm for span(F) for losses in C with the following regret bound for any f 2 span(F): where 0 := P T t=1 `t(0) `t(f (x t )).


The Exp3 variants most likely converge to the same values, however, they did not fully make it in the first million iterations in WC RM.

none of the players can improve their utility by more than by deviating unilaterally.


Figure 1 (a) plots the speedup of the sketched method relative to the exact solution.

running times were measured using a sequential execution.


This constraint reduces the number of learnable parameters by nearly half vs. a normal convolutional kernel.

here, however, we show that these neural networks and their recent extensions struggle in recognition tasks where co-dependent visual features must be detected over long spatial ranges.


LaSVM is an SMO-like solver for the dual version of problem (3-5) that optimizes one or two coordinates at a time, alternating process (on newly acquired examples, generated in our case by the FORCE-CONSTRAINT procedure) and reprocess (on previously seen support vectors or patterns) steps.


These techniques express low-order moments of the observable distribution as a product of matrix parameters and use eigenvalue decomposition to recover these matrices.

importantly, our unmixing technique does not require the training sentences be annotated with the tree topologies a priori, in contrast to recent extensions of [21] to learning PCFGs [24] and dependency trees [25,26], which work on a fixed topology.


Since we obtain that for any λ > 0, E 2n πe h ≤ 1.

the quantities π, S j and p j are allowed to depend on X 2n 1 in an exchangeable way (i.e.


Like the Neural Statistician, we also produce a summary statistic for each class.

this allows each class to have a concise representation independent of the number of data points and obviates the need to store the entire support set to make predictions.


1) Each curve that uses α > 0 (solid lines) improves with experience.

we prove the result for infinite planning, but the extension to depth-limited planning is straightforward.


A is here entirely determined by the covariance matrix of the vector ( X, Ỹ ) which also equals its correlation matrix (the normal scores have unit variance by definition), and thus the correlation matrix P parametrizing the Gaussian copula C P . In practice the problem is reduced to the estimation the Gaussian copula of (X, Y ).

m. Rey is partially supported by the Swiss National Science Foundation, grant CR32I2 127017 / 1.


The background class approach can be seen as an extension of the softmax approach by Matan et al.

there is often a modest overlap between the feature  the unknown samples (Da) are generally lower than the magnitudes of the known samples (Dc) for a typical deep network.


Then, we can formally represent the decision region of class ŷ as dd ŷ = i =ŷ db + ŷi and the corresponding decision boundary of this region as dd ŷ .

then the decision boundary between each pair of classes i and j is the hyperplane parallel hyperplanes w.r.t.


With Algorithm 2 and the parameters in Theorem 3, the IFO complexity to compute an ✏-accurate solution for a µ-strongly g-convex function ) log(1/✏)).

there is little analysis about its global complexity (a.k.a.


Our analysis is inspired by [16], where the NAG algorithm for general convex function is approximated by an ordinary differential equation under the limit of infinitesimal time step.

they do not clearly explain why the momentum leads to acceleration.


Finger flexion states are estimated from the behavioral flexion traces (e.g., Figure 1 (a)).

the overall average of mean square error reduces from 0.86 (pace regression) to 0.64 (SNDS).


Since the ι is given in each world, the distribution over the attributes can be represented using a Bayesian network as described in Section 3.

it arises whenever objects are not labeled with unique identifiers or when those identifiers may not be perceived perfectly.


Modern data is increasingly complex, however, with descriptions of increasing size and heterogeneity.

consider the following objective function for boosting F , where K ∈ S. Note that f is clearly a convex function in K with a Lipschitz continuous gradient.


To examine the effect of considering infinitely many possible candidates of the bounds, we introduce the following term.

it is often difficult to obtain a tight bound while maintaining correctness.


Larger receptive field would allow neurons to detect changes over a wider area, but result in a less precise perception.

one common approach is to explore and eliminate redundancy in pre-trained CNNs.


Our proposed method is related to graph-based semi-supervised learning (SSL).

incorporating labels from even a small portion of the objects may greatly refine the final hypothesis.


But in any case, unlike typical analysis for compressed sensing, where the goal is recovering w 0 itself, here we are only concerned with correlations inside the support of w 0 .

we consider the case where the objective (w, z) is H-smooth w.r.t.


This causes problems for an agent that is trying to use the collective "global" reward signal to learn an optimal policy.

in fact, all the learned values will be correspondingly lower by the same amount.


We could partially overcome this difficulty by adding the most common phrases to the lexicon, thus treating them the same as single words.

when merging QD-PageRank q 's, we need only to know the QD-PageRank q for documents that contain the term.


For standard PCA the asymptotic results are very accurate even for moderate data dimension, but for kernel PCA with a quadratic kernel we found that convergence to the asymptotic result was slow.

since C in equation ( 1) only contains a finite number of symmetry-breaking directions then in the limit N → ∞ these will have zero measure as defined by H. in this limit the eigenvalue density would appear to be identical to the isotropic case.


Hence utilities are additive over time, and the objective of maximizing E[U(WT)] can be stated in an average-cost framework where c(x, a) = Ex,a [log (1 + a S'±~:S' )].

i)m and hm need not exist unless 1'm ,a is defined appropriately.


In our implementation, each core will read n b for each process before an iteration.

the code for each method is publicly available via the library tick 4 .


From Section 2.4, assume r(•) is three times continuously differentiable on [0, 1], at the boundary, the asymptotic order of the bias is , which is smaller than the interior points.

the performance of our proposed model is not so sensitive to the accuracy of B, thus a rough estimate of the second order derivative is sufficient.


. . , h p ) = 1 n n i=1 p j=1 τj (y i − h j (x i )), where τ denotes the p dimensional vector of quantile levels.

for the sake of efficiency, we propose to use a Primal-Dual Coordinate Descent (PDCD) technique, recently introduced in [11].


We examine three different active learning algorithms by allowing them to sequentially select 15 data points.

according to the manifold assumption [3], we expect that a good solution for y u should result in a small value of L(D l , D u , y u , x s ).


Thus χ 1 directly reflects the typical multiplicative growth or shrinkage of a random perturbation across one layer.

even straight line segments can have a large Euclidean length.


These wrappers are then used as features by a decision tree learner to find a categorization of the pages on the site that implies a simple hub structure, but which also largely agrees with the original bag-of-words classifier.

on a real-world benchmark problem, this technique substantially improved the accuracy of a simple bag-of-words classifier, reducing error rate by about half.


Because of using ST-GS, the forward pass does not depend on the temperature.

the omission score of a word is equal to difference between the target image probability given the original message and the probability given a message with the removed word.


we let S = L T L, resulting in the following sampling procedure: (t) ∼ N (0, I).


To process the data, same tools employed in [29] and [32] are used, including spatial distortion, skull-stripping, and cerebellum removal.

our model operates under a semi-supervised learning setting, where both the labeled training and the unlabeled testing samples are de-noised simultaneously.


the likelihood that the two clusters have a common source.

since the algorithm also tries to maximize I(Tw; D), the words merged into the big cluster are usually the less informative words about D. a word must be highly informative to stay out of this cluster.


[10], the transformations should be "sufficiently small" so that the ground truth labels are preserved.

our algorithm runs iteratively, where at each iteration we sample new synthetic training points and use Monte Carlo to estimate the expected value of the network parameters given the previous estimate.


In machine learning terms, we would like to achieve a flow that is "sparser" in the number of paths it uses.

the boundary @M is regular in the sense that there exist positive constants ↵ > 0 and " 0 > 0 such that if " < " 0 , then for all points x 2 @M we have vol(B " (x) \ M ) ↵ vol(B " (x)) (where vol denotes the Lebesgue volume).


And with s = jω, our synthesized BM design (passive) is where the two first-order systems are both low-pass filters (LPFs), with time constants τ 1 and τ 2 , respectively; b is a gain factor.

both the cochlea's length (BM) and height (cochlear ducts) are discretized into a number of segments, with the original aspect ratio of the cochlea maintained.


The second task, IAM, is a large-scale continuous handwriting recognition task with real-life data.

for higher regularization parameters, the optimization is much faster.


The above simply says that the value of f (x) at a certain input x is the value of the standardised function s(z), for z = Wx ∈ R K , times a global scale σ f that changes the amplitude or power of the new function.

in this section we consider the 32-input, moderate noise version of the Puma dataset.


. . , X n+m ∼ p * (x), with m → ∞ as n → ∞.

first, a desirable property is consistency ( θλ n P − → θ ∞ ), i.e., convergence to the parameters that achieve the minimum possible risk in our hypothesis class.


For a p-dimensional MHP, we denote the intensity function of the i-th dimension by λ i (t).

furthermore, let K and G denote the Gramian matrices where the i, j-th element correspond to K(s, s ), with s and s being the i-th and j-th element in S. Suppose that a ∈ R |S| is the coefficient vector such that f (k+ 1 2 ) i,j (•) = s∈S a s K(s, •), and that the projection step returns f Non-convex approach.


First we find the analytical expressions relating the subthreshold voltage from the Adaptive Exponential Integrate-and-Fire model (AdEx) to the Spike-Response Model with escape noise (SRM as an example of a GLM).

even if the exponential link-function overestimates the firing probability at these low voltages it rarely produces extra spikes.


On CC and IC, the similarity coefficient of our solutions were 0.62 ± 0.04 and 0.57 ± 0.05 respectively.

unlike [9], where one seeks a segmentation of both images, here we are provided the second histogram -the epitome (representation) of the specific region of interest.


The reason for this reverse prediction is the following: most widely accepted performance measures target information retrieval (IR) applications -that is, given a label we want to find a set of relevant instances.

this means that the objective function being optimised by the method is tailored to the performance measure on which we want to do well in our specific application.


Using the tilted bound with NCVMP gives more robust estimates of the variance than the quadratic bound as the prior mean changes.

in Sections 2 and 3 we briefly review VB and VMP.


Given a LIMID L of treewidth ω, we can evaluate the expected utility of any strategy s in time and space at most exponential in ω.

when these conditions are not met, their iterative algorithm might converge to a local optimum that is far from the optimum.


Given X and y, the likelihood for w is: Consider the under-determined scenario n < d. In this case, the likelihood is not strictly concave and infinitely many values of w fit the training data perfectly well.

this model performs better than other multi-task alternatives from the literature.


We use the straight-through estimator for gradients.


simultaneously for all time points t E {ISO, 160, ... , 450} (see Fig.

a trained classifier is capable to reliably determine fro m a short sample of this distributed activity the identity of previously presented stimuli.


Assuming that EP already yields a good approximation, the computation of a small number of these terms maybe sufficient to obtain the most dominant corrections.

the small corrections arise as whenever terms y n m n are positive and large compared to the posterior variance, non-Gaussian terms f n (x) = t n (x n ) ≈ 1 for almost all values of x n which have significant probability under the Gaussian distribution that is proportional to q(x)/g n (x n ).


The simplest model we consider is a static (non-depressing) synapse, in which v is given by Eq.

the second term comes from the likelihood of the spiking observations.


Fortunately, as done by Niculae and Blondel [32], we can utilize the result of Yu [34] to significantly simplify (18).

sensitivity analysis of the set of optimal solutions has a long history in optimization theory [12].


after regressing out all the other groups, indexed by S\g.

α = 0.1) and check empirical coverage with respect to both P L µ 2 and dir L (Y ), µ , with results shown separately for true signals and for nulls.


Therefore, different disease sub-types are likely to appear in different ratios in the different hospital.

in the second part of this work we will assume that the mixture components have disjoint supports.


To compare, we also learned the 10-chain FHMM with SMF-EM on the last 5, 000 data points of the training data.

they can be approximated by the stationary distribution of the transition matrices as T become large assuming that the sequence is close to stationary [5].


it will accept any price p t < v t and reject any price p t > v t ), since its decisions there do not affect any of its future prices.

in general, the more explore rounds, the more revenue has to be sacrificed by a buyer that is lying during the explore rounds.


of features of Ii that rnatch the corresponding feature of the cue (njjm stands for the number of matching values in tl1e j-th image that have value i)} and the ntnnber of nlisulatcbing featq.res (njq stands tor the number of mismatching values in the fhimage).

the decrease is large en.oug:h.~this factor tnust cause the LF and .HF old-item distributions to reverse position.


In Section 7, we note that for several properties, the second term can be strengthened so that it does not depend on .

two additional advantages of f * may be worth noting.


The more uncertainty (ie the larger ¡ ), the smaller the role of the top-down expectation q ¡ in determining Examples of just such effects can be found in Figure 1 (d).

as long as the underlying parameters remain the same, ie `¡ does not change greatly, the inference process functions normally, as we can see in the first y steps in Figure 3(a).


Alternatively, since the distribution p(Θ, Z, Φ) in Eq.

we randomly select 7,505 documents from the whole set as the test set and the rest as the training data.


In essence, such extensions work in a self-training way; the unlabeled data are assigned pseudo-class labels based on the constructed ensemble learner so far, and in turn the pseudo-class labels achieved will be used to find out a new proper learner to be added to the ensemble.

finally it is worth stating that unlike most of existing regularization techniques used in semi-supervised learning, e.g., [5], [6], our regularization takes effect on both labeled and unlabeled data while theirs are based on unlabeled data only.


If we add a dual variable y and write µkrxk 1 = max kyk1µ y T rx, we obtain which is clearly of the form (1).

pDHG typically does not converge when non-constant stepsizes are used, even in the case that k ⌧ k < 1/⇢(A T A) [13].


While the formulation is similar to that of Yue and Joachims (2009), Assumptions 2 and 3 are stronger than those used in that study.

this can be regarded as stochastic mirror descent with noisy comparison feedback.


See Table (2) for scores per each output.

we will assume that the distribution over y d (x) is completely specified by a set of parameters θ d (x) ∈ X J d , where we have a generic X domain for the parameters and J d is the number of parameters thet define the distribution.


The new log-likelihood function is where f j (x) is an exponential family member with its expectation parameter equal to the jth data vector and the constant denotes a term that does not depend on the unknown variables {q j } n j=1 .

we can restrict the set of mixture components to the distributions centered at the data points, i.e., m j ∈ X .


Despite this currency, the question of how sparse or how over-complete a sparse representation should be, has gone without principled answer.

by constraining this distribution headway can be made.


Then, there is an absolute constant κ 0 > 0, such that for all large n, the following event holds with P X -probability at least 1 (ii) (variance inequality) There are absolute constants κ 1 , κ 2 > 0 such that for all large n, the following event holds with (iii) (mspe inequalities) Suppose that θ is chosen as θ = 2η/3 when η ∈ (0, 1 2 ), and that θ is chosen as θ = η 1+η when η > 1 2 .

an important practical aspect of Theorem 1 is that for any given contrast c, the variance v ρ (X; c) can be easily estimated, since it only requires an estimate of σ 2 , which can be obtained from F . whenever theoretical bounds on d 2 2 (F 0 , F ) and b 2 ρ (X; c) are available, the right side of line ( 10) can be controlled.


This quickly becomes intractable as the number of objects grows.

for each image we generated 10 relational questions and 10 non-relational questions.


To be more specific, we have encoder E take the image x c as input and derive its representation z, which is combined with its domain vector v c to reconstruct the image xc via Generator G. Thus, the objective function of VAE is defined as: where the first term aims at recovering the synthesized output in the same domain c, and the second term calculates Kullback-Leibler divergence which penalizes deviation of latent feature from the prior distribution p(z c ) (as z ∼ N (0, I)).

the contributions of this paper are highlighted as follows: • We propose a Unified Feature Disentanglement Network (UFDN), which learns deep disentangled feature representation for multi-domain image translation and manipulation.


Because of the match between the parallelism offered by hardware and the parallelism in machine-learning algorithms, mixed analog-digital VLSI is a promising substrate for machine-learning implementations.

we conclude from this experiment that the correlational-learning circuit, when implemented in the FPLA, operates as the original circuit.


Based on the new bound, we develop a distributed, key-value-free inference algorithm in the MAPREDUCE framework, which can fully exploit the memory cache mechanism in fast MAPREDUCE systems such as SPARK.

in comparison, InfTucker utilizes the Kronecker-product properties to calculate the gradients and has to perform eigenvalue decomposition of the covariance matrices in each tensor mode.


Notice that although we do not explicitly write the dependence on M , all of the above quantities implicitly depend on the choice of M . The analysis of the optimization in (3) shows that, with high probability, L RB (θ) is strictly concave with λ 2 (H(θ)) ≤ −C b γ 1 γ 2 γ 3 λ 2 (L) < 0 for all θ ∈ Ω b (Lemma C.3), and the gradient is also bounded with ∇L RB (θ * ) ≤ C b γ −1/2 2 ( j p j log d) 1/2 (Lemma C.2).

as the ground truth θ * , we use the ML estimate of PL weights over the entire data.


Furthermore, N is the number of possible output proof states for a goal of a given structure and a provided KB.

as NTPs operate on distributed representations of symbols, a single hand-crafted rule can be leveraged for many proofs of queries with symbols that have a similar representation.


Given observations y t , the goal of NMF is to compute basis functions W and linear coefficients x t such that the reconstructed vectors ỹt = Wx t best match the original observations.

intuitively, these fixed points occur where the notions of energy at frequency ω in eqs.


As expected, when the opponent matches one of the training models, FBR-experts and RNR-experts perform better, on average, than a near equilibrium strategy (see "Training Average" in Figure 2).

the results of this tournament are shown as a crosstable in Table 1.


We perform a much more careful analysis to show that all coordinates uniformly have low perturbation.

we establish the minimax rate in the simplest setting of a single binary split and compare it to our own results on spectral clustering.


The trends in speedup are opposite: our method requires extra optimizations that dominate training time at extremely small D; at very large D we use estimator ( 6), so our method requires less overall time.

we have a cost c : R × Y → R, where c(•, y) is convex for y ∈ Y, and a reproducing kernel Hilbert space (RKHS) of functions F with kernel K. Given a sample {(x i , y i )} n i=1 , the usual 2 -regularized learning problem is to solve the following (shown in primal and dual forms respectively): where • 2 denotes the Hilbert space norm, c * (α, y) = sup z {αz − c(z, y)} is the convex conjugate of c (for fixed y) and G = [K(x i , x j )] n i,j=1 denotes the Gram matrix.


In order to relate it to other values of , we need a little more flexibility: for given ✏ 0 and (`, F, P ⇤ ), we define which excludes a band of predictors that approximate the best predictor in the model to within excess risk ✏.

the setting of sequential prediction (also called online learning) [2] makes no probabilistic assumptions about the source of the data.


However, they did not focus on learning the input kernel.

eCoG signals of the subject were recorded at a 1KHz sampling using BCI2000 [27].


The proof of Theorem 3 is given in Appendix B.

we estimate the transition probabilities from the sample path using simple frequency estimates: as a consequence of the Markov property, for each state, the frequency estimates converge at a rate that depends only on the number of visits to the state, and in particular the rate (given the visit count of the state) is independent of the mixing time of the chain.


Consider a set of training data S = {(X i , Y i ), i = 1, . . . , n}, where we assume that for each i, Y i ∈ GEN(X i ).

the formulation over-penalizes classification error.


We treat each conversation side in the corpus as a "document."

we then consider the log of the likelihood ratio normalized by the number of observations, If we now "linearize" the log function in (5) by using log(x) (6) suggests we use a term weighting given by 1/ p(d j |background).


He proved that, if the designer is restricted to single-variable interventions, the worst case expected number of experiments required is Θ(n).

we prove, in Section 4, that for a random causal graph a constant number of experiments is sufficient in expectation.


It is reasonable to assume that biological auditory systems are designed to represent these structures in an efficient manner [e.g., 1,2].

but ultimately, it seems likely that one must also consider the auditory tasks, such as localization and recognition, that the organism must perform.


Furthermore, one may acquire a small subset of highly confident measurements.

we apply an alternating convex optimization method to solve this tri-convex problem efficiently.


We note that the Fisher kernel [4] is a special case of a MI kernel.

success/failure of this method should be closely related to the degree of purity of the component clusters w.r.t .


Indeed, if any such algorithm is initialized at the local maximum, then they will remain trapped.

the mere existence of bad local maxima is not a practical concern unless it turns out that natural algorithms are frequently trapped in these bad local maxima.


The computation of the fundamental matrix would not be a problem in this context of large sample size / low dimension, if the matching algorithms were perfectly correct.

using SIFT descriptors, we found more than 17.000 point matches in most pairs of images among the 10 pairs we are considering.


By taking into account the confidence information such as the number of available neighbors WLT is able to significantly improve over UB while using the same set of neighbors.

our approach achieves consistently better performance with only 17 parameters, and a single hyper-parameter K which is fixed to 200.


and a graph (V h , E h ) for n rows of H ? .

0 from below, the gains received from using our norm is clear compared to the standard nuclear norm.


We extend now this restart scheme to solve non-smooth or Hölder smooth convex optimization problem under the sharpness assumption.

in general, an error bound is an inequality of the form where ω is an increasing function at 0, called the residual function, and x may evolve either in the whole space or in a bounded set, see Bolte et al.


To deal with this problem, we treat the process X t for times t between consecutive observations kτ < t < (k + 1)τ as a latent unobserved random variable with a posterior path measure given by where y is the collection of observations y k and δ(•) denotes the Dirac-distribution encoding the fact that the process is known perfectly at times τ k . Our goal is to use an EM algorithm to compute the maximum posterior (MAP) prediction for the drift function f (x).

we have also defined the corresponding approximate posterior drift as well as the functions There are two main problems for a practical realization of this EM algorithm: 1.


We try three different solvers: regret-matching, Hedge, and projected replicator dynamics.

responses to equilibrium strategies computed by Double Oracle will (i) overfit to a specific equilibrium in the n-player or general-sum case, and (ii) be unable to generalize to parts of the space not reached by any equilibrium strategy in the zero-sum case.


We show in the supplement that SSVM parameters that assign nonnegative scores to all labelings achieve exactly the same hinge loss (and thus the same generalization error) as without the nonnegativity constraint.

a set function F : 2 V → R is submodular if its marginal gains, F (a|S) ≡ F (S ∪a)−F (S) are decreasing, i.e.


Our approach can provide more insights of the working factor brought by the heavy-tailed functions.

iteratively applying the update rule (14) thus results in a monotonically decreasing sequence of the linear approximation of HSSNE objective: Even if the second-order terms in the Taylor expansion of J (Y ) are also considered, the update rule ki are small.


The reader can find illustrations of these forcing mechanisms in Figure 2 of the supplemental material.

the focus of this paper is to understand how many experiments are required to discover G. This line of research was initiated in a series of works by Eberhardt, Glymour, and Scheines (see [4,5,6]).


Discriminative methods, such as Boosting and Support Vector Machines have significantly advanced the state of the art for classification.

the additional regularization from the unlabeled data can be represented as a new kernel -a "graph regularized" kernel.


Hence, its advantage over the untruncated one narrows as the number of measurements increases, thus straightening out the heavy tails.

observe that almost all {a i } vectors have a squared normalized inner-product smaller than 10 −2 , while half of the inner-products are less than 10 −3 , which implies that x is nearly orthogonal to many a i 's.


We consider a general continuous game model for the rewards in multi-agent online learning: ), where N is the set of N agents, X i is a convex and compact subset of R di representing the action space of agent i, and r i : For the rest of the paper, we set d = N i=1 d i , which denotes the dimension of the joint action space: A ⊂ R d . Variables associated with agent i are denoted by subscripts.

as a quick outline here (the details are in appendix), pick an arbitrary Nash equilibrium a * ∈ A * .


Despite the inherent similarity between problem instances arising in the same domain, classical algorithms do not systematically exploit this fact.

in many real-world applications, it is typically the case that the same optimization problem is solved again and again on a regular basis, maintaining the same problem structure but differing in the data.


We also considered B = n/10, the performance among these algorithms are similar to the case B = n/5.

regarding the comparison among these algorithms, we use the number of SFO calls (see Definition 2) to evaluate them since the number of PO calls of them are the same except ProxSVRG (which is already clearly demonstrated by Figure 2).


We will treat each rating type separately.

for consistency, we adhere to the use of correlation as our performance metric.


This suffices for many tasks, such as the SVM example above.

this motivates studying model selection over the space of neural architectures to optimise for generalisation performance.


Finally, we are experiment ing with mechanisms that allow new chains to be split off from old ones when the model determines that current stimuli differ consistently from t he closest matching t imeline.

adaptive Gaussian means Mild were initialized to small random values around a baseline of 10-4 for all states.


See supplementary materials for more detailed explanations.

using Lemma 1, we can reformulate the AT k loss (1) as the AT k loss is equivalent to minimum of the average of individual losses that are shifted and truncated by the hinge function controlled by λ.


However, traditional MCMC methods are based on random walk proposals which lead to highly correlated samples.

we first evaluate the benchmark MNIST dataset, using the Bayesian Neural Network (BNN) as in [5].


we next briefly discuss the relevant results from Cortes et al.


The resulting hypothesis, h S , is a stochastic function and not a deterministic one.

hence, once we calculate J a,b we can discard the original online hypotheses h a , .


The idea is that if our dataset X consists of linearly uncorrelated features (as can be obtained by applying a whitening procedure), then a measure of the higher-order dependence between two features can be obtained by looking at the correlation of their energies (squared responses).

for instance, the completely-connected layers are connected to all the maps within a 2-by-2 spatial window.


Figure 4(b) shows the recall results on METAFILTER.

the specific contributions of this paper are: (1) We formulate a continuous-time regression model for longitudinal network data with time-dependent statistics (and time-varying coefficients for the additive form); (2) we develop an accurate and efficient inference scheme for estimating the regression coefficients; and (3) we perform an experimental analysis on real-world longitudinal networks and demonstrate that the proposed framework is useful in terms of prediction and interpretability.


The bottom plot of Figure 1 compares lower bounds for graphs with up to 900 nodes; a larger bound is necessarily tighter, and the preconditioner bounds are seen to outperform mean field.

σ Φ (A, B) ≤ σ(A, B) from the definition of generalized support number.


2, satisfy certain constraints on their average sufficient statistics.

the finite temperature model is given by: Similar to herding [14], conditional herding introduces a temperature by replacing w by w/T and takes the limit T → 0 of T T , where = i log p(y i |x i ).


Let L be the solution returned by the locally greedy algorithm.

note that f t allows us to evaluate the performance of any possible ranking S t , hence we can apply TGBANDIT in the full-information feedback model.


Marginalizing over B, the number of active features in item i has distribution Poisson(γ), determined by mass parameter γ.

the binary vector f i determines a finite set of states available for item i.


The Fourier transform of (4) results in the stationary, positive definite autocovariance function where stationarity implies dependence on input domain differences k(τ The SG kernel may also be derived by considering a latent signal f (x) = √ 2 cos(ω(x + φ)) with frequency uncertainty ω ∼ N (µ, ν) and phase offset ωφ.

6 Experiments Section 6.1 demonstrates the performance of the CSM kernel and the accuracy of the DFT approximation In Section 6.2, the DFT approximation for the CSM kernel is used in a Bayesian HMM framework to cluster time-varying multi-channel LFP data based on the full cross-spectrum; the HMM states here correspond to states of the brain during LFP recording.


We took w ∼ U (−3, 3), x = w 2 + n x with n x ∼ U (−1, 1), y = 4 |w|+n y with n y ∼ U (−1, 1), z = 2 sin x+2 sin y+n z with n z ∼ U (−1, 1).

we accept the model where the time interval between the current and the next eruption is a function of the duration of the current eruption, but reject the reverse model.


Quite surprisingly, GC turns out to be equal to the complexity term used in one version of Minimum Description Length (MDL), a measure of generalizability developed within the domain of information theory [2,11,12,13].


We claimed that without selfsupervised feature disentanglement, i.e., without D v , the generator will be able to reconstruct images with the entangled representation and ignore the domain vector.

while both learning disentangled representation, our UFDN outperformed E-CDRD in terms translation quality.


Here, we propose to use Support Vector Regression (SVR) to solve the preimage problem.


The main reason is that RL algorithms provide optimal policies only in the long-term, so that intermediate policies may be unsafe, break the system, or harm their environment.

it is intractable to verify this condition directly on the continuous domain without additional, restrictive assumptions about the model.


Denote y i t as the appearance vector of o t , and Y t = {y 1 t , .

an observation model needs a classifier with proper probabilistic interpretation.


Among these models, the edge partition model (EPM) [8] is a fundamental Bayesian nonparametric model for extracting overlapping latent structure underlying a given binary matrix.

as U , V , and λ are independent of each other, the expected value operator is multiplicative for the EPM's intensity function.


The urn view allows us to compare this model to other priors on infinite trees.

if it has reached node but will not stay there, it descends to existing child i with probability (N i +N i≺• )/(N ≺• +γ) and instantiates a new child with probability γ/(N ≺• +γ).


In the template model of Perrone and Stone [3], a template invariant to translation velocity or depth structure is obtained by summing the responses of the most active sensor at each image location.

each flow template can become approximately rotation-invariant by subtracting a gain field activity that is a multiplication of the eye velocity t with a derivative template activity 80/ 8R that is specific for each flow template.


Given the walk-sum interpretation from Proposition 1, one can check that x (n) → J −1 h element-wise as n → ∞.

using this analysis, we show that the non-stationary ET iteration ( 6) converges in walk-summable models for an arbitrary choice of subgraphs {S n } ∞ n=1 .


In this section, we show that the variational objective provides a new perspective on some wellknown peculiarities of human probabilistic judgment.

as we explore in later sections, rewards and costs place strong constraints on the types of codes that are learned by the variational objective, and the available experimental data is congruent with this view.


Multi-armed bandit (MAB) problems are among the most fundamental sequential decision problems with an exploration vs. exploitation trade-off.

most of these algorithms only allow the decision makers to pull one single arm in each round.


Then we are not at a local minimum to L(γ) if there exists a second convex cone C formed from a subset of columns of Φ such that t ∈ C ⊂ C Φ , i.e., C is a tighter cone containing t. In Figure 1(right), we obtain a tighter cone by swapping x for φ 2 .

locally minimizing our new problem ( 14) is clearly superior to locally minimizing (1).


Fusion strategies often outperform pure single deep networks.

it is not wise to simply increase layer number due to parameter burden.


Though seemingly strange, this provides a perfect example of the behavior that motivates this paper.

since our premise is that agents have only a limited view of the world, the Q-learning agents will only exhibit convergence to the optimal policy if they converge to the optimal policy simultaneously.


Viewed in a different light our learning algorithm has a nice interpretation: as in reinforcement learning, the hidden neurons explore different sequences, where each trial leads to a global reward signal that modulates the weight change.

2) or static weights towards hidden neurons the time gap was not learned (see Fig.


While our goals are similar, we propose a rather different model based on the stick-breaking representation of the DP [16].

its usage of a "soft-max" (multinomial logistic) transformation requires a global normalization, which in turn presumes a fixed, finite number of topics.


Understanding the differences between approximated kernel methods and neural networks is crucial to use them optimally in practice.

we use validation sets of size 1, 000 for Gisette, 10, 000 for MNIST, 50, 000 for CoverType, 5, 000 for CIFAR10, 3, 560 for Adult, 4, 500 for Letter, and 1, 290 for USPS.


Since quantiles of a distribution are closely related, joint quantile regression is subsumed under the field of multi-task learning [3].

the bound on the Rademacher complexity of [24, Theorem 3.1] concludes the proof.


Each project is represented as a 112-dimensional vector specifying the distribution of skills required for its delivery.

based on the algorithmic intuitions embodied in the algorithms above, we develop two semisupervised classification algorithms that extend the spectral bipartite graph partitioning approach and the matrix approximation approach respectively.


The initial state distribution is π 0 ∈ R K . The Markov structure dictates that z t ∼ Mult(π zt−1 ), and the observations follow x t ∼ Φ(θ zt ).

if we introduce a new parameter β, and generalize the transition probabilities to be Pr(z where φ = βφ, then the mean of the distribution is the same in the scaled distribution (namely, m j ) while the variance is scaled.


Relation to eligibility traces In TD(λ) [11], a well-known and successful variant of TD, the value function (1) is not learned by a one-step update, but instead relies on multiple value estimates from further in the future.

natural value approximators may also be helpful in partially observed environments.


Recently, Opper and Archambeau [19] discussed the relation between the Laplace approximation and VB, and proposed a variational approximation directly for the latent variables and tried it with a Cauchy likelihood (they did not perform extensive experiments though).

the compared observation models are Gaussian (G) and Student-t (T).


Note that we correlate the features before applying ReLU following what [25] does for the last layer.

we usually started from layer 2 and finished at layer 8.


The significance of this work is to address these challenges by a new design of online algorithm and novel high probability analysis of the proposed algorithm.

we overcome this shortcoming by learning the optimal threshold through solving a strongly convex optimization problem.


In this case, the sequence { i } as defined will decrease until it reaches the largest value such that max ts g ts (log ) = log .

similarly to (18) and ( 19), we have The steady-state solution of (20) yields an estimate of the variances of the log-belief log p t by σ 2 t = u∈Γt σ 2 ut ; this estimate is typically much smaller than the bound (18) due to the strict sub-additive relationship between the standard deviations.


. . , w ⇤ T } over the m functions, by randomly perturbing the uniform distribution.

w t [i] is the probability of picking function L i 2 L. The adversary picks a distribution w t based on some arbitrary no-regret learning algorithm on the m actions in L. For concreteness consider the case where the adversary picks a distribution based on the multiplicative weight updates algorithm, i.e., Subsequently the learner picks a solution x t that is the output of the ↵-approximate stochastic oracle on the distribution selected by the adversary at time-step t. Write ✏(T ) = q 2 log(m) .


The differences in performance between DFacTo (ALS) and CPALS and between DFacTo (GD) and CPOPT can partially be explained by the fact that DFacTo (ALS, GD) is implemented in C++ while CPALS and CPOPT use MATLAB.

we downloaded Version 2.5 of the Tensor Toolbox, which is implemented in MATLAB 4 .


The radii of these sublevel sets tell us how clusterable the data is, in a norm that depends on the relaxation X . )

sp for data with K = 4, n = 1024, as well as one instance of the data used.


By correlating the input signal and encoding redundant information, the channel signal to noise ratio (SNR) can be balanced to reduce the vulnerability of those independent channels with low SNR.

one goal (infomax) is to maximize the mutual information I(r, s) = H(r) − H(r|s).


We then need to handle the case when we have multiple actions that could trigger arm i.

in this paper, we fix the environment instance D, unless we need to refer to more than one environment instances.


The resulting state of applying a sequence of complete actions π = a 1 , ..., a n in s with respects to D i is defined as: A planning problem with incomplete domain D is P = D, I, G where I ⊆ F is the set of propositions that are true in the initial state (and all the remaining are false), and G is the set of goal propositions.

since possible preconditions and effects can be represented as random variables, they can in principle be modeled using graphical models such as Makov Logic Networks and Bayesian Networks [14].


Here we provide a simple condition on the membership probabilities P(ilx) so that any noise in the sampled labels for the available examples would not preclude accurate decisions.

the unique solution to the maximum entropy estimation problem is found via introducing Lagrange multipliers {AI} for the classification constraints.


As discussed in § 3.2, even though the topic-specific distributions  lexicon mappings of "meet" and "power" under ten topics.

extracting the optimum alignment amounts to applying an Viterbi algorithm on q( a| λ).


Finally, in Section 6.4 we empirically demonstrate the differences between our approach and the previously discussed fast-adaptation algorithms.

as we might have expected, the only difference between the bounds for the two versions of Algorithm 1 is in the term ϕ(W s ), i.e., the distance between the optimal weights w * and the source weights W s . for the mixture version we have the (smoothened) minimum distance to the source tasks' weights (Equation ( 5)), while for the Gaussian one we have the distance to the mean of such weights.


(2) W-RankNet and W-ListMLE also outperform other baselines on LETOR such as Regression, Ranking SVM, Rank-Boost, FRank [15], ListNet and SVMMAP [18].

the pointwise approach, such as subset regression [5] and McRank [10], views each single object as the learning instance.


Θ ∈ {0, 1} h×t , Θ 1 = k1), then M can have negative elements, but the spectral constraint M 1 = 1 still holds (see proof in Appendix C).

the totally corrective update is expensive because given α and β, each evaluation of the objective f itself requires an optimization over S 1 , S 2 , and Z 3 .


Under the competition (mediated by recurrent connections and divisive normalization) from the neighboring neurons which are less affected by SFA, the bump tends to shift to the neighborhood; and at the new location, SFA starts to destabilize neuronal responses again.

interestingly, we find that when the intrinsic speed of the network is greater than that of the external drive, anticipative tracking occurs for sufficiently weak stimuli; and different SFA amplitude results in different anticipative times.


We can extend the marginalize-and-condition strategy above to more complicated models.

autoconj can work with log_joint_bound() even though it is not a true log-joint density.


Notice that λ K and σ are eigengaps in HPFM model and PFM model respectively and depend only on the preference frame, and likewise for g row .

the clustering C would not accurately capture the cluster structure of the matrix P . Hence, condition (3) amounts to requiring that no other cluster structure is present, in other words that within each block, the Markov chain induced by P mixes well.


Now, the expected utility to agent i when it reports type θi , substituting for the payment term We can ignore the final term because it does not depend on the choice of θi at all.

the online auction work considers a much simpler setting (see also [4]), for instance the allocation of a fixed number of identical goods, and places less emphasis on temporal strategies or allocative efficiency.


For a specific task, a sketching algorithm often outperforms random sampling.

for each pair, we obtain 50 runs and average the absolute errors.


Immediate reconstruction result at each stage is shown under each reconstruction layer.

it is challenging to choose the transform D l and shrinkage function S(•) for general regularization function g(•).


To detect adversarial inputs, Defense-GAN projects an input onto the range of the GAN generator by a Gradient Descent (GD) procedure to minimize the Wasserstein distance between the input and the sample generated by the GAN generator.

this indicates that I-defender can be used to effectively defend attacks.


We also refer to this target object as the agent object.

the combinatorial explosion problem is predicated on another seductive notionthat separate units are used for each possible conjunction.


The primal-dual gap error curves are plotted in Figure 1.

the experience replay trick improves the mixing property of the data process, and hence improves the convergence rate.


1 We analyze the following variant of the usual central path algorithm for linear programming, which we call A cpr .

naive parallel algorithms that learn a γ-margin halfspace in time that depends polylogarithmically on n have Ω(1/γ 2 ) runtime dependence on γ.


Whenever lim m→∞ ǫ(δ, m) = 0 the gap between the upper and lower bounds in Theorems 1 and 2 approaches R(ŷ) − min q R(q) as m → ∞ (ignoring constant factors).

our first set of experiments involved two binary classification data sets that belong to a benchmark suite 1 accompanying a widely-used semi-supervied learning book [1]: the Columbia object image library (COIL) [17], and a data set of EEG scans of a human subject connected to a brain-computer interface (BCI) [18].


Using our techniques, we are able to relax these assumptions and still derive convergence rates.

for any > 0, we define the success set S to be we are only concerned with the direction of x, not its magnitude; this algorithm only recovers the dominant eigenvector of A, not its eigenvalue.


The regret for the Successive Reject algorithm is constant as it depends only on the reward distribution and has no knowledge of the causal structure.

cumulative Regret Although we have focused on simple regret in our analysis, it would also be natural to consider the cumulative regret.


For any possible answer to any question, we define the worker's confidence about an answer as the probability, according to her belief, of this answer being correct.

in preliminary experiments involving over several hundred workers, we observe a significant reduction in the error rates under our unique mechanism for the same or lower monetary expenditure.


Similarity search algorithms based on MinHash [13,14] originally aimed to find duplicate webpages or search results, which have much larger natural language alphabets.

another feature of our algorithm is the use of binary signatures.


These matrices whiten the input and output data, as well as making the cross correlation diagonal and "maximally compact."

thus the derivatives are defined and a Taylor-series approximation is valid.


Augmented Lagrangian Method (ALM) was invented early in 1969, and since then there have been several works developed Linear Program solver based on ALM [15,16,17].

one of the most popular approach to this solves a program of the form [6] min which is primal-sparse due to the .


Acknowledgments AS gratefully acknowledges support through an Ernst-von-Siemens scholarship.

we have shown how parameter tuning and classifier training can be done on basis of the scarce available data.


This can be expressed without creating new timestamps.

to do well, the agent must remember the location of the next pellet.


Alternative means to strive towards similar results would be to make use of priors such as in [15,16].

reducing the entropy of the joint distribution P t (z, s) is equivalent to reducing the conditional entropy of the source dependent mixture weights and the entropy of the source priors.


Second, we checked the sample efficiency of our algorithm by reducing the number of state-action pairs used for each training iteration from 50000 to 1000 for Hopper-v1, Walker2d-v1, HalfCheetah-v1 and to 5000 for other much high-dimensional tasks.

this gives us a hint that a robust discriminator is an important factor in improving the sample efficiency of generative-adversarial approaches to imitation learning.


The condition in Figure 1b is a case where five different balls are drawn from the urn.

in both conditions participants observed a sequence of 16 tokens sampled from the urn.


(1) allows learning of the stochastic transitions between reward functions (specifically, by learning !

to extend such a partitioning to work for trajectories traversing through any (possibly unvisited) region of the state space, we propose using a generalized linear model to represent and predict the stochastic transitions between reward functions at any state (i.e., including states not visited in the expert's demonstrated trajectories) by exploiting features that influence these transitions (Section 2).


We extend the multinomial logit model to represent some of the empirical phenomena that are frequently observed in the choices made by humans.

the attraction effect cannot be represented by these variants of the MLM [13].


The simplest form of MARL is independent RL (InRL), where each learner is oblivious to the other agents and simply treats all the interaction as part of its ("localized") environment.

there have several proposals for treating partial observability in the multiagent setting.


For instance, the first two synergies shown in figure 3 were seen in all sets of synergies, from ¡ to ¤ .

using these synergies, 50 episodes of duration 30 time steps were generated by scaling each synergy ¡ ¢ ¥¤ §¦ with random coefficients © and shifting it by random delays ¤ .


In practice, it is often the case that n is very large (10 5 ∼ 10 9 ) while the target accuracy is moderate (10 −1 ∼ 10 −3 ).

sCSG makes faster progress in terms of both training loss and validation loss compared to SCD in wall clock time.


This is often done following one of two complementary approaches.

alternatively, one can formulate a realistic model of a small subnetwork where few transcription factors regulate a small number of established target genes, trying to include the finer points of the dynamics of transcriptional regulation.


Fine-grained 3D shape estimation may still be difficult with such a strategy.

this means that one can use rank constraints to learn a 3D morphable basis.


Based on S, we have X L = XS and L L = S T LS.

as we mentioned before, the criterion of TED coincides with minimizing the out-of-sample error bound of ridge regression.


Algorithms based on cubic regularized Newton's method [28] and its variants [1,7,12,23,33,31] have been proposed to find such approximate local minima.

we illustrated that third-order smoothness can help faster escape saddle points, by proposing a new negative curvature descent algorithms with improved theoretical guarantee.


We will use this fact to efficiently train deep structured models with continuous outputs.

deep learning approaches learn complex data abstractions by compositing simple nonlinear transformations.


They also consider the broader class of spectral risk measures, which can be represented as where µ is a probability measure on [0, 1] (cf.

the mean and second moment satisfy both by Lemma 1.


We thank the anonymous reviewers for their hints to improve the paper.

we then obtain the following dual problem of eq.


Two simplest types of grammar fragments are And-fragments and Or-fragments.

the prior gain of learning from the And-Or fragment is:   where s a and s o are the number of bits needed to encode each node on the right-hand side of an And-rule and Or-rule respectively.


For x •j = 0 we have a contribution αj +βj αj +βj +N βj βj .

for many distributions, such as diagonal covariance Gaussians, even though the score is nonlinear in U, it can be computed by applying the nonlinearity elementwise to U.


Our algorithm assigns each point to exactly one cluster.

we can evaluate all possible assignments for an image efficiently.