Factored model in the multi-study case: using target study alongside all other studies.

our general goal is to extract and integrate biological knowledge across many brain-imaging studies within the same statistical learning framework.


In such a model, an exogenous Markov process X t taking values in a set X influences rewards.

the implications of these decompositions are discussed further in earlier work [16].


For the multinomial family £ ¦¥ ¨ § © E w0 , is an element of the 2 -simplex, ¥ ( gf ¢ B RQ ¢ B ¡ d . The transformation B 5 6 ih e B ¡ pG B maps the 2 -simplex to the 2 -sphere of radius 2.

a "bag of words" representation was used for all three kernels, using only the word frequencies.


Introducing Lagrange multiplier λ for the constraint k p k = 1, we need to have p = C (d − λ1) which results in λ = 1 Cd−1 1 C1.

the proof is by induction on the number n of rounds played.


All Rep-typed values (and computations depending on Rep-typed values) are treated as IR and translated into generated code, while all other typed values are treated as normal Scala expressions and are "staged away" from the generated code.

the automated transformation will reorganize it into CPS format, realizing delimited continuations.


For this reason, we evaluate the score of each decoding, but show the most recent decoding rather than the best (as is standard in MAP) to simulate behavior in practice.

, 31] give a class of easy-toevaluate upper bounds which can be directly optimized using coordinate descent [36,6], subgradient updates [14], or other methods [e.g.


A prior co-regularization based idea to harness unlabeled data in domain adaptation tasks demonstrated improved empirical results [10].

we use an alternate formulation of the hypothesis classes and work in the original space X ⊂ R d . As discussed briefly in Section 2.2, EA can be thought to be simultaneously training two hypotheses h s = (g c + g s ) and h t = (g c + g t ) for source and target domains, respectively.


This work approaches the exploration of a family of SAT solvers as a learning problem.

therefore the algorithm expands no more than 2N nodes, where N is the length of Ω.  it is computed on a seperate validation set (see figure 5).


For example, in density estimation, the goal is to find a model that has the smallest negative log-likelihood.

it is also easy to observe that they will not lead to the exponential decay of classification error in the separable case.


For this reason, all require critical smoothing hyperparameters to converge.

like O-SGD, RAIS selects the tth minibatch by sampling indices from a discrete distribution p (t) .


Known pre-miRNAs have distinctive structural characteristics, and therefore most computational methods make first-order decisions based on the secondary structure of the input RNA sequence.

this can take various forms, but in our system, a weighted combination of the output vectors at each point in time replaces the single final output vector of a standard RNN.


This is due to the fact that the variance in each cluster is comparable with the error in the prediction function h. The results are reversed for the bimodal scenario where RIC-h outperforms both algorithms under low noise.

one could use one of several clustering algorithms to solve it.


Disclosure: Dr. Hochberg has a financial interest in Synchron Med, Inc., a company developing a minimally invasive implantable brain device that could help paralyzed patients achieve direct brain control of assistive technologies.

we matched the speed of both decoders and evaluated decoding error and smoothness.


Highway networks also contain residual modules and skip connections that bypass them.

to empirically investigate the effect of vanishing gradients on residual networks we perform the following experiment.


Unlike the random policy, which includes both an unstable spiral fixed point and limit cycle structure and requires a 3-dimensional embedding to preserve locality, the learned policy exhibits a 2-dimensional unstable spiral fixed point.

sufficiently large refers to a cardinality of dimension which is certain to be greater than twice the dimension in which the actual state-space resides.


This source of alignment allows us to solve our task using existing methods.

due to the small number of identities, we cannot test in this case the generalization to unseen identities.


Thus, the beta part of the corresponding approximate factors can be removed and the multivariate Gaussian distributions simplify to univariate Gaussians.

the approximate factors ψ are constrained to belong to the same family of exponential distributions, but they do not have to integrate to one.


unlike the λ and γ-returns, the Ω-return is not simple to compute, and often can only be approximated.


With this number, τ 0 is as small as ~10 ns.

scan mapping of the input image on CMOL CrossNet inputs.


In this section, we present an iterative algorithm for computing both the conditional means and error covariances of a Gaussian process defined on any graph.

if p(A) > 1, then the algorithm will not converge, whereas if p(A) < 1, then (xn -x) n~ 0 geometrically at rate 'Y ::@, p(A) 10.


Because each fixed point update uses the output of a previous fixed point update as input, this optimization procedure can be viewed as a recurrent neural network.


Fundamentally different from existing methods that typically reduce the dimension of the data to lessen the computational complexity and speed up the search, our approach projects the data into an even higher-dimensional space while ensuring the sparsity of the data in the output space, with the objective of further improving precision and speed.

in one run, all samples were used as a query in turn.


This allows but discourages each day to add a new category if there is evidence of unusual activity.

this means that posterior sampling of the parameters θ is no longer possible in closed form.


An orthogonal projection P i (φ(x j )) of a feature vector φ(x j ) into a subspace defined only by the set of indices i can be expressed as: P i (x j ) = X ( X X ) −1 Xφ(x j ), where X = X[i, :] are the i training examples from data matrix X.

we give a novel bound that views the choice of subspace of the KMP algorithm as a compression scheme and hence provide a VC bound to upper bound its future loss.


In our experiment, the size of  In this section we mainly evaluate our proposed MetaAnchor on COCO object detection task [24].

in addition, we introduce a data-dependent variant of anchor function generator, which takes the input feature x into the formulation: where r(•) is used to reduce the dimension of the feature x; we empirically find that for convolutional feature x, using global averaged pooling [13,38] operation for r(•) usually produces good results.


The use of environmental models in RL is quite popular for both off-line learning by simulations and for on-line action planning.

in order to assure robust performance under changing environment or unknown disturbance, we introduce the notion of worst disturbance in 1i<x> control to the reinforcement learning paradigm.


1. kCNNs effectively improve over CNNs by leveraging the prior knowledge, and also outperform SVMs that use the same kernels.

because the regularization term defined by Eq.


Notice also that as SEBOOST is added on top of baseline stochastic optimization method, it does not require any internal changes to be made to the original algorithm.

we will use the notation a → L b to denote a classic linear layer with a inputs and b outputs followed by a non-linear Tanh function.


We also need the following quantity for our analysis: Theorem 1.

in this paper, we focus our attention on the parallel setting.


we also use the logistic models for p k (t | x): where b is varied over 25 equally spaced points in [0, 10].


Two cornerstones of our ESS-CRF approach, namely using models that become more sparse when evidence is instantiated, and using multiple tractable models to avoid restrictions on the expressive power inherent to low-treewidth models, have been discussed in the existing literature.

we have found it useful to regularize the conditional Chow-Liu (Alg.


[11] provides other variants of the deterministic algorithm, including two ergodic averaging schemes that feature improved theoretical rate of convergence.

the proximal operator of a function f ∈ Γ 0 (R d ) is defined as follows Roughly speaking, the proximal operator is tractable when the computation of (3) is cheap.


In this case, one could still use gradient descent to minimize the mismatch between model-predicted covariance and empirical covariances.

while this approach can be very effective and is important for theoretical analysis, it can perform sub-optimally when data is noisy.


Thus, each hypothesis h i in the original problem is now associated with a set H i of hypotheses in the modified problem instance.

the behavior of most subjects (7 out of 10) was best described by EV.


If we instantiate the model as a CRF, the conditional probability of a truth assignment y to the hidden ground atoms (query atoms) in an MLN, given truth assignment x to the observable ground atoms (evidence atoms), is defined as: where f i,j (x, y) = 1 if the jth grounding of the ith formula is true under truth assignment {x, y}, and f i,j (x, y) = 0 otherwise.

we will partition the weights (parameters) of our model based on whether they belong to transition or to emission part of the model.


For finetuning the whole framework end-to-end, we use Adam for optimizing E, G and V , and SGD for D id , D pd after loading the pre-trained weights from stage-II.

the quality of learned person features have direct impact on the generated person images.


It was shown that pairwise interactions are sufficient for retinal ganglion cells and cortex cells in vitro [4].

as an example, consider the Clayton copula family [6].


For greater modeling flexibility, we take a nonparametric approach in defining the mode space of our switching dynamical processes.

the Hamming distance error is calculated by first choosing the optimal mapping of indices maximizing overlap between the true and estimated mode sequences.


Since Q(v l ) is Gaussian, v l is always µ l at the optimal point and thus this optimization is equivalent to maximizing the determinant of the inverse covariance max Note that if T nl is one for all n, our method turns into a MAP-based sparse Gaussian process.

our gating network is more flexible than previous generative approaches as inputs for each expert are modeled by a Gaussian mixture model.


Consider a consistent and symmetric θf = f ( θ1 , .

one may make θlinear exact by using the special parameterization ϑ = µ(θ).


Since their method learns an inverse dynamics model, it does not provide for any mechanism to handle novel events that do not correlate with the agent's actions, though it does succeed in avoiding the need for generative modeling.

these methods typically require maintaining state-action visitation counts, which can make extending them to high dimensional and/or continuous states very challenging.


In this paper we develop the SLEEC classifier to address both limitations.

we now present our algorithm SLEEC which is designed primarily to scale efficiently for large L. Our algorithm is an embedding-style algorithm, i.e., during training we map the label vectors y i to L-dimensional vectors z i ∈ R L and learn a set of regressors V ∈ R L×d s.t.


Taking a closer look the following additional observations can be made: (1) During quantization the direction of vectors is better preserved with the forward pass compared to the backward pass; (2) validation accuracy follows tightly the cosine of the angle in the backward pass, indicating gradient quantization as the primary bottleneck; (3) as expected, the bound on E(cos(θ)) in Eq.

for more complex models and challenging datasets, the extreme compression rate resulted in a loss of accuracy.


The ground truth from human annotators reveals that the level of generalization varies according to the conceptual diversity, with greater diversity leading to broader generalization.

there is still significant room to improve performance on this task, and we present our visual concept learning dataset as the basis for a new challenge problem for machine vision, going beyond assigning labels to individual objects.


This risk-sensitive Kalman filter is equivalent to a distributionally robust filter proposed in [12], which minimizes the worst-case mean square error across all joint state-output distributions in a Kullback-Leibler (KL) ball around a nominal distribution.

the hope is that hedging against the worstcase distribution has a regularizing effect and will lead to a filter that performs well under the unknown true distribution.


We then considered edges that were found in at least 50% of all 100 restarts.

optimizing for Ĉ−1 The third step, optimizing with respect to Ĉ−1 , can be done efficiently, using similar ideas as in Section 2.


KBSF's computational cost also compares well with that of LSPI, as shown in Figures 2b and 2d.

when the stochastic factorizations are exact, we recover (1), which is a computable version of Sorg and Singh's bound for soft homomorphisms [10].


We concisely denote the transformation from a reference triangle to an observed triangle via a matrix A ∈ R 3×4 .

mesh-ddcrp is significantly better than all other methods, including for settings of K which allocate 50% more parts to competing approaches, according to a Wilcoxon's signed rank test (5% significance level).


Stochastic search algorithms [1,2,3,4] are black box optimizers of an objective function that is either unknown or too complex to be modeled explicitly.

due to the feature transformation, the output R [k] depends non-linearly on the projection W . Therefore, the posterior p(W |D) cannot be obtained in closed form any more.


In order to alleviate the aforementioned deficiency of the state-of-the-art, we introduce DISCO Nets, a new class of probabilistic model.

in the subsequent subsection, we describe how to estimate the parameters of the model.


To select the exemplars we compute: which represents the amortized cost of selecting point j as exemplar and assigning points to it.

the approximation properties of the relaxation and the convergence of the subgradient algorithm are discussed in Section 4.


We propose and study the known-compensation multi-armed bandit (KCMAB) problem, where a system controller offers a set of arms to many short-term players for T steps.

update(↵ a2(t+1) , a2(t+1) , X(t + 1)) The third algorithm we propose is a Thompson Sampling (TS) based policy.


In this example, the goal is to infer the rate θ of an exponential distribution, with a gamma prior p(θ) = Gamma(θ|α, β), based on M draws from Exp(θ): where r um = − ln(1 − u m ) (the inverse CDF of the exponential).

the case D θ > D y is less interesting than the other ones above as we expect to have more summary statistics than parameters for most problems.


Finding an exact solution to the optimization of the acquisition function in ( 13) can be challenging in practice.

since the proof of Theorem 1 is based on confidence bounds, the only change required is selecting t to be that used for the Bayesian setting in [31].


Estimating precise 3D models of objects from a single image is an extremely difficult problem and probably requires recognition of object classes such as couches and tables.

our experiments show that volumetric reasoning improves the estimate of the room layout and provides a richer interpretation about objects in the scene.


We use the following three problems in our experiments.

now we would like to prove that on the event E, we find the best arm for all the bandits, i.e., J m (n) = k * m , ∀m ∈ {1 . . . M }.


This quantity is initially bounded, decreases by a substantial amount after every hard query, and never increases.

static PMW works on a fixed database of size n and answers k linear queries.


More formally, consider a set W ⊆ [m] such that ∀i / ∈ W , φ i is linear, meaning φ i (x) = a i , x + b i for some a i and b i .

this dataset was generated by a team of particle physicists.


These included four UCI datasets 6 (ion, bupa, hepatitis and wine) and the previously used SRBCT data-set.

formally, we look for a diagonal matrix F such that Σ ′′ i = Σ ′ i + F which also maintains x ⊤ Σ ′′ i x ≥ x ⊤ Σ i x for all x ∈ R d . we want to satisfy: where, for ease of notation, we take F(i) = F(i, i).


The heuristic that we chose for dimensionality reduction was simply one of reconstruction error, as in equation 5: a reduction that minimises reconstruction error should allow nearoptimal policies to be learned.

pCA minimises squared error, while E-PCA with the Poisson loss minimises unnormalised KL-divergence, so it is no surprise that E-PCA performs better.


In respect of objectives, the works in [28,29] and our approach all intend to ameliorate the performance and efficiency of exploration.

as our diversity-driven exploration strategy relates to several prior works in RL, this section provides a comprehensive comparison with those researches in terms of objectives and implementations.


The resulting algorithm is given as Algorithm 1.

we must partition the units in each layer into two groups, denoted x 1 and x 2 ; for the remainder of the paper, we assume this is done by partitioning the channels, since we found this to work the best in our experiments.


Whether this algorithm is guaranteed to terminate in a finite number of iterations remains an open issue.

in this section, we formulate a non-zero sum stochastic dynamic game.


They formulate a saddle point problem where strictly speaking the inner loop should be converged before moving to the outer loop.


At each step of iterative optimization, the method is guaranteed to reduce the discrepancy between the observed spectrogram and the spectrogram of the estimated waveform.

let M = {m 1 , m 2 , m 3 ....} denote the spectrogram of s; m k is the magnitude spectrum of the kth window and m f k is the magnitude of the f th frequency component.


Third and most importantly, even with modern multi-electrode arrays, one is limited in the number of neurons which can be recorded simultaneously during an experiment.

the net effect of the decorrelated pairs is stronger and improves the overall discriminability in the population as compared to the "statistical average".


The variations of x as mostly restricted to an m 1dimensional subspace of R m , called the principal subspace, for some m 1 ≤ m. On this subspace we adopt a multivariate normal with mean µ ∈ R m1 and variance K ∈ R m1×m1 .

from the observed values of x j ∈ R m , one can estimate the principal subspace and the covariance matrix.


The main difference between slack and margin rescaled training is how they treat the case of λ(Y i , y) = 0 for some y ∈ Y.

our experiments of Section 5 show that this leads to low multilabel prediction accuracy, because the training setup is not designed for this evaluation procedure.


[10] presented such a (batch) dictionary learning approach for detecting novel documents/topics.

the running time of the online  1. algorithm is almost the same across different timesteps.


Each region will re-compute its feature by pooling over all its pixels.

we define a graph block as (6) where GCU k denote a GCU with k vertices and ⊕ can be either a residual connection or a concatenation operation.


Much recent research has explored the relationship between the statistical complexity of some categorization task and the ease with which humans learn the task [7,5,9,11].

if F is simple (e.g., in the extreme containing only one function f ), it is unlikely that f (x i ) will match σ i , and its fit will be close to zero.


By enforcing sparsity, we have thus increased the implicit limit on the number of bases that can be estimated without indeterminacy from the smaller dimension of V to the larger one.

the aim of the model is to determine P (f |z) such that the model 1 PLSA actually represents the joint distribution of n and f as P (n, f ) = P (n) P z P (f |z)P (z|n).


Of course, we would not know ahead of time how to bin the data to avoid losing accuracy.

the artificial dataset [5] was meant to remove any variance caused by the quality of features and/or relevance labels.


We have shown that competition makes life-and computation-more complex.

dashed arrows indicate transitions with probability 1 2 independent of the actions.


Here we address an easier problem in which the analyst's queries only need to be answered when they overfit.

let S be a random dataset in X n and A be an algorithm with range Y such that for some β ≥ 0, P[(S, We remark that mutual information between S and A(S) would not suffice for ensuring that bad events happen with tiny probability.


The prediction of eye movements has been less studied.

the method we propose shares some resemblance with these later methods, in that we also aim at maximizing the future expected reward, albeit our reward function is learned instead of being pre-specified, and we work in an inverse optimal control setting, which allows, in principle, an arbitrary time horizon.


We expect that both the REINFORCE and Bayesian optimization methods used here can be improved to compensate for some of their individual drawbacks.

we now consider two distinct approaches for this.


Prism learning or Blindness may interfere this alignment and cause loss of the capability of accurate prey.

in the deep Superior Colliculus (SC), visual and auditory information are integrated together.


4 (d) and (e) correspond to the estimated temporal correlation β and the time average of µ, which is defined by µ n = 1 ∑ Tn t=1 µ n t , where T n denotes the sojourn time in the nth label or the total observation time T . The estimated temporal correlation differed significantly between the 1st and 2nd neural states (Wilcoxon signed rank test, p<0.00005).

have proven the effectiveness of this method in estimating stationary firing rates [12].


To achieve the CUR-type row sparsity, we propose the following modification of (4): Problem 2 (Group lasso SPCA: GL-SPCA).

it computes a p × k orthogonal matrix W that minimizes Writing the SVD of X as UΣV T , the minimizer of ( 1) is given by V k , the first k columns of V. In the data analysis setting, each column of V provides a particular linear combination of the columns of X.


Almost all these methods learn their ranking functions by minimizing certain loss functions, namely the pointwise, pairwise, and listwise losses.

learning to rank has become an important research topic in machine learning.


When there are only two labeled points, the unlabeled distribution does not encourage humans to perform manifold learning (comparing 2 l grid U vs. 2 l moons U ).

instead, we used unfamiliar stimuli, from which we could add or remove a manifold structure easily.


The analysis of FLL guarantees that the oblivious component of the player's expected regret (without counting the switching costs), as well as the expected number of switches, is upper bounded by O( √ T ), implying an expected regret of O( √ T ).

we show that with switching costs, the attainable rate with bandit feedback is � Θ(T 2/3 ).


Because drift rates determine the signal-to-noise ratio of the diffusion process, they reflect the difficulty of the task at hand.

we refer to this generalized class of models as multiresponse diffusion models or MDM.


• We obtain theoretical regret bounds for D-TS and D-TS + .

details can be found in Appendix C.1 D-TS is a TS framework for dueling bandits, and its performance can be improved by refining certain components of it.


4: (Acceleration step) ẑk := (1 ⌧ k )z k + ⌧ k zk with z = (x, y).


The next lemma shows that δ t is a consistent estimate of the advantage function A π . Lemma 3 Under given policy π, we have E[δ t |s t , a t , π] = A π (s t , a t ).


First, the topic mixture h is drawn from the Dirichlet distribution.

we may also allow η to be heteroskedastic (i.e., the noise may depend on h, provided the linearity assumption E[x v |h] = Oh holds).


Mean-square and absolute-error regression: Our discussion assumes an even simpler form when the loss function D(., .)

once again, this maximum likelihood problem may be regularized by prior information 1 , maximizing the a posteriori likelihood L(p) − q[p] instead of L(p); this problem is similarly tractable by ascent methods, by the concavity of −q[.]


To test the robustness of this setting, we vary c over {0.1, 0.2, 0.5, 0.7, 1, 3, 5, 7, 9, 15, 30, 50} and keep v = = 0.1 ( and c play similar roles and so varying one is enough).

we compare our DPMMGM with the well established KMeans, nCut and DPGMM clustering methods 3 .


Another possible objective function is to maximize the scatter of the responses.

the mean response vector for the p neural units was then appended to the previously-recorded responses and input into Adept.


WS353 (WORDSIM) [13] MEN (WORDSIM) [4] MIXED ANALOGIES [20] SYNT.

it lags behind the SGNS-derived representation on word-analogy tasks.


Assume m new data z z z i , for i " 1, . . . , m, are partially observed and the missing entries are to be filled in.

based on this construction of multivariate Corp, a straightfoward generalization of the electroGP model to a p-dimensional manifold could be made, where p ą 1.


In order for the complement generator to work, according to condition (3) in Assumption 1, the discriminator needs to have strong true-fake belief on unlabeled data, i.e., max K k=1 w k f (x) > 0.

in this work, we take a step towards addressing these questions.


we consider the following: where minimization is with respect to the choice of a decoder for a given kIC code.


For future work, we are interested in relaxing the (potentially hard) proximal update in (21).

between epochs, the gap (z s ) decays (in expectation) by a factor of 45 64 , and each epoch needs to conduct the proximal update (21) for m = Θ(L 2 ) number of times.


. . , ω m } and M ∈ R m×s a matrix of codes of length s with as many rows as classes.

in [5,7] two frameworks have been proposed which aim at inducing a label ranking function from examples.


Our approach builds on earlier work of Lawrence and Herbrich [2] which we extend here by considering randomized greedy selections and focusing on an alternative representation of the GP model which facilitates generalizations to settings such as regression and multi-class classification.

when including i into the active set I, we need to update diag(A) and h accordingly, which in turn requires the matrices L and M to be kept up-to-date.


In this work, we propose Covariance-Preserving Adversarial Augmentation Networks to overcome existing limits of low-shot learning.

we propose Covariance-Preserving Adversarial Augmentation Networks (CP-AAN), a new class of Generative Adversarial Networks (GAN) [14,15] for feature augmentation.


To see why this is useful, observe that minimising the pinball loss on scores F = f (X) is equivalently The second term on the right hand side is independent of ρ, and may be ignored.

this will produce an estimate of the sublevel set where p(x) < ρ * (by Proposition 4), and ρ * corresponds to a quantile of f * (by Proposition 9).


Thus, for a fair comparison, these hyperparameters are specified using cross-validation on a subset of data.

in this analysis, we can choose k = 20 to balance the performance and computational cost.


A common approach for avoiding a bad local minimum in these cases is to use multiple runs with random initializations and pick the best solution amongst them (as determined, for example, by testing on a validation set).

we refer the reader to [8] for more details.


High dimensionality poses significant challenges for assessing the uncertainty (e.g., testing hypotheses) of the constructed estimators.

note the assumptions in (4.6) imply that s ⇤ w = kw ⇤ k 0 needs to be small.


Among the deep learning models, TrajGRU performs the best and 3D CNN outperforms 2D CNN, which shows that an appropriate network structure is crucial to achieving good performance.

as rainfall events occur sparsely, we select the rainy days based on the rain barrel information to form our final dataset, which has 812 days for training, 50 days for validation and 131 days for testing.


This interpretation shows that spectral methods for clustering and segmentation have a probabilistic foundation.

here and in the following, an image will be represented by a set of pixels I.


As is standard in non-convex settings [18], we settle for a weaker notion of convergence, namely: that is, the algorithm converges ergodically to a point where gradients are 0.

the effect of ⇠ is dampened by the number of nodes.


The main result of this work is the following.

it is not clear how to apply an RNN to problems whose input and the output sequences have different lengths with complicated and non-monotonic relationships.


In Section 3, we propose the parsimonious triangular model (PTM), in which the dimension of the triangle-generating parameters only grows linearly in K. The dramatic reduction is principally achieved by sharing parameters among certain groups of latent roles.

nMI close to 1) across almost all networks, validating its ability to recover latent roles under a range of network sizes N and roles K. as N (and thus K) increases, MMSB Variational exhibits degraded performance despite having converged, while MMTM/PTM Gibbs converge to and become stuck in local minima  Mutual Information) and runtime per data pass for our method and baselines.


Another important advantage is that it allows us to use kernels, and therefore gives a systematic way to extend QBC to the non-linear scenario.

since the x i 's do not form an orthonormal basis of T , sampling the α's uniformly is not equivalent to sampling the w's uniformly.


However, we notice that methods based on influence functions usually underestimate overfitting making them impractical for model selection.

we also show that ALOOCV is asymptotically equivalent to Takeuchi information criterion (TIC) under certain regularity conditions.


More effectively, we tackle the campaigning problem in a dynamic and adaptive manner where we can postpone deciding the intervention by observing the process until the next stage begins.

1 summarizes the performance of the proposed algorithm (CLL) and 4 other baselines on different campaigning tasks.


To complement this, we also propose a parameter-free algorithm, which still achieve a good regret bound and may have independent interest of its own.

even when there is no variance in distributions, with Λ = 0, and the distributions only change once, with Γ = 2, any bandit algorithm cannot avoid a regret of about √ T , while a full-information algorithm can achieve a constant regret independent of T . Next, we study the tradeoff between Λ and V . We show that in the bandit setting, a regret of about 3 ΛV T + √ V T is achievable.


Once a stable matrix is obtained, it is possible to refine this solution.

sVD yields D ≈ U ΣV T where U ∈ R m×n and V ∈ R τ ×n have orthonormal columns {u i } and {v i }, and Σ = diag{σ 1 , .


Finally we showed that our proposed method accelerated the learning phase when solving discrete and continuous domains using different learning algorithms.

maintaining an estimate for each expert and state-action pair would not be practical for large spaces, so we follow Downey and Sanner [2010] and replace (σ i s,a ) 2 by the sample variance σ2 of D. This permits constant-time updates per sample without any additional memory overhead, and this worked very well in our experiments.


This indicates that, as expected, HM does a better job of optimizing the Hamming loss.

the initial set of documents that we consider consists of all NIPS papers 1 from 1987 to 2014.


The probability of making a specific time series of observations of length T can be shown to be a homogeneous polynomial P of degree T with nonnegative (integer) coefficients of the model parameters.

our convergence results are robust to any affine cost transformation.


As both RM and SML scale badly with input dimension, we restrict the dimension of the dataset to the p = 1, 000 most frequent words.

the challenge is finding a good approximation for (x i − P (x i = 1|x −i )) 2 and to define a proposal distribution that is efficient to sample from.


This means we could include any sentence s in the learning process (semi-supervised learning).

none of these models finely capture semantics, again because of the bag-of-word assumption.


In Figure 2(b), we show the cost as varies.

alice can attack Bob to change his behavior.


All the models are explored sufficiently long so as to be able to estimate the optimal reward level in the true model, and to learn its policy.

the process is known to be k-order Markov, where k is unknown but un upper bound K >> k is given.


Also as is standard practice when training neural networks [15], we also impose an 2 penalty on the weights so as to prevent them from diverging.

as seen in figure 1(b), the higher the AUC, the easier is the example to classify.


For example, the single treebank category NP (noun phrase) may be better modeled by several finer categories representing subject NPs, object NPs, and so on.

many of the techniques used in [12,14] are orthogonal to what was presented here (additional non-local/overlapping features, merging of unnecessary splits) and could be incorporated into the discriminative model.


When an item is studied, its integrators receive a boost in activity.

the KF model has a very different update rule, based on the Kalman gain.


We first present results in the exact scenario and then we move toward the approximated one.

they have been largely employed in motor control and robotic applications, thanks to their ability to cope with continuous state and action domains and partial observable problems.


We denote the subset of views that specify the effects for action a by T a ⊂ T . The main challenge is to build and maintain a comprehensive set of views that can be used in new environments likely resembling the old ones, but at the same time allow adaptation to new tasks with completely new transition dynamics and feature distributions.

unlike our work, these studies usually assume a common concrete state space.


For any fixed , letting N = 0 , it follows that ).

observe that the term tr(D 0 Ñ † D K) is again jointly convex in Ñ and D (also a perspective function), while it is easy to verify that L1 (D K, Ñ ) as defined in Lemma 3 below is also jointly convex in Ñ and D [32]; therefore the objective in ( 8) is jointly convex.


This is because the choice of q(x) for G-BP is favored by log-supermodular models, i.e., most of configurations are concentrated around (0, 0, • • • ) similar to the choice (7) of q(x) for G-BP.

this implies that G-BP generalizes BP well: the former provides a lower bound of Z for any GMs, while the latter does only for log-supermodular GMs.


Next we compare the lifts of SINGLE, which enforces revenue sharing constraints per impression, versus REFUND, which enforces constraints in aggregate.

we introduce a Lagrange multiplier for the revenue sharing constraint to get the optimal solution to the Lagrangian relaxation.


Suppose that H is any triangulated subgraph of G. Let P G (i) and P G (j) be the (marginalized) distributions of P G on V (i) and V (j) respectively, and P H (i) and P H (j) be the (marginalized) distributions of the distribution P H on V (i) and V (j) where ) ] and The following result assures us that the KL-divergence also factors according to the separator  Proof.

a graphical model is a pair (G, P ) where P is the joint probability distribution for random variables X 1 , X 2 , .


This is why scalable solutions for the submodular cover problem have recently gained a lot of interest.

one of the key ideas behind FASTCOVER is that finding elements with marginal values τ = τ can be done in a distributed manner.


The room and cuboid hypotheses are then combined to form the set of possible configurations of the entire scene (Figure 2(h)).

the reasoning approaches used in these block world scenarios (synthetic line drawings) proved too brittle for the real-world images and could not handle the errors in extraction of line-segments or generalize to other shapes.


The statistical properties of PEM (and Maximum Likelihood) methods are well understood when the model structure is assumed to be known.

the system and the predictor poles are restricted to have modulus less than 0.95 with the 2 norm of each h k bounded by 10.


We start from the conductance-based neuron model [1]: where, ḡleak =: g leak /C m , J ion =: I ion /C m , J syn (t) := I syn (t)/C m , V is the membrane voltage, ḡleak is the normalized leak conductance, E leak is the reversal potential, J ion are the voltage-dependent ionic inputs, ⃗ w := (w 1 , w 2 , • • • , w d ) are the gating variables that characterize the states of ion channels, J syn is a synaptic input, C m is the membrane capacitance, I ion are the voltage-dependent ionic currents and I syn (t) is a synaptic input current.

in our examination of biological data, we have explored parameters empirically from current-voltage data.


Γ 0 (X ) denotes the space of functions h : X → ]−∞, +∞] closed, proper and convex.

beyond the sparsity patterns of the data, there might also be a more complex structure, which is widely referred to as structured sparsity [16,22,23,29].


Because of differences in fabrication, the left and right images had slightly different brightness and contrast characteristics.

the subsampling ratios are 3 horizontally and 4 vertically.


Using all KM nodes to obtain stochastic gradient estimates at the same point, we can perform T iterations of A-MB-SGD with a mini-batch size of KM , yielding an upper bound of This is a reasonable and common approach, and it is optimal (up to constant factors) when KM = O( L 2 H 2 T 3 ) so that the statistical term is limiting.

. . z n } in parallel (⇤), and sequential variance-reduced stochastic gradient updates in between (⇤⇤).


these previous approaches are appropriate for objective with a non-composite structure.


Let T denote the estimated transition model based on data ∆, which approximates the true model T . In general, we assume that learning T (s, a) implies minimizing the loss L( T (s, a); D s,a ) where D s,a = {s i } ns,a i=1 are the successor states in the transitions (s, a, s i ) from s, a in ∆.

if ζ(s, a) is small, then the last k visitations in the data-set D s,a did not have a significant effect on improving T and in turn s, a does not require further exploration.


T log log T for some universal constant C 1 ą 0; furthermore, there exists another universal constant C 2 ą 0 such that no policy can achieve worst-case regret smaller than C 2 ?

one exception is our LIL-TRISECT algorithm, in which we remove the coefficient of 4 in front of the square root term in the confidence bands in Eq.


This problem may be due to the intrinsic overestimation behavior of Q-learning because Q-learning update uses maximum approximated action value as a target.

medical check-up data In order to evaluate our model under a more realistic diagnosis situations where cost comes to play, we perform an additional experiment on check-up data provided by a major hospital.


Putting Together: We are now ready to pose our general optimization problem: The objective function penalizes excess loss and ensures through the second term that this excess loss can be enforced through admissible gating functions.

another set of related work includes classifier cascade [5] and decision DAG [3], both of which aim to re-weight/re-order a set of pre-trained base learners to reduce prediction budget.


A crucial exception to this perspective occurs when γ (t+1) is highly sparse, or nearly so, in which case there are limited degrees of freedom with which to model even small differences between some φ i and φ i .

here we first empirically examine the trajectories of SBL iterations produced via the LSTM-like rules derived in Section 2.3.


We transform these pseudo-counts into exploration bonuses and obtain significantly improved exploration in a number of hard games, including the infamously difficult MONTEZUMA'S REVENGE.

we use a simplified, pixel-level version of the CTS model for Atari 2600 frames proposed by Bellemare et al.


When a new trigger or action is released, the training data will contain few corresponding examples.

from a training set (S, S), we create a rebalanced dataset, by randomly choosing 10 recipes for each function in S and all recipes using functions in S. the numbers of recipes using each function are similar in this rebalanced dataset.


Assuming that the hypothetical units can be replaced by time-bounded general recurrent networks, we determine an upper bound on the VC dimension of the resulting networks in terms of size and computing time using an idea from Koiran and Sontag (1998) and Proposition 1.

we emphasize that the only constraint on the parameters of the product units is that they yield real-valued, that is, not complex-valued, functions.


Then the optimal joint assignment for a given x can be specified by arg max y∈Y l k=1 y k s k (x).

to obtain scalable training we require some further refinement.


For example, the vanishing gradient effect is a well-known hardship to backpropagate an error signal through a long-range temporal interval.

since the sentence sequence generation from image streams has not been addressed yet in previous research, we instead extend several state-of-the-art single-sentence models that have publicly available codes as baselines, including the log-bilinear multimodal models by Kiros et al.


We first show a strong hardness result: there is no 1/n γ c approximation for influence maximization (unless P = NP) for all networks with up to n γ ε-almost submodular nodes, where γ is in (0, 1) and c is a parameter depending on ε.

the process ends when no new node becomes active in a step.


While it is sufficient to define the filter on the same grid in these cases, this is not possible for unevenly spaced inputs such as the atom positions of a molecule (see Fig.

the forces are zero by definition and do not need to be predicted.


LSTD-Q learns a control policy π from a batch of samples by estimating a linear approximation Qπ = Φw π of the action value function Q π ∈ R |S||A| , where w π ∈ R k are a set of weights and Φ ∈ R |S||A|×k is a feature matrix.

moreover, the BP regularizer was not sensitive to the scale of the regularization coefficient.


The global convergence results presented above for convex problems show that, in general, both the SR and BC algorithms converge to within O(∆) accuracy of the minimizer (in expected value).

some results below also assume the domain of the problem is finite.


A key aspect of PDCTs is their spatial adaptivity, which enables local (rather than global) polynomial fitting of the decision boundary.

we also study DCTs equipped with polynomial classification rules at each leaf, and show that as the smoothness of the boundary increases their errors converge to the Bayes error at a rate approaching n −1/2 , the parametric rate.


[40] proposed to first sparsify the benefit matrix and then run the greedy algorithm on this new sparse matrix.

additionally, we have worst case dependency on the number of edges in the ⌧ -threshold graph and the approximation factor.


Principal component analysis (PCA) has been applied profitably to neuronal recordings (see for example [14]) but these analyses often plot activity trajectories corresponding to different network states using the fixed principal component coordinates derived from combined activities under all stimulus conditions.

although chaotic intrinsic activity can be completely suppressed by the input in this network state, its imprint can still be detected in the spatial pattern of the non-chaotic activity.


To do that we start with some initial assignment π and consider a subset of items in U ; for illustration purposes we will use two items u i and u j .

for the general energy based distributions considered here finding the MAP state can be very expensive and in many cases intractable.


Our method (as well as the static low rank method based on the low rank hypothesis) however fails when the rank of S(t) is high.

given the last adjacency matrix A T , a set of features Φ, and an estimate F of F T +1 based on the sequence of adjacency matrices A t , t ∈ {1, 2, ..., T }, we want to find a matrix S which fulfills the following requirements: • S has low rank -this is a standard assumption in matrix completion problems [15].


For each table, sample parameters φ k ∼ G 0 .

unlike the HDP, however, the rddCRP allows within-group clusterings to depend on external distance measurements.


Appealingly, the advantage of NPNBP grows with the domain size due to the growth in complexity of matrix inversion.

copulas are "distribution generating" functions that allow us to separate the choice of the univariate marginals and that of the dependence structure, encoded in the copula function C. Importantly, this flexibility often results in a construction that is beneficial in practice.


Beginning with a comparison to KTF, fix θ ∈ H k+1 d (L), corresponding to evaluations of f ∈ H(k + 1, L; [0, 1] d ), and consider a point x ∈ Z d that is away from the boundary.

an extension of trend filtering to additive models was given in [21].


In order to illustrate the interplay between graph structure, sample complexity and interaction strength θ, it is instructive to consider a warmup example.

for θ > const./∆, there exists families of bounded degree graphs with long-range correlations.


Let θ (H−1) * be a critical point of L H−1 with γ * H−1 = 0, and θ λ be a parameter given by eq.

in mixture of FA and PCA, this does not necessarily work well, because the decomposition V = F F T + S does not give a natural parametrization.


The decision making of the ant agent thus relies on the competition between its active and passive neurons.

is Dirac distribution and t i j is the firing time of the j th spike from the i th presynaptic neuron.


Most research efforts in scRNA-seq methodology research focus on using generalized linear models and two-way ANOVA [40,35] to regress out the effects of quality control metrics.

let (A, B) ∈ R d×n × R d×m be random matrices with iid normal entries.


In the architecture of Figure 1, we can use independent samples of x ∼ D 1 at the input and instead of imposing a Gaussian distribution on the latent code, we can impose the distribution of the second domain using its independent samples y ∼ D 2 .

the question that has remained unanswered is whether it is possible to achieve a complete decomposition of content and style in an unsupervised fashion, where the class label or discrete structure information is encoded in the latent code z, and the remaining continuous structure such as style is captured by a powerful and deep PixelCNN decoder.


samples {(x i , y i )} m i=1 ∈ B d × [0, 1], from an unknown distribution D. We assume that there exists a predictor w * ∈ R d such that E (x,y)∼D [y|x] = φ w * , x , where φ is an activation function.

• We introduce a new setup: stochastic optimization of locally-quasi-convex functions; and show that this setup captures Generalized Linear Models (GLM) regression, [14].


When all the eigenvalues of A are real, we denote them by λ min .

again, in this regime, our procedure is closer to the diagonal and safely commits fewer than the allowed number of false positives.


We observe that the model is able to resolve the analogies in a satisfactory, position and illumination are transferred correctly although these positions have not been seen at train time for   Quantitative evaluation.

the generator is trained to produce samples that confuse the discriminator into mistaking them for genuine images.


Indeed, as we are considering G to be a grid, both estimators in (4), ( 5) can be computed very quickly, in nearly O(n) time, since the columns of V here are discrete cosine transform (DCT) basis vectors when d = 1, or Kronecker products thereof, when d ≥ 2 (e.g., [9,17,20,28]).

even the best linear smoothers have the same poor performance as the mean over T d (C n ).


Further, if the observed affinity scores from various explicit and implicit feedback are treated as exact (or mildly perturbed) entries of the unobserved preference value matrix, then the preference completion task naturally fits in the framework of low rank matrix completion [22; 38].

the bound provides a trade-off between observable training error and complexity defined by nuclear norm of the estimate.


The Euclidean metric in R N induces a metric g E (θ) = v(θ) • v(θ) on the curve, so that the distance dL E moved in R N as one moves from θ to θ + dθ on the curve is dL E = g E (θ)dθ.

now at each point θ, when both are nonzero, v(θ) and a(θ) span a 2 dimensional subspace of R N . Within this subspace, there is a unique circle of radius R(θ) that has the same position, velocity and acceleration vector as the curve h(θ) at θ.


In Section B, we provide a common technique, regression calibration to deal with measurement error problem.

we conduct a general risk analysis of this framework and in particular, we show for the first time, if two domains are related, HTL enjoys faster convergence rates of excess risks for Kernel Smoothing and Kernel Ridge Regression than those of the classical non-transfer learning settings.


Our policy model consists of a recurrent neural network (RNN) decoder coupled with an attention mechanism.

[35], which extracts the relevant information from the inputs using a variable-length alignment vector a t . a t specifies how much every input data point might be relevant in the next decoding step t. Let xi t = (s i , di t ) be the embedded input i, and h t ∈ R D be the memory state of the RNN cell at decoding step t. The alignment vector a t is then computed as ) Here ";" means the concatenation of two vectors.


Though units of α are consistent with a general optimization setting where step-size has units of objective −1 , in these problems, picking a good α that is consistent with the scales of the reward was difficult.

this architecture can also be interpreted as a two layer neural network: the bottom layer is clamped with random weights, a sinusoidal activation function is used, and the top layer is finetuned.


Each brain-image was processed using the Configurable Pipeline for Analysis of Connectomes (CPAC) [27].

x lives on a swissroll embedded in a  Our goal is to develop an approach to learn about f Y |X from n pairs of observations that we assume are exchangeable samples from the joint distribution, , where [n] = {1, . . . , n}.


We evaluated the usefulness of our architectures for control in two ways: 1) by replacing emulator frames with predicted frames in a previously-learned model-free controller (DQN; DeepMind's state of the art Deep-Q-Network for Atari Games [21]), and 2) by using the predicted frames to drive a more informed than random exploration strategy to improve a model-free controller (also DQN).

we approximate the tensor by factorizing into three matrices as follows [33]: where and f is the number of factors.


Other lines of research which are related to this paper are multiple-instance learning (MIL) problems [1,5,10], and multi-instance multi-label learning (MIML) problems [24,25] which extends the binary MIL setup to multi-labels scenario.

in this paper, we investigate a special kind of semi-supervised learning which considers ambiguous labels.


For instance, non-stationary dynamic Bayesian networks are introduced in [9], where the structures are learned via MCMC sampling; such approach is not likely to scale up to more than 1000 nodes and without a regularization term it is also prone to overfitting when the dimension of the data is high but the number of observations is small.

we propose a kernel reweighted 1 -regularized auto-regressive approach for learning this sequence of networks.


Complex numbers are represented in the polar form as z = |z|e iφz with |z| ∈ R + denoting the magnitude of z and φ z ∈ [0, 2π) denoting the phase.

there are of course many other implicit and explicit sources of inductive bias-here we show that merely parameterizing transformations via convolutions and using gradient descent for training already induces sparsity in the frequency domain.


Moreover, by definition we have β j = f j (Gr j ).

the main theorem of this section follows immediately.


The plot shows very little net progression toward regions of increasing mean salary 3 .

they are not concerned with the generative process that produces the graph, nor with the interpretability and statistical properties of their algorithms.


As in recent methods [12], we build on the observation that the Newton direction computation is a Lasso problem, and perform iterative coordinate descent to find its solution.

moreover, for p = 10000 random pattern, there are p 2 = 100 million variables, the selection of fixed/free sets helps QUIC to focus only on very small part of variables, and can achieve an accurate solution in about 15 minutes, while other methods fails to even have an initial guess within 8 hours.


where Li is the instantaneous linear response of filter i, 0' is a constant and Wji controls the strength of suppression of filter i by filter j.

he showed that, as with visual images, the spectral energy falls roughly according to a power law, and that the histograms of filter responses are more kurtotic than a Gaussian (i.e., they have a sharp peak at zero, and very long tails).


We can see that our algorithm converges in dozens of iterations, which confirms our theoretical guarantee on linear convergence rate.


There have been some recent theoretical results but they have been confined to specific assumptions on abstraction structure and are specific to various disjoint types of abstraction, and specific solution concepts, for example, exact Nash equilibria or strategies with bounded immediate regret.

corollary 1 yields tighter results despite also being more general.


The National Football League (NFL) forecasting data was collected by Massey et al.

the joint estimator may require significantly more control items if model misspecification exists; in this case one might better switch to the more robust two-stage estimator, or search for better models.


Here, we define a set of abstract methods for incorporating monotonic features into any existing learning algorithm.

this paper introduces the Monotonic Feature (MF) abstraction-where the probability of class membership increases monotonically with the MF's value.


Results over 5 runs of each algorithm in Figure 3 show that Crystals ensemble is about 0.25% -0.30% more accurate on the testing set over a broad range of ensemble sizes.

the computation scales linearly in K, but the K training jobs can be parallelized.


We also conduct experiments to demonstrate the impact of the supervision rate for DSD's disentangling capabilities, where we set the rates to be 0.0, 0.1, 0.2, ..., 1.0.

the former one is employed for both labeled and unlabeled pairs while the latter is for unlabeled only.


Now consider a protocol in which users send randomized responses of their corresponding bits.

in the first invocation, LocalRnd of user i performs its computation on the i -th prefix of the item v i of user i, while in the second invocation, it performs the computation on the entire user's string v i .


the variance of R is a well-explored topic in traditional importance sampling.


The proposed model is a semiparametric methodology, which offers modeling flexibilities and reduces the effect of model misspecification.

for instance, in 1950 and 2000, topic 9 (related to mouse, cells, human, transgenic) and topic 17 (related to virus, rna, tumor, infection) are highly correlated.


All synapses connecting the input and output layers are equally likely to be active during an anti-causal regime.

modulating the timing of the "global decay events" allows us to dynamically warp the time axis.


Hence, y w (x) is obtained by solving the so-called inference problem, which is known to be N P-hard for many output feature maps [6,7].

we observe, from Figure 1, on some datasets (e.g., Medical, NCI60), that the inference task is very easy since exact inference can be computed for most of the examples even with K values that are below 50% of the number of microlabels.


At each word in the answer sequence, we use a Gumbel-Softmax sampler S to sample the answer token from that distribution.

discriminative models can not be deployed as dialog agents with a real user where canned candidate responses are not available.


figure 2(c), MCAC/CCAC still maintain similar individual profits, but their unserved demand decreased significantly (by 32%) as shown in figure 2(d).

given a small step size, the linear approximation is sufficient to estimate the direction of the policy gradient to move towards a higher value.


This phenomenon is examined more closely in Figs.

our framework differs from previous approaches in three key aspects.


So in this particular setup the incremental training due to the simple recursion for the symmetry problem indeed provided useful training for the more complex Hanoi recursion, speeding up the search by a factor of roughly 1000.

use £ to efficiently restore only those H c '& £!


This final link probability provides the evaluation metric for a given missing data entry.

if group birth and death dynamics is not explicitly modeled, then the model could interpret that the two groups correspond to a single latent group where all the members of k leave the group before the members of l join the group.


If sensors are perfect, this domain is acyclic: after we sense a square we know its true state forever after.

for the problem with perfect sensing, on average MCP was able to plan 9.5 times faster than LAO*, 7.5 times faster than RTDP, and 8.5 times faster than VI.


The values of h are not observed in the training set, and will become the hidden variables of the model.

unlike previous work [10], our model does not require manual specification of the parts.


Now, the remaining problem is how to efficiently draw samples from p(Θ, Z, Φ) and estimate the expectations E[z] as accurate as possible, which are needed in learning classification models.

directly applying importance sampling to p(Θ, Z, Φ) may cause some issues since importance sampling suffers from severe limitations in large sample spaces.


Furthermore, [1] explicitly point out such a compression using a helper string (corresponding to the initialization in our setting).

there is a polynomially large m so that we can couple these two gradients until the network reaches a small generalization error.


Secondly, in Section 5.2 we cheapen the convolutions of a network trained for semantic segmentation.

the networks with half, or quarter that number of groups perform substantially better for a modest increase in parameters.


Readers are referred to [15] for a detailed description of hGMRFs.

for precision matrices Q u and Q z , we assumed a 5 × 5 Markov neighborhood (corresponding to a 5 × 5 convolution kernel), which was loosely chosen to optimize the tradeoff between accuracy and overfitting.


We used a 2×2 within subject factorial design for this experiment, testing for the effect of the retrieval mode -recognition/recall and either a stimulus heavy, or cue heavy selection of task materials.

mcClelland's equally influential CLS model is explicitly a dual-process model, where a fast learning hippocampal component primarily responsible for recollection sits atop a slow learning neocortical component responsible for familiarity [9].


The dataset to learn includes 5 sequences of 10 length, which are artificially generated by a MinSR HHMM of biased parameter set.

using Lagrange multipliers, we can obtain parameters π, Ā, B, which maximize the function Q under the constraint we can calculate the update parameters using α and β.


(2016) implies that, for the probabilistic s-step Adams-Bashforth integrator, the exponent ⇢ should be taken to be 2s + 1.

it is still a three-part procedure, analogous for example to paired Adams-Bashforth and Adams-Moulton integrators used in PEC mode (Butcher, 2008).


Bayesian observer models are very effective in describing human performance in perceptual tasks, so much so that they are trusted to faithfully recover hidden mental representations of priors, likelihoods, or loss functions from the data.

we determine the shape of p meas (x|s) with a maximum-entropy approach by fixing the first four moments of the distribution, and under the rather general assumptions that the sensory measurement is unimodal and centered on the stimulus in internal measurement space.


In this paper, we revisit the Empirical Risk Minimization problem in the noninteractive local model of differential privacy.

in machine learning it is quite common to have high dimensionality, i.e., n p. Thus, can we obtain some more meaningful bounds for the high dimensional case?


LSPI solves an infinitehorizon variant of problem (9) with discount factor λ = 0.9, polynomial basis features of degree 3 and a discrete action space comprising 1,000 points sampled uniformly from the true continuous action space.

we emphasize that all systematic estimation errors of this type accumulate as they are propagated through the dynamic programming recursions.


While this approach yielded efficient learning algorithms for multiclass categorization problems [2] and aesthetic solutions for structured output problems [3,4], devising these algorithms required dedicated efforts.

mira employs a different approach in which there is a single input instance (instead of the set X t ) and constructs multiple predictors (instead of a single vector ω).


Since the sensitivity of T is 1, by Theorem 6.1, T + N satisfies ( , δ)-DP.

we give a DP version of the sign and median test allowing one to test the median of either paired or independent samples.


Recent works consider a graph structure [26,38,22,33,7,6].

in term of ADE dataset, we use 20,197 images for training and 1,000 images for testing, following [6].


( 5) can be written as a feed-forward pass in a recurrent neural network by stacking multiple computation blocks.

multi-loss: Intermediate layer outputs y (t) should gradually converge towards the final output.


Mean shift: All the three distributions are isotropic multivariate normal distributions: p = N ([0.5, 0, . . . , 0], I), q = N ([1, 0, . . . 0], I), and r = N (0, I), defined on R 50 .

fID requires computing the square root of the feature covariance matrix (2048 x 2048), and is computationally too expensive for permutation testing.


The problem can be solved by different methods.

the proposed SVR-SVM does not appear to be affected by the witness rate.


This image is distorted by variations between the properties of individual target cell and neurotropin circuits that are introduced during fabrication.

finally, we induced growth cones of both cell types to self-organize coordinated retinotopic maps by illuminating the retina with center-surround stimuli that oscillate radially from light to dark or vice versa (Fig.


• We propose a fast and accurate softmax approximation, SVD-softmax, applied for calculating the top-K word probabilities.

differentiated Softmax (D-softmax) [19] restricts the effective parameters, using the fraction of the full output matrix.


While the reward function is KWIK learnable through linear regression [7] and though DBN CPTs with small parent sizes are also KWIK learnable, the high connectivity of this particular DBN makes autonomous exploration of all the parent-value configurations prohibitive.

we need to show: (i) The number of steps between traces where V A < V T − is polynomially bounded.


We use CoPRAM to establish its extension Block CoPRAM, which is a novel phase retrieval strategy for block sparse signals from Gaussian measurements.

these models have not been understood in the context of phase retrieval.


The first mechanism is the sparsemax of Martins and Astudillo [33].

in the remaining of this section we will assume that the sets B j are chosen maximally.


Some of the very best results on benchmark image classification tasks today use multiple kernel learning approaches [1,2] or sparse coding dictionaries for local features (e.g., [3]).

unlike [28], our regularizer will yield truly disjoint features when minimized-a property hinging on the metric-based classification scheme we have chosen.


Aggressive SHAMO with prior achieves average error of 1.47 (vs. 2.73 with no prior) on 1-vs-1 USPS and 4.97 (vs 4.93) on one-vs-rest USPS, with score rank of 1.0 (vs 2.9) and 1.7 (vs 2.0) respectively.

1 by noting that, there is a multiclass mistake if there is at least one prediction mistake of one of the one-vs-rest problems.


In our experiments, these hashing schemes do not prove powerful enough to compete in classification accuracy with the kernels that really do use the continuous-valued features.

the SVM slack parameter was trained using nested cross validation on 90% of the entire dataset, and the classifier was tested on the remaining 10%.


( 21) are thus found using the Gaussian free energy eq.

we also speculate that a structured variational approximation, using the same heuristics as described above to construct the spanning tree, in many cases will be superior to the Bethe approximation as also observed by Ref.


If v is influenced at time t, add v to S t . The process stops at T if S T = ∅ at the end of the step t = T . The set of the influenced nodes at the end of propagation is defined as S = ∪ T −1 i=0 S t . We often refer an edge (u, v) being open if node u influences node v. The IC model is equivalent to the live-arc graph model, where the influence happens at once, rather than sequentially.

the bounds can be efficiently obtained by message passing implementation.


We study the runtime required to learn a predictor such that with high probability over the choice of S, the error rate of the learnt predictor satisfies L γ (w) .

[2012] have shown that without utilizing kernels, no convex surrogate loss can guarantee an approximation factor smaller than α < 1 2 ( 1 γ − 1).


From a computational standpoint, entanglement seems intuitive enough -it is simply the fact that correlations can exist between different qubits -for example if one qubit is in the |1 state, another will be in the |1 state.

quantum search did well on this problem, finding a solution in an average of 2.32 searches.


The proof alongside the derivation of the ELBO for BLR can be found in the Appendix Theorem 2.

we make BOCPD robust by using β-D posteriors p βrlm (r t , m t |y 1:t ), π βp m (θ m |y 1:t ) for β = (β rlm , β p ) > 0 1 . β rlm prevents abrupt changes in p βrlm (r t , m t |y 1:t ) caused by a small number of observations, see section 2.3.


In this way, we can readily distinguish statistical significant interactions between neurons from spurious couplings.

the receptive fields of the STA seems to be Figure 2: Predicted rate for the GLM neuron model with and without any spike history and the predicted rate for the STA for the same neurons as in the other plots.


Due to the conditional independence of these draws, f ℓ can have discontinuities at the partition points.

this procedure generates cut points only at the observed locations x i .


Despite the excellent results of these models, they are limited by the lack of variation of their generated outputs, which are virtually deterministic, as the input noise is mostly ignored.

the generator encoder consists of several convolutional layers of stride 2, followed by batch normalization [22] and leaky ReLU activations.


The essential difficulty of 'multiple-label' problems comes from the ambiguity in the class labels for training data, i.e.

the given conditional distribution of the class label for every training instance is a delta function or jJ(y Yi) where Yi is the given class label for the i-th instance.


When a state variable is introduced, we wish to solve Eq.

similar methods have been proposed in an approximate dynamic programming setting that use basis functions, such as linear and polynomial predictors, to construct approximate value functions [22,14].


In our setting we can only ever determine that an arm is in H 1 and not H 0 , but it is impossible to detect that an arm is in H 0 and not in H 1 .

because µ 0 is known, there exist schemes that guarantee FDR-or FWER-even if the arm means µ i and the cardinality of H 1 are unknown (see Section 2.1).


Indeed, most 'real-world' learning problems have more structure than what this assumption captures.

it is not straightforward to find the kernel associated with an RKHS norm.


[10] to exploit the unlabeled data efficiently.

as a first experiment, we compare the three algorithms from Section 3 and logistic regression as a baseline.


It is easy to understand why this occurs by considering the prior distribution over amplitude and phase implied by our choice of prior distribution over x t (or equivalently over z t ), Phase and amplitude are dependent in the implied distribution, which is conditionally a uniform distribution over phase when the amplitude is zero and a strongly peaked von Mises distribution [15] when the amplitude is large.

we have demonstrated the utility of the new method on synthetic and natural signals, where it outperformed conventional approaches.


At first glance, the assumptions in Theorem 1 (specifically, the bounds M and B) seem strong.

( 6) is empty, and we recover the sequential improvement.


Algorithm 2 tries to estimate the gap ∆ to within a constant multiplicative factor.

regret is defined as the difference between cumulative reward of the learner's strategy and the best fixed learner's action in hindsight.


Pseudocodes of both learning schemes are described in Table 1.

the fMRI data are extremely high dimensional (i.e.


Nonlinear A i (x) allow a greater number of linearly independent measurements of p(x).

for simulations I distinguished between two types of units, hidden and visible, x = (h, v).


In general, it is not possible to give a more explicit version of the critical time of Corollary 3, or of the anytime influence bound of Proposition 2.

while the first algorithms focused on discrete-time models and the special case T = +∞ [3,4], subsequent papers [5,6] brought empirical evidences of the key role played by temporal behavior.


We make several observations based on Table 1:  For this case, it can be seen that DVAE# usually outperforms DVAE++ .

reparameterization cannot be applied to binary latent variables because the CDF is not differentiable.


We show that 1) our proposed solver achieves much faster convergence than previous methods and 2) that the Hierarchical SO-MTL approach outperforms considered non-MTL methods.

the algorithm is able to handle any (non-)smooth convex loss function , since only the subgradient needs to be computed.


More details on the OpenML set-up are given in the supplemental material.

one popular approach is to impose a Gaussian process (GP) prior over f and, in light of the observed queries f (x 1 ), .


Convolutionnal Neural Networks (CNN) have been very successful for many different tasks in computer vision.

this demonstrates that CNNs trained on artificial images generalize well to real images.


This is the standard formulation for expectation maximization [9], and has been applied to policy optimization in previous work [8,21,3,11].

this trajectory is only used for initialization and need not be reproducible by any policy, since it will be modified by subsequent DDP invocations.


. . , i |i| ) of indices i j ∈ {1, . . . , m} such that i 1 < i 2 < .

it consists of choosing the (Boolean-valued) feature i with the largest utility U i defined as where N i is the set of negative examples covered (classified as 0) by feature i, P i is the set of positive examples misclassified by this feature, and p is a learning parameter that gives a penalty p for each misclassified positive example.


The posterior mean µ(x) of the model can be evaluated for any x.

it is unclear how general noise correlation structures can be integrated in these models in a flexible manner, and whether the additional complexity of using a more involved noise model would lead to a substantial increase in performance.


Incorrect values for this parameter can result in failure to converge, not just slower convergence.

this results in a total runtime of O(K N /m + T ) -a linear speedup so long as m < KN/T .


In the experiments, monosyllabic words were presented in which the last phoneme from one word was partially replaced by one from another word (through digital editing) to create word blends that retained residual information about the identity of the phoneme from both words.

these concerns are part and parcel of the well-known problem of model selection.


To address this challenge, we approximate 4 using a simple penalty method.

let T u,i be the set of events induced between u and i.


The best solution we are aware of is one by Huber and Law, who recently presented an algorithm to approximate the permanent of dense non-negative matrices [10].

second, the estimator is not only statistically consistent but also in practice it seems to benefit more from increasing sample sizes than its max-margin alternative.


Since our definition of each vocabulary shape model assumes that its parts are conditionally independent, we can calculate the likelihood of the part hypotheses ) by taking a product over the individual likelihoods of the parts: The term stands for the spatial constraint imposed by a vocabulary edge e Ri between a parent hypothesis z R and its part hypothesis 1) is above a threshold, we add edges between z R and its most likely part hypotheses.

we employ a second step which revisits each class separately.


We use a Metropolis-within-Gibbs sampler with two main steps: First, we change the path of the Chinese restaurant process conditioned on the current parameters with a Metropolis Hastings random walk.

this property makes computing the data likelihood very fast in each iteration of our sampler and leads to a highly efficient estimation of the rate.


We will in the following consider tree-consistent partitions, where each data block in a partition corresponds to exactly one node for a cut (possibly across different levels) in the tree-see Figure 1.

the last plot in Figure 4 reveals an important difference between chunky EM and CS-EM: with a fixed ratio between number of data points and number of clusters, the EM-speedup declines a lot for chunky EM, as the number of clusters and data points increases.


This approach introduces an interaction between G and our classifier that we do not fully understand yet, but empirically we find that optimizing G using feature matching GAN works very well for semi-supervised learning, while training G using GAN with minibatch discrimination does not work at all.

semi-supervised learning with minibatch discrimination does not produce as good a classifier as does feature matching.


It seems to be particularly good when estimating small eigenvalues and their associated eigenvectors.

we show that a recursive local optimization procedure is simple, intuitive, and yields good results.


Because the number of values of α such that |α| ≤ p is r pd = C(p + d, d), the total complexity of the algorithm is where n c is the number of cluster centers that are within the cut-off radius of a target point.

few sources have a contribution greater than q i ǫ at low bandwidths, since the cut-off radius becomes very small.


Since C is complete, the intrinsic mean as defined above always exists.

we will select a hypothesis according to the likelihood ratio test: l(θ) ≡ log( h1(θ) h2(θ) ) > < 0 .


Based on prior work (see [7,8]), the large sample behavior of d ∞ is well understood.

the following Lemma gives some basic relationships between the three metrics d ∞ , d M and d MM .


Indeed, if X p , X q , X r are any three observed nodes in T , then T |{X p , X q , X r } must have the configuration on the left panel of Figure 2.1, and it can be seen that ph T (π p , π q ) ∪ ph T (π q , π r ) = ph T (π p , π r ) for any permutation (π p , π q , π r ) of (p, q, r).

now we present the polynomial characterization of a Gaussian latent tree graphical model that extends the results in Shiers et al.


Provided that the time horizon satisfies T ≤ µm, then yielding the theorem statement.


As can be seen from the last three rows, our proposed A 2 -block constantly improves the performance compared with both the Notably the extra cost is very little.

we combine the above two attention steps to form our proposed double-attention block, with its computation graph in deep neural networks is given in Figure 2.


We implemented the algorithm as described in the original paper.

refined solutions then are limit points of NEs as the mistake probabilities approach zero (different refinement concepts have different additional constraints on the trembles, which we will make specific in the next sections).


Linear interpolation of the edge weights between the t i is used to smoothly add the new edges and gradually delete the ones to be deleted.

under the constant-trace assumption, we construct an estimator for tr(B) For a time-varying trace tr(B(t)), use the time-averaged kernel In the future we will derive rates for the time varying case by choosing an optimal h. These estimators allow us to construct a sample covariance matrix for A: We (similarly to B(t)) apply the GLasso approach to Ã.


Our results paint a bleak picture for the use of value-iteration-based algorithms for computing stationary equilibria.

a NoSDE (pronounced "nasty") game is a deterministic turn-taking Markov game Γ with two players, two states, no more than two actions for either player in either state, and no deterministic stationary equilibrium policy.


The training process aims at seeking the optimal paramaters Θ * that encodes the source sequence and provides an output sentence as close as the target sentence.

experimental results show that our method significantly improves the performance on several large-scale MT datasets.


The learning rate is multiplied by the decay every 1M steps.

vPN is trained to approximate the true expected value because there is no explicit constraint or loss for the predicted abstract state.


At each time t, given the history h t , the agent can compute the posterior distribution µ t given by µ t (Θ) = P(θ * ∈ Θ|h t ) for any set Θ.

based on the key property of Lemma 2, we derive an upper bound on R 0 .


The standard LDA model does not include any notion of relationships, or dependence, between topics.

this is not yet a working definition unless we explicitly state which nodes are in the set F t . Our model does not in general assume any specific form for F t . Instead, the user is free to define it as they like.


To reduce the computational complexity, Greengard and Strain proposed the Fast Gauss Transform (FGT) [5], using two expansions, the far-field Hermite expansion and the local Taylor expansion, and a translation process that converts between the two, yielding an overall complexity of O(M + N ).

ǫ is modified every iteration) if we use inexact Krylov subspaces [23] for the conjugate gradient iterations.


In order to train the CAI model, we group θ into four categories -front, left, right and back, and provide it this information as a one-hot encoded vector.

more notably, CAI performs significantly worse than our baseline models, indicating that the supervised approach of invariance induction can worsen performance with respect to nuisance factors not accounted for during training.


In such problems, there are often demands to incorporate additional structural properties of matrices in addition to the low-rankedness.

be a fixed point of the AMP algorithm for the MAP problem and suppose that ∑ m i=1 S ∞ i and The proof is in the Supplementary Material.


Next, we define more formally the problem setup (Section 3).

the algorithms proposed by these authors heavily rely on the assumption that the advertisers' bids are drawn i.i.d.


We will pick the stage, weight, and function of the subclassifier in order to make the largest negative change in the exponential bound to the empirical risk.

the label of x k ī is the sign of z k ī , and the weight of the same example is the magnitude of z k ī .


PLML does not overfit on any of the datasets.

here we learn one local metric for each cluster and we assign a weight of one for a basis metric M bi if the corresponding cluster of M bi contains the instance, and zero otherwise.


We then observe that Φ c−θ γ plays an analogous role in Equation 3 to w1 in (1).

under G 1 the probability of E occurring (assuming b + ) is a similar noisy-AND-NOT parameterization can be used for preventive causes [4], but we focus on generative causes in this paper.


5 For example, navigating around suboptimal local minima could require adaptively adjusting the number inner-loop iterations in subtle, non-obvious ways.

we now walk through these correspondences.


For both datasets, we preprocessed with a high-pass filter at 800 Hz using a fourth order Butterworth filter before we analyzed the time series.

observe that making this decision involves marginalizing over all possible cluster assignments ⌫ t , and all values of the weight vector y t . having made this decision, we collapse these posterior distributions to point estimates b ⌫ t and b y t equal to their MAP values.


This function is a popular choice as the final layer for an MLP used for classification, but it is by no means the only possibility.

we can now attempt to bound the norm of a perturbation R to X such that We find Theorem 4.2.


We emphasize that N (0) is the component of A (0) outside the column space of A * , and is not the difference between A (0) and A * .

it only requires the columns of A * to be linear independent, which is very mild and needed to ensure identifiability.


Our method and the theoretical analysis do not make assumptions based on specific structures.

all methods are based on the 1st-order Markov dependency.


They proposed a scalable MCMC framework referred to as Stochastic Gradient Langevin Dynamics (SGLD).

finally the last term Γ 1/2 K A 3,K goes to 0 as K goes to +∞.


This is achieved by exploiting adversarial domain classification in the resulting latent feature space.

with the above discussions, we define the objective functions L adv Dx and L adv G for adversarial learning between image discriminator D x and generator G as: the objective function for domain classification is derived as: where l x denotes the domain prediction of image discriminator D x .


The second term for the error of the Uluru algorithm does not contain r at all.

solving an overdetermined linear system ( ŵ = arg min w∈R p Xw − Y 2 ), while we are working in a statistical set up (a regression problem Y = Xβ + ) which leads to different error analysis.


Since we consider models where η = O(1) is a small constant, this implies that we have a polynomial sample complexity in p, d, r. The final step involves using the estimated pairwise marginals of each component { P spect (Y a , Y b |H = h)} to obtain tree approximation of the component via Chow-Liu algorithm [10].

if we resort to operations over only low order statistics, we require additional conditions such as (8) for identifiability.


The top six eigenvalues of its gradient covariance matrix are well separated from the rest as seen in Figure 4(a).

as an alternative, Wilson and Nickisch [28] proposed the structured kernel interpolation (SKI) approximation, where U is a uniform grid of inducing points and W is an n-by-m matrix of interpolation weights; the authors of [28] use local cubic interpolation so that W is sparse.


[2008], FASTSWAP uses a specific initial distribution at each round, applies the power method to a modification of the original stochastic matrix, and uses, as an approximation, an average of all the iterates at that round.

theorem 3 implies that FASTTIMESELECTTRANSDUCE achieves the same timeselection swap regret guarantee as the algorithm of Khot and Ponnuswami [2008] but with a perround computational cost that is only in ), which is an exponential improvement!


Nevertheless, we also report classification accuracy in Table 1 to show that a) the learned models have similar characteristics as earlier work, in particular to [29], where the an identical model was trained using structured SVM learning, and b) adaptive MMP can achieve as high prediction accuracy as ordinary Gibbs sampling, as long as the confidence parameter is not chosen overly optimistically.

sequential sampling with the option of early stopping has a long tradition in Bayesian statistics.


We compare against multiple recent domain adversarial unsupervised adaptation methods.

we do not assume a shared label space between the source and target domains and as such can not assume that each target image maps to a single source label.


. . , x n then we reduce it to MDP with n + 1 states,s 1 , .

. . c T over actions A, the algorithm selects a distribution q t over A (using only the previous loss functions where c t (a) ≤ M . Furthermore, we also assume that decision distributions do not change quickly: These assumptions are satisfied by the multiplicative weights algorithms.


Notice that these concepts could not be discovered with a standard Multinomial-based topic model.

this is most likely due to the extreme simplicity of Multinomial parameter estimation-simple frequency counts-that is usually smoothed by the simple Dirichlet conjugate prior.


[8,7], since we train object models that predict a complex, structured label (an object track) rather than a binary class output.

by judiciously choosing which frames a user should annotate, we can obtain highly accurate tracks with minimal user effort.


Hence, for the proposed approach, there is an improvement in both accuracy and MaF 1 measures.

standard OVA and M-SVM have a complexity that grows linearly with K thus the total runtime and memory usage explodes on those datasets, making them impossible.


In this case, volume sampling once again offers very concrete guarantees.

the input vectors obtained from volume sampling are selected jointly and this makes the chosen subset more informative.


[2017] introduce a modern max-margin technique with an approximate planner in the optimisation.

this is another form of unidentifiability of the reward function, beyond the well-known ones Russell, 2000, Amin andSingh, 2016].


We analyze TranSync under both deterministic and randomized noise models, demonstrating its robustness and stability.

in the second application, we apply TranSync to predict global rankings of Netflix movies from their relative comparisons provided by users.


Such M ( w) is denoted M 0 ( w) in the following text.

let W i,j,k denotes the set of all possible walks w satisfying s 1 =s i , s |w| =s j and s |w|+1 =s k . Then we have V (s i ) = w∈W i,j,k (γ |w|−1 (s t ,s t+1 ) on w p s t ,s t+1 ).


Following the same lookahead strategy as LSID3, we sample the space of trees under each candidate split.

assume a problem with |C| classes and a misclassification cost matrix M . Let c be the class label in a leaf l. Let m be the total number of examples in l and m i be the number of examples in l that belong to class i.


The better separated the clusters are, the less membership constraints need to be enforced in order to avoid degenerate solutions.

the multi-cut problem has still to be solved via the greedy recursive splitting technique.


In the case of a neural population, we are not only looking for the stimulus feature a, but also need to determine what pattern of spiking activity b it is coupled with.

for comparison, we also plotted the single-cell receptive fields in Figure 3 .


Agents can only pick up one key per episode -the first they encounter.

this means that Bob has a shorter path to the goals, and thus if Alice telegraphs the goal right away, Bob will beat her to it.


Combining the last two inequalities we conclude that holds with probability at least 1 − 2e −n ∆ 2 8 − e − η 2 2 .

for the loss in (1.1) the generalized gradient takes the form projected gradient descent takes the form where µ τ is the step size and K = {w ∈ R d ∶ R(w) ≤ R} is the constraint set with P K denoting the Euclidean projection onto this set.


else false reward = s(1) + s(2) + s(3) AROLLOUT translates the RDDL code into algebraic expressions using standard transformations from a logical to a numerical representation.

anytime algorithms are typically scored using the log of marginal probability; the score for solution Current state of the art exact algorithms use branch and bound techniques (e.g., [11]).


An initial step size must be selected, but the adaptive step size adjustment rules make this choice less important.

this requires the global policy to search for the hole, since no input to the global policy can distinguish between the different initial state x i 1 .


the fits minimize the block's squared loss.

the list C is updated with the optimal cuts in both sub-groups generated.


When p 2 C, excluding [n] \ S will only reduce Z.

for the class C = M d n of monotone distributions over [n] d we require an optimal ⇥ n d/2 /" 2 number of samples, where prior work requires ⌦ p n log n/" 6 samples for d = 1 and poly (1/") for d > 1 [6,7].


We can further improve on this method by using trusted data to train the corrected classifier.

a sample of error curves are displayed in Figure 2.


We call the union of the regions defined in Equation (4) a tube.


See Figure 2 and the accompanying text in Appendix E for a plot of the points (⇢, log 10 ( )), where is the final average change in the messages at termination of the algorithm.

we show that in the pairwise Bethe case, the polytope may be expressed geometrically as the convex hull of single-cycle forests formed by the edges of the graph.


This translates into only up to n nonvanishing eigenvalues in K. Contrast this observation with plain MVU.

one may show that feature selection [7] and clustering [8] can also be seen as special cases of this framework.


For example, [26] directly used the bits from b-bit minwise hashing [20,23] to build hash tables and demonstrated the significant advantages compared to sim-hash [8,12] and spectral hashing [29].

no such provable guarantees are known for SR and other heuristic based search methods.


In this paper, we instantiate the loss using the structured hinge loss [25].

first, distributed representations for inputs have led to performance gains by uncovering shared characteristics across inputs.


To allow probability measures P without densities (i.e., P µ), we assume each basis element φ z : X → R is a bounded function, so that P z := EX∼P [φ z (X)] is well-defined.

then, for any P ∈ F G , we define the implicit risk of X at P by R I (P, X) := E X1:n∼P (P, P X(X1:n,Z)|X1:n ) .


This is expected for deterministic sketching which focuses on the dominant part of the spectrum.

the diagonal adaptation already greatly reduces the condition number on all datasets except splice (see Fig.


This contribution is concerned with the generation of samples from the Bayesian posterior over the hypothesis space of lin-ear classifiers in arbitrary kernel spaces in the case of label noise.

the KGS is a Markov Chain Monte Carlo method that chooses a random direction in parameter space and samples from the resulting piecewise constant density along the line chosen.


We use the logistic loss as the learner's loss function +1 (h(x), y) = log(1 + e −yh(x) ) for the Minimax and the Nash model.

the emails are sorted chronologically and tagged with label, date, and size.


While these algorithms worked well in practice, until recently, little could be shown analytically about their performance.

proof sketch: Using tail distributions of chi-squared random variables, it is shown that the minimum value for the correlation |a ′ j y| 2 when j ∈ I true is greater than the maximum correlation when j ∈ I true .


Our method makes strictly weaker assumptions than existing approaches, and we prove conditions under which it yields a consistent estimator.

our conditions are strictly weaker than imposing unconfoundedness on the observational data.


We can bound the expected change using the Dobrushin parameter and the property of the greedy coupling (Lemma 1).

the results extend to Ising models with external fields when the functions under consideration (in Section 4) are appropriately chosen to be centered.


In SNE, the class posterior probabilities p(c k |x n ) are replaced by the probability p(x m |x n ) of object x n under a Gaussian distribution centered on x m . When the inputs (posterior probabilities) to PE come from an unsupervised mixture model, PE performs unsupervised dimensionality reduction just like SNE.

1 The computational complexity of PE is O(N K), which is much more efficient than that of pairwise (dis)similarity-based methods with O(N 2 ) computations (such as SNE, MDS, or Isomap).


When β = 1, all tensor slices have equal Frobenius norm.

there can only be o(n 2/3 ) slices j for which T j, * , * for each of them we can afford to take O(n 2 ) 2 -samples and still have an O(n 2+2/3 ) = o(n 3 ) sublinear running time.


In order to add additional appearance-based hyper-features, such as contrast, oriented edge energy, etc., we moved to a smooth parametric representation for both the distribution of d j and the model by which the the hyper-features influence this distribution.

(3) to classify each test pair as matching or not, producing a precision-recall curve.


In principle, this makes them an appealing choice for large POMDPs.

we prove convergence for POMDPs with finite horizon T ; this can be extended to the infinite horizon case as suggested in [8].


This belief state b can be treated as a random variable with a distribution parameterised by belief-mean m and belief-certainty V seen Figure 3.

there are two main reasons which make this assumption necessary.


In this work we present a novel approach to incorporating prior knowledge in the form of polyhedral knowledge sets in the input space of the given data.

the ten-fold, cross-validated test set correctness achieved by standard SVM using all the data is 66.2% [2].


Let α j k and β j k be the sensitivity and specificity respectively of the j th annotator corresponding to the threshold k, that is, Hence each annotator is parameterized by a set of 2(K − 1) parameters [α j 2 , β j 2 , .

if the true label is zero, the specificity (1−false positive rate) β j is defined as the probability that annotator labels it as zero.


Qualitatively, GP learning curves are relatively well understood for the scenario where the inputs x come from a continuous space, typically R n [3,4,5,6,7,8,9,10,11].

in section 2 we give a brief overview of GP regression and summarize the approximation for the learning curves used in previous work [4,8,12].


For the negative training sets, we obtained noncoding RNAs other than pre-miRNAs and exonic regions of protein-coding genes from NCBI (http://www.ncbi.nlm.nih.gov), fRNAdb [23], NONCODE [24], and   snoRNA-LBME-db [26].

reliable pre-miRNA identification requires features other than the secondary structure to be considered, since false positives may be generated due to the limitations of structure prediction algorithms and the inherent unpredictability of these structures [21].


. . , w K ) ∈ R K . Note minimizing the cross-entropy loss is equivalent to maximizing the likelihood of , which is biased towards fitting neither the data with y i = 1 nor these with y i = 0, since NLL(x i ) = ln(e −yiw ln(1+e Bx i ) + e (1−yi)w ln(1+e Bx i ) ).

it is straightforward to show that iSHM with a single unit-weighted hyperplane reduces to logistic regression To interpret the role of each individual support hyperplane when multiple non-negligibly weighted ones are inferred by iSHM, we analogize each β k to an expert of a committee that collectively make binary decisions.


The form of (2) shows that DUDE is a sliding window denoiser with window size 2k + 1; namely, DUDE returns the same denoised symbol at all locations i's with the same value of z i+k i−k .

it is clear that s cannot evaluate its loss since it does not know what x is, but the following shows an unbiased estimate of the expected true loss, which is only based on Z and s, can be derived.


For fair comparison, in the experiments described above in Section 4.1 we only trained our feature extractor backbone on the subset of training categories of the target dataset (same as in other works).

we also tested a variant where no noise is injected to the input, i.e.


Theorem 1 Given two simple, undirected graphs G 1 = (V 1 , E 1 ) and G 2 = (V 2 , E 2 ), with combinatorial Laplacians L G1 and L G2 ,the combinatorial Laplacian of the Cartesian product graph G 1 × G 2 is then given by: Here, D G denotes the degree diagonal matrix of the graph G. Now, by the definition of the Laplacian, However, the degree of any vertex uv in the Cartesian product is deg(u) + deg(v), because all edges incident to a vertex will either be derived from one of the original graphs or the other, leading to corresponding nodes in the product graph.

this work was supported by NSF grant #IIS-0705681 under the Robust Intelligence program.


This approach tackles a variant of (1) where the regularization term is replaced by an upper bound on the total variation norm; the associated constraint set is the convex hull of all Diracs and negatives of Diracs at elements of θ ∈ Θ, and thus adapted to conditional gradient algorithms [19].

there is a direct link between the velocity field (5) and the functional F . The differential of F evaluated at µ ∈ M(Ω) is represented by the function F (µ) : Ω → R defined as Thus v t is simply a field of (minus) subgradients of F (µ m,t )-it is in fact the field of minimal norm subgradients.


This work was supported by a Dorothy Hodgkin fellowship for the Royal Society and the BIBA European Project.

we found Fano factor close to 1 and quasi-exponential ISI distribution (figure 1-E) on the entire range of parameters tested.


To exactly recover M ⇤ , a common assumption is the incoherence of M ⇤ , which will be specified later.

the QR decomposition can be accomplished in O(k 2 max{m, n}) operations, while the rank k singular value decomposition can be accomplished in O(kmn) operations.


Here, we generalize this algorithm to the mixed margins case and apply it to the C-vine.

statistical methods for their concurrent analysis are currently lacking.