Even though the renderer is quite fast, MCMC with simple proposals fails: after proposing a change to a single variable, it must re-render the image in order to compute the likelihood.

we assume that each type t ∈ T is a parametric family of distributions p t (x|θ t ), with parameters θ t . Now, consider what happens while executing f . As f is executed, it encounters a series of ERPs.


The analysis of Algorithm 2 relies heavily on a new decomposition idea of matrices in S d that suggests that given a matrix X in the form of a convex combination of rank-one matrices: i , and another matrix Y 2 S d , roughly speaking, we can decompose Y as the sum of rank-one matrices, such that the components in the decomposition of Y are close to those in the decomposition of X in terms of the overall distance kX Yk F . This decomposition and corresponding property justifies the idea of solving rank-one regularized problems, as suggested in Eq.

multiplying a vector with a rank-one matrix takes O(d) time.


For small values of η the two networks relax to a state of a mutual agreement, R → 1 for η → 0.

[6] has been calculated analytically [6].


Ergodicity need not always hold, and proving that it does hold may require considering the particulars of the model.

for validity of the sampling method, we need these transitions to leave π invariant: (If X is continuous, the sum is replaced by an integral.)


Different algorithms have been proposed so far to take advantage of this advance knowledge of the test points (such as in [1], [2], [3], [4], [5], [6] and others).

this means that such a v i will provide a good approximation for the labels.


Turning now to the M-step update for the eigenvectors, the derivative of Equation ( 13) with respect to V involves an exponential-size sum over J similar to that of the eigenvalue derivative.

this is a standard technique for developing EM schemes for dealing with hidden variables [25].


Then, w 2 b µ(1 ✏) • S for any w 2 W and consequently S ✓ W ✓ b µ(1 ✏) • S with probability at least 1 1/m.

we consider instances of problem (1) where Bij are i.


This monotonicity simplifies the problem.

2 For simplicity, our experiments are carried out for a two-tier (single cache) system such that the only design parameter is the relative queries.


This reduction of the bias typically comes at the cost of an increase of the variance.

additive Models are a class of nonparametric regression methods which have been the subject of intensive theoretical research and found widespread applications in practice (see [1]).


al rely on a sparse coding representation in layer 2, which is likely to be more effective than the simple Gaussian units of HMAX.


In general, such learning formulations are limited in that the learned kernel cannot readily be applied to new data points.

frob LR reduces the rank of the learned matrix W (equivalently, it reduces the dimensionality) using Frobenius norm regularization by taking the top eigenvectors.


(Note that v * can be larger than v * if the optimal compressed action is already part of M c .) Property 3 uses v * rather than v * since the latter is not known while it is possible to compute a lower bound on the former efficiently (see below).

as a result, f best ≤ v * (s pivot ) and is used as a new estimate for v(s pivot ).


Another interesting finding is that when good features are given (1d), IMC (and SVDfeature) still fails to achieve 0 relative error as the number of observations increases, which reconfirms that IMC cannot guarantee recoverability when features are not perfect.

we study the matrix completion problem with side information.


If we observe the response of a neuron but don't know the identity of the individual generating this response, then we are observing responses drawn from the ensemble distributions defined above, pens(WJt) and pens(w).

nine different flies are shown precisely the same movie, which is repeated many times for each fly (Figure Ia).


The problem, then is to find x = argmax c(j) eq.

5 lies along a single axis in the set of axes represented each row of G. gIll =< 0,.


Let pv (x v ) be the estimated pdf for component v, and Fv be the corresponding cdf.

given a set of estimated quantile values A, a suitable parameter values β (edge weight matrix) and θ (parameters for bivariate edge copulas) can be found by maximizing the log-likelihood of A: the parameter optimization of l (β, θ) cannot be done analytically.


Only the von Mises approach [22] is known to achieve the minimax rate for general β and D, but due to its computational demand (O(2 D n 3 )), 3 the authors suggest using other statistically less efficient estimators for moderate sample size.

(A3) p is supported on all of R D . the support of p has no boundary.


In the extreme case when µ = ∞, the second term in ( 7) can be shown to be the generalization bound using the weighted samples in the source domain only (the target data will not be effective in this case), and the last term equals to 2λ α,β + d H∆H (D α,β , D T ).

in contrary physiological signals, such as SEMG are predominantly different in conditional probability distributions due to the high subject based variability in the power spectrum of these signals and their variations as fatigue sets in [25,26].


This key-value-free procedure is general and can effectively prevent massive disk IOs and fully exploit the memory cache mechanism in fast MAPREDUCE systems, such as SPARK.

we propose a distributed, flexible nonlinear tensor factorization model, which avoids the expensive computations and structural restrictions of the Kronecker-product in the existing TGP formulations, allowing an arbitrary subset of tensorial entries to be selected for training.


The individual GPs represent connections between different endpoints.

the Wasserstein distance allows the inherent uncertainty in the estimated GP data points to be appropriately accounted for in every step of the analysis, giving truthful analysis and subsequent interpretation.


In its basic setting, the only domain knowledge applied to HRA is in the form of the decomposed reward function.

once the optimal value function is known, an optimal policy can be derived by acting greedily with respect to it.


This is the case already for the set of hyperplanes in R k !

all the computation for this experiment takes approximately 6 minutes on a standard laptop.


Remarkably, when subjects perform movements in a force field that changes randomly from one movement to the next, the pattern of errors predicts a generalization function, and therefore a set of basis elements, indistinguishable from the condition where the force field does not change.

the simpler notation allows us to write Eq.


4, this softmax construction produces noisy, less spatially coherent partitions.

spatial structure plays a crucial role in general scene interpretation [3], particularly when few labeled training examples are available.


When signals have a complex nature, it is difficult to decide in advance which nodes contain the sparsest sets of coefficients.

this yields significantly better results than those obtained by applying standard Infomax and clustering approaches directly to the raw data.


A binary relation R ∈ R, corresponding to a specific type of link between two variables, specifies the types of its input arguments, and a set of features f R k (•, •, E) and feature weights w R k . We will write X i , X j ∈ inst(R, X ) if the types of X i and X j match the input types specified by the relation R and there is a link of type R between X i and X j in the data (for example, a hyperlink between two webpages).

given the concrete value E of evidence E, one can write down the conditional version of the tree structure likelihood (7) for that particular value of evidence: If exact conditional distributions P (X i , X j | E) were available, then the same Chow-Liu algorithm would find the optimal conditional structure.


Our algorithm can also be used, as a special case, to simply select -not learn -a few common features across the tasks.

we modify the computation of the matrix D (penultimate line in Algorithm 1) as D = Diag(λ), where the vector λ = (λ 1 , .


. . ⇥ n T order-T tensors M 6 = M 0 of rank r with coherence parameter  µ 0 such that P ⌦ (M) = P ⌦ (M 0 ) with probability at least .

for tensors, the algorithm becomes recursive in nature.


A generative model, denoted the binary dynamic system (BDS), is proposed to learn both the distribution and dynamics of different activities in this space.

all of these representations are BoF-like, in the sense that they represent actions as orderless feature collections, reducing an entire video sequence to an attribute vector.


The SVM results are reported in Table 1 where the "SVs" column refers to the number of support vectors present in the final classifier and the "errs" column refers to the number of classification errors obtained on the testing set.


The probability of trial k being a stop trial, P (s k = 1|s k−1 ), where s k {s 1 , .

where r = P (s = 1) is the prior probability of a stop trial.


Let m i be the mean of the elements of S i encoded in the latent space, that is E Si [µ φ (x)].

we consider both attribute transfer, in which the goal is to transfer a specific style of an attribute to the generated image, and identity transfer, where the goal is to transfer the style of a specific image onto an image with a different identity.


We investigate an approach for simultaneously committing to multiple activities, each modeled as a temporally extended action in a semi-Markov decision process (SMDP).

each set Λ i (s) contains a set of actions in state s that are all i -ascending with respect to the superior controllers C 1 , C 2 , .


One further limitation of the thresholding model is that it does not take into account the fact that the likelihood of a new shot transition is dependent on how much time has elapsed since the previous one.

comparing this with (4), it is clear that the inclusion of the shot duration prior transforms the fixed thresholding approach into an adaptive one, where the threshold depends on how much time has elapsed since the previous shot boundary.


We downloaded the log ratio normalized data collected in this study.

most interactions are still correctly recovered.


In what follows, we first present the results of the time-oriented validation scenario stratified for the length of treatment history, followed by the results stratified for the abundance of the different therapies.

also the various levels of therapy experience ranging from therapy-naïve to heavily pretreated are represented with different sample abundances.


If G is directed, we can still associate with it an independence number: we simply view G as undirected by ignoring arc orientation.

then the regret of Exp3-SET satisfies In the above, the expectations �[•] are w.r.t.


gratefully acknowledge partial support from the PASCAL Network of Excellence (EU #506778).

an increasing number of papers are now dealing with more structured parameters.


By tying the parameters v r −1 to the negative of v r , we can conclude that h ej , v r , t ei and h ei , v r −1 , t ej become negative.

the table also shows that bilinear approaches tend to have better performances compared to translational and deep learning approaches.


Then, without any modification on the pre-trained softmax neural classifier, we obtain a generative classifier assuming that a class-conditional distribution follows the multivariate Gaussian distribution.

in this paper, we propose a simple yet effective method for detecting abnormal test samples including both out-of-distribution and adversarial ones.


A full analysis is carried out for linear gradient flows (quadratic optimization) and provides compelling explanations for the acceleration phenomenon.

to extract h, we will assume that the method is consistent (see conditions ( 5)).


Rejection learning [8,10] proposes a solution: allow models to reject (not make a prediction) when they are not confidently accurate.

the model can choose to say PASS, and pass the decision downstream, as explored in rejection learning.


Spectral pooling is straightforward to understand and to implement.

every convolution and pooling layer is followed by a ReLU nonlinearity.


This section presents the experimental results using the benchmark image recognition dataset, CIFAR-10.

necessarily { ∇V (x k ) } → 0 and the estimates approach a stationary point.


An even more interesting finding is that the solutions found by RM were sparse while achieving lower test misclassification errors than standard deep learning methods.

the total utility for each zanni s v is given by The utility for the antagonist a is then given by The utility for all protagonists are the same, U p (σ) = −U a (σ).


There have been quite a few implementations of GBDT in the literature, including XGBoost [13], pGBRT [14], scikit-learn [15], and gbm in R [16] 4 .

in GBDT, there are no native sample weights, and thus the sampling methods proposed for AdaBoost cannot be directly applied.


there has been an exciting line of ongoing work to make the resulting algorithms faster and scalable [7,17,4,15,24,20].


Let p 1 (α) ≡ p 1 (α|y (1) , γ (1) ) denote the prior for α, e.g., an exponential distribution p 1 (α) = λe −λα .

( 1)) are proportional to k =K+ n−1+αn−1 Ln,K+ (y n ) and αn−1 n−1+αn−1 L n,K+ (y n ), respectively.


One specific application of this result is as a way post-process learned predictions to ensure fairness.

algorithmic predictions are now being used to answer questions of significant personal consequence; for instance, Is this person likely to repay a loan?


1 A few algorithms require matrix inversion or an eigen-decomposition of an n-by-n matrix; we did not parallelize these steps in our experiments, because for us m >> n, and so their cost is small.

in the definition for Σ, the term m i=1 x i x T i is already expressed in summation form.


We further use only 14 images per class which correspond to illumination and expression changes.

formally, let X = [X 1 , X 2 . . . , X K ] be a K class dataset in R n such that vectors from class i (x ∈ X i ) lie along subspace S i .


We assume for simplicity that receptive fields of sensory neurons do not overlap with each other (in the supplementary materials, we discuss the more general overlapping case).

let n j k+1|k be the number of proposed samples in j-th sub-population, we have the prediction probability in equation 1 is represented by the expected number of neurons that receive recurrent inputs.


We extend the domain of each f (i) to include the meta-actions by defining t was appended to S (i) , and f (i) (S ⊕ ãt ) = f (i) (S) otherwise.

the problem of maximizing f (S T ) is a slight generalization of the problem of maximizing a monotone submodular set function subject to a knapsack constraint [14,20] (which in turn generalizes BUDGETED MAXIMUM COVERAGE [12], which generalizes MAX k-COVERAGE [16]).


The variant of ConvLSTM can be formulated as: The gates i t , f t and o t are all one-dimensional vectors, so that the elements in each feature map are weighted by the same gate value in Eqs.

the different gates values for each element of the feature maps in the spatial domain seemingly do not have the function of spatial attention.


The selection strategy in step 6 above picks out the mode which produces the largest linearized increment in dX (¡ a ¥ ¡ ¨¢ ©¤ X (¡ ¡ r a .

(' ) X x q 7r 5a is the X t a -element of the R pS R matrix Notice that !


One standard way is to perform parametric EM within an outer-loop structural search.

from the machine learning point of view, this paper provides an innovative application of Dynamic Bayesian Networks in modeling dynamic neuronal circuits.


The neuroscience community recognizes the value of such vocabularies and develops ontologies to cover the different aspects of the field such as protocols, paradigms, brain regions and cognitive processes.

indeed, in [5], the terms cannot be disambiguated from the studies.


We infer that the performance has almost saturated in this case.

hF-PIM combines the advantages of 3D and GAN based methods and frontalizes profile images via a novel texture warping procedure.


This attenuation of brain rhythms is C4 termed event-related desynchronization (ERD), see [13].

only the results of those datasets are displayed whose classification accuracy exceeds 70 % for at least one classifier.


An efficient algorithm to solve the traveling salesman and many similar problems has not yet been found and such problems remain reliably solvable only in principle [2].

statistical mechanics has inspired widely used methods for finding good approximate solutions in hard discrete optimization problems which defy efficient exact solutions [3,4,5,6].


The theorems show that only a subset of Ising models are equivalent to cascaded logistic models.

since the UBM relies on the base measure to provide smoothing over words, it is critical to properly regularize our estimate of ✓.


[10] argue that if X causes Y , then the factorization in the causal direction, i.e.

while causal inference is preferably performed on data coming from randomized control experiments, often this kind of data is not available due to a combination of ethical, technical and financial considerations.


Theorem 2 Let d i = |K(x i , w)|/ K(w, w) denote the perpendicular distance in the feature space from x i to the maximum margin hyperplane, and let d = min j d j = 1/ K(w, w) denote the one-sided margin of the classifier.

the multiplicative updates for computing the maximal margin hyperplane in hard margin SVMs are given by: where A ± are defined as in eq.


Most CRF models use a linear potential function to represent the relationship between input features and output.

to obtain good performance, we also linearly transform X into values in [0, 1] as suggested by Kim et al [24].


For each model, we first review the standard EM algorithm formulations, and discuss the extensions to the high dimensional setting.

we assume the model is under Gaussian design X ∼ N (0, I p ), W ∼ N (0, σ 2 ).


Let ψ θ (x) be a function on X and throughout the paper, we assume without loss of generality that the unnormalized model q θ (x) can be written as q θ (x) = exp(ψ θ (x)).

by setting ψ θ (x) as ψ θ (x) − log Z θ , the normalized model (1) can be written as (2  where ∑ x h is the summation with respect to the hidden variable x h . Let us assume that a dataset D = {x i } n i=1 generated by an underlying distribution p(x), is given and Z be a set of all patterns which appear in the dataset D. An empirical distribution p(x) associated with the dataset D is defined as where n x = ∑ n i=1 I(x i = x) is a number of pattern x appeared in the dataset D. Definition 1.


Overall, KLIEP(CV) is shown to be a useful method in importance estimation.

let us model the importance w(x) by the following linear model: where {α } b =1 are parameters to be learned from data samples and {ϕ (x)} b =1 are basis functions such that ϕ (x) ≥ 0 for all x ∈ D and for = 1, 2, . . . , b.


A split or merge move, denoted by Q, is first selected at random.

posterior MCMC inference in a DPMM could, in theory, alternate between the following samplers where ∝ ∼ samples from a distribution proportional to the right side, x {k} denotes the (possibly empty) set of data labeled k, and f • (•) denotes a particular form of the probability density function of •.


First of all, our algorithm generalizes easily to MAP inference in trees by using a similar structure but a different reduced cost expression that considers messages flowing in both directions across each edge (appendix A.1).

the U.S. Government is authorized to reproduce and distribute reprint for Governmental purposes notwithstanding any copyright annotation thereon


The ML model, like the Bayesian model, operates at the level of a single DSC neuron.

[9], the neuron's behavior is solely based on the a-priori probability of a target and the likelihood function for the different sensory inputs.


The notation (R x y) means that x and y are related by R. In miniKanren queries, data flow is not directionally biased: any input to a relation can be unknown.

a candidate is viable only if the entire conjunction can be satisfied.


For pairwise multi-label MRFs, we may create a weighted graph from the topology by assigning each node i a weight of log L i , and then compute the corresponding ν w (G).

in the numerator, ξ st − q s q t = Cov q (X s , X t ), increasing with W ij and equal to 0 at W ij = 0 (Weller and Jebara, 2013), and in the denominator, q s (1 − q s ) = Var q (X s ), hence the ratio is exactly what is called in finance the beta of X t with respect to X s . 5 Theorem 8 shows that for any j ∈ N (i) whose component is a tree, .


The choices of both λ and g can help control the cardinality of the support set S(z), thus influencing the sparsity of ρ(z).

this observation is also supported in our analysis of sparsity in outputs (see Fig.


In a POMDP, the goal is to find a sequence of actions to maximize the expected discounted reward, The states are not fully observable and the agent must rely on its observations to choose actions.

t is a transition function defined as T : S × S × A → [0, 1] which determines P (s|s , a), the probability of going from a state s to another state s after performing a particular action a. O is an observation function defined as O : Z × A × S → [0, 1], which determines P (z|a, s), the probability of observing z after performing an action a and ending in a particular state s. R is the reward function, defined as R : S × A → R, determining the reward received by performing an action in a particular state.


LSDR transforms D into M datasets, where M , and M K such that the multi-label classification problem can be tackled efficiently without significant loss of prediction performance.

pBR randomly selects M labels from the original label set during training and only learns those M binary classifiers for prediction.


For observations P Ω B : R n2×n3 → R m and P Ω C : R n3×n1 → R m represents the influence of X, Y, Z on the m observations.


Stepping beyond the TID-2008 database, and using the more stringent eigen-distortion test, yielded a very different outcome (Figs.

the most noticeable eigen-distortions from representations within VGG16 become more discriminable with depth, but so generally do the least-noticeable eigen-distortions.


This way, we empirically confirmed that the performance of the HOO algorithm is greatly impacted by the choice of this ρ parameter for the function we considered.

pOO does not require the knowledge of a (ν, ρ) verifying Assumption 1 and 4 yet we prove that it achieves a performance close 5 to the one obtained by HOO using the best parameters (ν , ρ ).


Although this quantity is defined between arbitrary probability distributions (and thus could be used with non-GP model spaces), we focus on the multivariate normal case.

our method does not depend on stationarity.


This is a main difference with previous tree structured algorithms or solvers.

the convergence rate of FISTA is O(1/k 2 ).


While the ✓ (c) j⌫ 0 is drawn as in (6), assigning ✓ ji } are executed as they would be in ( 4) and ( 5), without an MH step.

the combined Dirichlet process and dictionary learning (DP-DL) give similar results to the GMM with 2 principal components (PCs).


This work has spurred considerable interest and there have been several follow up papers [CC17,Das16,RP16].

there is much more to explore in this direction.


A pleasing property of this model is that computing the approximate gradients of the CD objective (Eq.

this is in contrast to directed topic models, where most of the existing inference algorithms are designed to be run in a batch mode.


Instead of computing the log-determinant directly, we choose to compute it in an alternative efficient way.

it tied with Fisher regarding overall measure, but had a slight win regarding pointwise measure.


The results suggest that BFGS approximation dramatically reduces the sample autocorrelation with a small increase of computational overhead on this dataset.

consider minimising the function f : R d → R, quasi-Newton methods search for the minimum of f (x) by generating a sequence of iterates where H k is an approximation to the inverse Hessian at x k , which is computed from the previous function values and gradients.


Prediction is usually estimated from a set of known responses of a given neuron to a set of stimuli (sounds).

we combine equivalence constraints gathered from pairs of cells which have similar responses, and train a single distance function for both cells.


Existing methods for interactive image retrieval have demonstrated the merit of integrating user feedback, improving retrieval results.

the empirical result is summarized in Figure 4, including relative attribute feedback using one, three and ten attribute phrases.


Although β2X2 is strongly associated with Z, it is not influential enough to be a proxy.

if a component is inside the red double cone, it exceeds the association threshold , where the angle θ is set such that = cos 2 θ.


the row, column and scale information in V i,r , U i,r and S i,r , respectively.

to this end, the Z i in equation ( 3) are replaced by their singular value decompositions The rank constraint can then be imposed by allowing only the first r diagonal elements of S i to be non-zero.


Throughout the paper we make minimal assumptions that consist of only a general set of axioms that hold for every probability distribution, which gives these algorithms universal applicability.

the proof of m-correctness of GS (m) is included in Appendix B.


Examples of kernels in this class include the k th -order Sobolev spaces for some fixed integer k ≥ 1 with Lebesgue measure on a bounded domain.

for LogitBoost, we sampled Y i according to Bern(p(x i )) where p(x) = exp(f * (x)) 1+exp(f * (x)) with the same f * .


In this paper, we analyze and generalize the above works and introduce the concepts of conditionally concave and probably conditionally concave energies E(X).

that is F are well-defined maps from graph G A with n vertices to G B with n 0 vertices.


Theorem 3.2 states that XOR_MMAP provides a constant-factor approximation to the Marginal MAP problem: Let us first understand the theorem in an intuitive way.

without losing generality, we assume w(a, x) is an indicator variable, which is 1 iff (a, x) satisfies constraints represented in Conjunctive Normal Form (CNF).


A major question is how restrictive is our independence assumption.

the expected gain of choosing an item is always non-negative and does not increase as the observations become more specific.


In this section we change the primitive that is being defined by the axioms from clustering functions to clustering-quality measures (CQM).

[3], modeling the requirement that clustering should be indifferent to the individual identity of clustered elements.


Since the restricted iteration for θ new is expensive, only a few cluster merges may be proposed at a time.

to generate the observations {y ∈ R N has observation times t = {t 1 , .


Under this policy, the probability of an action a in state s can be shown to be proportional to the exponential of the expected total reward after taking the action, denoted P (a|s) ∝ exp(Q r sa ), where Q r = r + γT V r . The value function V r is computed with a "soft" version of the familiar Bellman backup operator: V r s = log a exp Q r sa .

discrete features again discretize the continuous features, with distances discretized in the same way as in the objectworld.


More precisely, the theorem asserts that the determinant of the Hessian of the Bethe free energy function is the reciprocal of the zeta function up to a positive factor.

(See the supplementary material for further discussions.)


JMHL acknowledges support from the Rafael del Pino Foundation.

3(b)), finer-grained approximations were found to be advantageous if the datapoints from each mixture component are assigned to the same approximating factor.


w := P w has its components sorted by decreasing magnitude, | w| 1 ≥ .

we recover several well-known regularizers as particular cases, and reveal a connection between the hyperoctahedral group and the recently proposed sorted 1 -norm.


In the line-parallel processing scheme employed in [7], both row-parallel and column-parallel processing scan the target image several times and the entire filtering finishes in O (N+M) steps.

the hardware implementation of focalplane parallel processing is highly demanded.


One might ask if monotonic feature classification is equivalent to cotraining with the monotonic features serving as one view, and the other features forming the other.

in document classification, the name of the class is a natural MF-the more times it is repeated in a document, all other things being equal, the more likely it is that the document belongs to the class.


3g), we find that the reconstruction is overly blurry compared to the jigsaw, despite having a similar mean squared reconstruction error.


We experiment on the MNIST dataset and the YearPredictionMSD dataset in the UCI repository, where the training data is partitioned into 10 sub-groups randomly and evenly.

following Efron's intuition, full exponential families can be viewed as "straight lines" or "linear subspaces" in the space of distributions, while other distribution families correspond to "curved" sets of distributions, whose deviation from full exponential families can be measured by their statistical curvatures as defined by Efron (1975).


There exists a constant C such that if then applying Mitra's algorithm on D returns a partition { Ũ1 , .

the algorithm recovers the left clusters U i of G. Proof.


While the infrastructure is general, we apply it here to a sample of projects in Java.

in the literature [5], these more recent approaches have been found to produce better results than more traditional methods such as latent semantic analysis (LSA) [6].


We distinguish graph CNNs defined in the spectral [12,6] and spatial [8,9,13] domains.

this not only identifies the most relevant objects in the image associated to the question, but the most important interactions (e.g.


the best algorithm for the general bandit convex optimization problem guarantees a regret of e O(T 5/6 ), while the best known lower bound is ⌦(T 1/2 ).


The simplicity of the prior allows for efficient Gibbs style inference, and we provide an example model and demonstrate that it can achieve similar performance to that of the DDT.

this gives the posterior density for the location of the unobserved point: Z li,ri (x, π l ) Z li,ri,pi (x, π l ) p(π({l}, i, t)) where p(π({l}, i, t)) is as in (7).


(11b), we need to solve the following subproblem min Notice that X 0 is constraint on the eigenvalues of X.

the observation of similarity graphs often contain noise which sometimes mislead the learning algorithm, especially in unsupervised and semi-supervised learning.


Second, the state identity test requires solving the following problem over the function class G: The objective and the constraints are linear functionals of G, all empirical expectations involve polynomially many samples, and the number of constraints is |D h | which remains polynomial throughout the execution of the algorithm, as we will show in the sample complexity analysis.

if this optimistic policy πk is close to optimal, OLIVE returns it and terminates.


Use of such Kronecker product is quite common in tensor decompositions (see [19]).

the condition of number of clusters becomes more strict in such cases.


One way of doing so is computing time-varying tuning curves of neural populations in different regions to the individual components of the accumulators we propose in equations ( 11) and (15).

we start the inference machine at t of f c , using the following update when t of f c ≤ τ ≤ t on g : Then, once the target appears the update becomes: For samples after the context disappears, we introduce a simple decay mechanism wherein the probability with which the context sensor provides a sample from the true context decays exponentially.


For image interpolation, we only observe a fraction of the image pixels, sampled uniformly at random.

the proposed KBP construction has the significant computational advantages of only requiring kernels centered at the locations of the dictionary-dependent covariates {x * i }, while the model in [18] has a kernel for each of the image patches, and therefore it scales unfavorably for large images.


The phase of the components (L<I>(w) = -rr 12, by one convention) implies the predictive nature of the kernel: Xi(t) is being correlated with led (ie future) values of noise-filtered, significance-normalized, outputs.

they suggested, and showed in an example, that learning proceeds more proficiently if the output is filtered by an optimal noise-removal filter (in their case, a Wiener filter) before entering into the learning rule.


To do so, we evaluated our procedure on both synthetic and real-life data sets.

it forms clusters even in cases where the dependencies can be fully explained by a standard Bayesian network structure.


Here, we restrict ourselves to the first level of this reasoning hierarchy.

model predictions were generated using Eq.


Boosting algorithms are efficient procedures that can be used to convert a weak learning algorithm (one which outputs a weak hypothesis that performs only slightly better than random guessing for a binary classification task) into a strong learning algorithm (one which outputs a high-accuracy classifier).

if a branching program is constructed naively based on this approach, it is possible for the number of nodes to increase exponentially with the depth.


Principal Component Analysis is one of the most popular and successful forms of dimensionality reduction [10].

exponential family Principal Component Analysis [1] (E-PCA) varies from conventional PCA by adding a link function, in analogy to generalised linear models, and modifying the loss function appropriately.


Thus, it is not surprising that m is set to a very small value in the related methods-for example, m = 10 in (Weinberger et al., 2007) and m = 15 in .

in this paper, we investigate the possibility of further speedup by studying a class of convex quadratic semidefinite programs (QSDPs).


In general, even writing down S • φ(A) would take a prohibitive d q amount of time.

the hash functions in TEN-SORSKETCH are only 3-wise independent.


Since, N ≥ n Λ = Λ/λ (M ) , any multi-fidelity strategy which plays a suboptimal arm a polynomial number of times at any fidelity after n time steps, will have worse regret than MF-UCB (and UCB).

our work in this paper builds on UCB ideas, but the multi-fidelity framework poses significantly new algorithmic and theoretical challenges.


In certain cases, parity fairness may well be the eventual goal [3] and the more desirable notion.

(4) One can also rewrite the above condition for group-conditional classifiers, i.e., ✓ = {✓ z } z2Z and ✓ 0 = {✓ 0 z } z2Z , as follows: (5) Note that, given any classifier ✓ 0 ensuring impact parity, it is easy to show that there will always exist a preferred impact classifier ✓ with equal or higher utility.


Once the dereverberation operator is calculated from the periodic parts of speech signals for almost all the frequency ranges, it can dereverberate both the periodic and non-periodic parts of the signals because the inverse transfer function is independent of the source signal characteristics.

more accurate F 0 can be obtained in step 2 than in step 1.


ÔÖ ÓÖ is the width of each Gaussian which is set to 0.5 cm.

feedback midway through the movement was always blurred (spheres distributed as a two dimensional Gaussian with Ñ) and feedback at the end of the movement was provided on every trial.


In the proposed model, computations do not rely on the shape of PSPs, which alleviates the restriction imposed by the length of their rising segment.

this means that spike times can encode only positive values.


Next, the central server chooses a step size α t , which can be chosen as constant, decaying, or through exact line search 1 by having the workers compute Xd t that is needed to compute the step size.

we again assume the central server only hears from the fastest k nodes, denoted by where where X D = [S i X] i∈Dt , and 0 < ν < 1 is a back-off factor of choice.


Using the Bayesian regularization procedure, the resulting estimate for α M L correctly models the direct path time delay as well as the secondary echo.

the mean-field parameters µ are optimally obtained by minimizing the KL-divergence: This integral can easily be computed in terms of the parameters µ and yields the minimization: where bI = (Aα M L + b) I , Â = A II + diag(A II ).


In recent years, significant effort has gone into developing trainable image representations for finding correspondences between images under strong appearance changes caused by viewpoint or illumination variations [3,4,10,13,17,37,38,44,45].

we evaluate two variants of the approach.


It is known from [12] that Reg(T ) has a lower bound of ⌦( , where KL(P, Q) denotes the Kullback-Leibler (KL)-divergence between distributions P and Q, even when a single controller is pulling arms for all time.

next, we discuss how to bound its compensation.


For the network outputs, the Softmax function is used to generate the network outputs.

in this way, the intragroup sparsity structure avoid the poor data locality issue associated with typical sparse neural networks.


The conditional expectation of u given z is interesting because it has a sigmoidal-like saturating and monotone non-linearity: .

until recently it was not clear how to train such deep networks, since gradient-based optimization starting from random initialization appears to often get stuck in poor solutions.


The random projections method achieves low A-distance but high Huber loss, and the classifier which uses this representation achieves error rates much lower than the a classifier which uses the identity representation.

this also seems to be difficult to separate.


Consider online convex optimization on a sequence of loss functions f 1 , .

this calls for the development of an algorithm that is not based on a reduction to the Follow-The-Leader algorithm, as discussed after Lemma 4.1.


For further details and extensions, see [15].

in order to use harmonic information, we need to estimate potentially several pitches.


Knowledge distillation is introduced to facilitate training a smaller network by transferring knowledge from another high-capacity model, so that the smaller one obtains better performance than that trained by using labels only [10].


The inference networks express the mean and variance of the variational distribution as a function of the data point.

we split the data set into equally sized training, validation, and test sets.


Using our analysis, we may also obtain sparse approximation bounds for these different loss functions.

our problem in its most general form can thus be described as to find a vector ¤ ¡ ¡ © in the convex hull of ¤ ¡ ¦ ¨¡ © to minimize a functional ( of ¤ that measures the quality of ¤ .


For example, the children f 1: ∅ of the root node (assuming that none of them is a leaf) follow the distribution This implies that f 1: ∅ can be represented as a product of two independent random variables Dir n 1 /p ∅ , ..., n ∅ /p ∅ following a Dirichlet distribution (see Additional Material).

it is usually removed and modelled separately.


The minimax DDP coped with larger disturbances than the standard DDP and the hand-tuned PD servo controller.

the function H() in equation ( 21) includes the mapping (velocity change) caused by ground contact.


Despite the high non-convexity of DNNs, we can apply ACS to find a local minimum.

too large of a q hampers the classification accuracy, and thus a larger q is not always preferred.


. . , X N } where each X i ∈ {0, 1} are independent causes of a reward variable Y ∈ {0, 1}, as shown in Figure 1a.

if all the variables are observable, any causal distribution P {X 1 ...X N |do(X i = j)} can be expressed in terms of observational distributions via the truncated factorization formula (Pearl, 2000).


Although the superlinear 2GD algorithm improves the logarithmic term, all four algorithms are dominated by the polynomial term in (1/ε).

considerable refinements of this framework can be expected.


We finally analyze AFW-2 on general polytopes with line search.

although solving RC-Hull requires the knowledge of K (which is unknown a priori if we are only given C), in practice, it is equally justified to tune the value of K via model selection tools in the first place, which is approximately tuning the number of support vectors.


We note that our method is related to KPCA, where data is projected onto the space spanned by the top few eigenvectors of the kernel matrix and classification or regression task can be performed in that projected space.

when T 1 (x) and T 2 (x) are small enough then φ L,1 0 and φ L,2 0 are eigenfunctions of L p K with corresponding eigenvalues π 1 λ 1 0 and π 2 λ 2 0 respectively.


We learned the object structure for each category over a 15-image subset of our data for training purposes.

the images we selected for our data set have the furniture object prominently in the foreground.


centered random variables with variance σ 2 and kurtosis κ.


On the memory problem, having norm-preserving state transition matrices is critical for stable learning, while on the adding problem, having gates is important.

gating, as used in gated recurrent units (GRUs) [4] and long short-term memory (LSTM) networks [12], has become common-place in recurrent architectures.


By better preserving the Hamiltonian, reflective Hamiltonian Monte Carlo (RHMC) accepts more moves and thus has a higher effective sample size, leading to much more efficient probabilistic inference.

for non-quadratic U , the Hamiltonian dynamics rarely have a closed-form solution, and one must resort to numerical integration, the most successful method for which is known as the leapfrog dynamics.


Concretely, the network outputs a heatmap of per-pixel detection scores and a set of per-pixel embeddings.

we propose associative embedding, a novel method to express output for joint detection and grouping.


repulsive property of matching behavior, let us substitute the condition of the matching law, ⟨r|A⟩ = ⟨r|B⟩ = ⟨r⟩ into Equations 11, for the no normalization condition.

if we can describe the evolution of these order parameters, we can completely describe how the behavior of the model changes as a consequence of learning.


We consider learning of linear classification and regression models, in the setting where the training data is decentralized over many user devices, and the learning algorithm must run ondevice, on an arbitrary communication network, without a central coordinator.

decentralized learning aims at learning this same global machine learning model, without any central server.


It seems that it improves the accuracy when it is used with a small number of prototypes.

it cycles through the training data S and on each iteration modifies the set of prototypes in accordance to one instance (x t , y t ).


The parameters of ADM and LADM are the same as those in [12] and [20], respectively.

by linearizing the quadratic term in (4) at x k and adding a proximal term, we have the following approximation: (8) where A * is the adjoint of A and η A > 0 is a parameter whose proper value will be analyzed later.


The optimization here is mainly designed to take new concepts involved in collaborative learning into account, including a group of classifiers, and ILR sharing.

for the hierarchical sharing, the two split points are located after the first and second blocks, respectively.


We update the prior for each word as the product of these votes with the previous probability.


If a single stimulus can possibly elicit millions of different responses on a neural layer, how can this plethora of data be effectively decoded by downstream networks?

in order to test the hypothesis of a purely feed-forward information transfer at the CN level, no collateral projections between CN neurons are considered in the current version of the model.


We have shown that under standard assumptions, normalized spectral clustering always converges to a limit partition of the whole data space which depends only on the probability distribution P and the similarity function s. For unnormalized spectral clustering, this can only be guaranteed under the strong additional assumption that the first eigenvalues of the Laplacian do not fall inside the range of the degree function.

step 1: Construction of the operators U n on C(X ).


For any h and η, the expected number of near-optimal points is bounded as This lemma answers a question raised by Munos (2011): What is the near-optimality dimension of the Brownian motion?

for any interval I, We now define and First, for any a < b, the law of the maximum of a Brownian bridge gives us  Combining it with the definition of A h,k and the first inequality of the proof we get .


For example, if the columns of V represent word count vectors for a collection of documents, V f n would be the count of the f th word of the vocabulary in the n th document in the collection.

it is easy to show (as demonstrated in the supplementary material) that the maximum likelihood estimator for P (f |z) and P n (z) attempts to minimize the Kullback-Leibler (KL) distance between the normalized data distribution V n and P n (f ), weighted by the total count in V n . the model of Equation ( 1) actually represents the decomposition V ≈ WGD = WH (4) where D is an N × N diagonal matrix, whose n th diagonal element is the total number of counts in V n and H = GD.


JADE, FastICA-tanh, and 1FICA each have a bias in the presence of additive Gaussian noise which keeps them from being SINR-optimal even when given many samples.


g is a good approximation of f 2 B with reasonably large n. Formally, this is stated in the following theorem.


Finally, just as we have successfully merged HL(λ) with Sarsa(λ) and Watkins' Q(λ), we would also like to see if the same can be done with Peng's Q(λ) [3], and perhaps other reinforcement learning algorithms.

it would also be good to generalise the result to episodic tasks.


Thus there is a worsening comparing to the i.i.d.

this could be, e.g., classification tasks of increasing difficulty.


The KECO procedure, described in Algorithm 2 , reduces the computational burden by computing the p-truncated SVD decomposition of the input matrix M via its kernel matrix (lines 3-4) if the number of rows of M is no larger than the number of columns, otherwise the covariance matrix is used (lines 6-8).

for large data matrices exact SVD decomposition cannot be achieved, so we proposed a computationally efficient procedure to get an approximation that turned to be effective for our goals.


Compared to soft-attention approaches, we loose the ability to naively backprop through read-operations and we have to use approximations like VIMCO.

we use 2 layered enand decoders with 256 and 128 hidden units with ReLU nonlinearities and a 32 dimensional Gaussian latent variable z.


pose information for images of people) one alternative is to define neighbourhoods based on the distance in the real-valued label space and proceed as usual.

at the core of our method is a learned parametric mapping from high-dimensional space to a low-dimensional space in which distance is efficiently computed.


DMD has recently attracted considerable attention in physics such as fluid mechanics [2,10,21,25,27] and in engineering fields [4,6,32].

this is certainly not applicable to all systems (in particular, beyond the region of validity for local linearization).


Continuous Bayes-Adaptive (PO)MDPs have been considered using an online Monte-Carlo algorithm [4]; however this tree-based planning algorithm expands nodes uniformly, and does not admit generalization between beliefs.

the height map is a draw from a Gaussian process (GP), f ∼ GP (0, K), using a multi-scale squared exponential kernel for the covariance matrix and zero mean.


While the resulting outputs fare better, the target shape is still obscured (Unguided (Equal Time)).

a partial mean field approximation [23]).


Building on this observation, a much stronger assertion can be proven for every pair of points in the input space simultaneously: Claim 1 (Uniform convergence of Fourier features).

if we number the bins of the grid so that a point x falls in bin x = x−u δ and y falls in bin ŷ = y−u δ , then Pr u [x = ŷ|δ] = k hat (x, y; δ).


pairwise data may violate the triangular inequality.


Therefore, we expected the improvement from learning the tree to be marginal.

for example, the superclass fish contains aquarium fish, flatfish, ray, shark and trout; and superclass flowers contains orchids, poppies, roses, sunflowers and tulips.


Wouter Koolen acknowledges support from the Netherlands Organization for Scientific Research (NWO) under Veni grant 639.021.439.

the sample complexity analysis is much more intricate, hence we stick to the above Hoeffding-based confidence intervals for the next section.


Now we make explicit the possibility of the submodels sharing features, which give us more structure for deriving approximations.

the product EM algorithm is summarized below: The product M-step is tractable provided that the M-step for each submodel is tractable, which is generally the case.


We can thus simplify the objective function: We thus have So we must find a polynomial which takes small values in the interval [0, σ].

this problem can be solved exactly using a semi-definite solver because it can be reduced to a SDP program (see Appendix A.4 for the details of the reduction).


The second ablation experiment tests the necessity of mental updates, without which the model would only attend to the past time steps without passing gradients through them to preceding time steps.

for the copy task, the network is given a sequence of T + 20 inputs consisting of: a) 10 (randomly generated) digits (digits 1 to 8) followed by; b) T blank inputs followed by; c) a special end-ofsequence character followed by; d) 10 additional blank inputs.


In the general case, the effectiveness of a particular intervention in a trial participant depends on the inherent effects of the intervention, as well as the participant's expectations (conscious or not).

put differently, it is always possible that a particular variable which can reveal the nature of the treatment to a trial participant is not identified by the trial designers and thus that no blinding with respect to it is attempted or achieved.


Therefore, we ran independent experiments with varying horizons and recorded the accumulated regret: the markers on the curves corresponding to these algorithms represent these numbers.

furthermore, the denominator of this result has much better dependence on the "gaps" arising from the dueling bandit problem than most existing results (cf.


We start with four predetermined queries to "seed" the parameter space, and after that use the learned model to select gallery images.


Writing the update with these terms gives: where we have combined the terms J( w), b( w) and v into a single random variable ξ( w).

to study this property, we investigate a cost function with a significant degree of anisotropy.


. . , x n } is an ε-additive perturbation of X if for all i, x i − x i ≤ εD.

6 if the n points were drawn from a mixture of spherical Gaussians in high dimensions (with d k), then the margin condition required for [15,6] is weaker.


An iteration of SMD -comprising ( 5), (2), and ( 7)thus requires less than 3 times the floating-point operations of simple gradient ascent.

in practice policy gradient methods have shown slow convergence [2], not least due to the stochastic nature of the gradients being estimated.


The "true value" was estimated using AIS with 10 000 intermediate distributions and 5 000 importance samples.

in many common PGMs an intuitive ordering can be deduced from the structure of the model, see Section 5.


We aim to find the posterior P (W|D N ) in an online setting, where samples arrive sequentially.

given a supervised classification task with labeled training data and a prior over the weights, this deterministic online algorithm can be used to train deterministic MNNs (Eq.


We calculate predictive probability by first setting aside held-out testing documents C (test) from the full corpus and then further setting aside a subset of held-out testing words W d,test in each testing document d. The remaining (training) documents C (train) are used to estimate the global parameter posterior q(β), and the remaining (training) words W d,train within the dth testing document are used to estimate the document-specific parameter posterior q(θ d ).

indeed, Bayes theorem yields we can calculate the individual minibatch posteriors p(Θ | C b ), perhaps in parallel, and then combine them to find the full posterior p(Θ | C 1 , .


The immediate reward model is naturally constructed for these problems, as the reward comes from the starting article based on its features, so it is not dependent on the action taken (and thus not the option).

learning an LOEM model is faster than learning a UOM for a single fixed reward function, but the UOM can produce an accurate option return quickly for each new reward function.


In Figure 4 we visualize attention in the model (suggesting that image label supervision can successfully train a visual attention mechanism to localize new objects).

since image labels and object classes can be interpreted as partial captions, we formulate this problem as learning from partiallyspecified sequence data.


if |Q V | < |S|, then how would we know when to stop?


These architectures together with recent large databases (e.g., ImageNet [3]) have obtained astonishing performance on object classification tasks [12,5,20].

with this database and a standard CNN architecture, we establish new baselines of accuracies on various scene datasets (Scene15 [17,13], MIT Indoor67 [19], SUN database [24], and SUN Attribute Database [18]), significantly outperforming the results obtained by the deep features from the same network architecture trained with ImageNet 1 .


Our experiments were conducted on heads-up no-limit Texas hold'em, as well as two smaller-scale poker games we call No-Limit Flop Hold'em (NLFH) and No-Limit Turn Hold'em (NLTH).

if P 1 instead chooses Play, then P 2 may guess how the coin landed.


Here we briefly cover previous work on regression and eigenvector computation (Section 1.4.1), sparse finite sum optimization (Section 1.4.2), and matrix entrywise sparsification (Section 1.4.3).

ultimately, we hope this paper provides useful tools for even faster algorithms for solving large scale learning problems.


When the spike input is on (0 < t < t pw ), the dynamics of the circuit for a step input is governed by Equation ( 7) can be changed into a linear ordinary differential equation for i syn (t): In terms of the general solution expressed in (3), we have When the spike input is off (t > t pw ) and we neglect the leakage current from M 2 , then i syn (t) will exponentially decay with the same time constant defined by (11).

in the following sections, we describe the kinetic model of synaptic conductance, describe the circuit implementation and function, provide a theoretical analysis and finally compare our theory against testing results.


The best classifier is selected by empirical risk minimization.

a faster convergence can be obtained however using the more precise bound of Theorem 8 at the expense of readability.


The original corpus is somewhat inconsistent in that not all paths end in a leaf, but rather end in some inner vertex.

employing the domination loss yields significantly better results than using the disagreement loss which has been the commonly used decomposition method in categorization problems [7,10,6,4].


An important open question is to understand the effect of having additional budget to choose multiple coordinates at each time t. The challenge lies in designing appropriate algorithms to invest this budget to update the coordinate selection strategy such that B_max_r performance becomes even closer to max_r.

[6], and p t i = G i (x t )/G(x t ) [15,14], have also been considered.


analyzing the structure of these losses is one of the main goals of this paper.


Though it is difficult to bound p aprirori, we can check after the solution that our chosen value was sufficient for the global solution, and we have found that very low values (p = 1 or p = 2) were sufficient in our experiments.

there has been a great deal of work on developing O(k) algorithms that are guaranteed to converge to the LSTD fixed point even in the case of off-policy sampling [16,15].


Several lines of work have focused on consistent estimators for such structurally constrained high-dimensional GLMs.

sampled from a zero-mean distribution with covariance matrix ⌃ such that for any v 2 R p , the variable hv, X i i is sub-Gaussian with parameter at most  u kvk 2 for every row of X, X i .


In the next section, we formalize this notion by defining the manifold description of data as a doublet (the shape of the manifold and the projection map).

presumably, the manifold M has a well defined intrinsic dimensionality d. If we imagine a little ball of radius r centered at some point on the manifold of intrinsic dimensionality d, and then we begin to grow the ball, the number of points on the manifold that fall inside will scale as r d . this will not be necessarily true for the original data set, since it is more spread out and resembles locally the whole embedding space R D . The Grassberger-Procaccia algorithm [12] captures this intuition by calculating the correlation dimension.


We develop a general variational inference algorithm for fast approximate posterior inference.

mixed membership does not absorb noise in this example, rather it accommodates variability in the friendship relation that is instrumental in producing better predictions.


Whenever one wishes to compute the difference between the leading eigenvector of any matrix and that of its noisy version, one can obtain ( 6), ( 8) and ( 9).

via a voting method like Borda count [11,3]).


A gamma process is a completely random measure over X with gamma marginals.

for notational simplicity we assume that all the partial rankings are length m. Suppose we have M choice items, with item k ∈ [M ] having a positive desirability parameter w k . A partial ranking ρ = (ρ 1 , .


By substituting this equality into the equation for computing η k in Algorithm 2, we have Without taking the absolute value, the denominator of ( 12) is ĝ k ĝk−1 / ĝk 2 2 − 1, which is usually negative in stochastic settings.

we apply SVRG-BB and SGD-BB to solve two standard testing problems in machine learning: logistic regression with 2 -norm regularization (LR), and the squared hinge loss SVM with 2 -norm regularization (SVM): (SVM ) min x where a i ∈ R d and b i ∈ {±1} are the feature vector and class label of the i-th sample, respectively, and λ > 0 is a weighting parameter.


This generalization improvement seems not to depend much on how much of the first network we keep to initialize the second network: keeping anywhere from one to seven layers produces improved performance, with slightly better performance as we keep more layers.

we also document that the transferability of features decreases as the distance between the base task and target task increases, but that transferring features even from distant tasks can be better than using random features.


. . , X n ∈ R p and a column y ∈ R n . We will assume that each X i 1 ≤ 1 and |y i | ≤ 1.

before we formally introduce the covariance perturbation algorithm due to [19], observe that the optimal solution θ * can be computed as θ * only depends on the private data through X y and X X.


A parameter of paramount importance to linear classification is the margin, defined as follows Definition 1.

in practical applications the margin is usually a constant independent of the problem dimensions; a justification is given next.


Our simulations and behavioral results begin to clarify the connection between theoretical analyses of language learnability and human behavior.

linguistic exceptions, such as the restrictions on verb alternations mentioned above, are cited as being impossible to learn empirically.


The histograms clearly show that the model on the left failed to generate all classes (loss in recall), while the model on the right is producing a more balanced distribution over all classes (high recall).

fID has been shown to be robust to image corruption, it correlates well with the visual fidelity of the samples, and it can be computed on unlabeled data.


We use Σ CL = CL( Σ) and E CL = CL E ( Σ) to denote respectively the covariance matrix and the set of edges learned using the Chow-Liu algorithm where the samples have empirical covariance matrix Σ.

using Algorithm 3, the objective function of (3) decreases with the number of iterations, i.e., D KL (N (0, ΣT )||N (0, Σ )) ≤ N (0, ΣT )||N (0, Σ T )).


For example, a USENET news posting includes both a subject region and a message body region.

6 standard uniform convergence results do not apply to our problem, because the "features" b i given to the discriminative logistic regression component also depend on the training set.


In the subsequent sections, we present a model of the ventral stream that is consistent with a large body of experimental results 1 and additionally predicts the existence of discrete face-selective patches organized in this manner.

within the class of faces, knowledge of the image transformation evoked by 3D rotation can be reliably transferred from previously viewed faces to help identify a novel face at a new viewpoint.


The constraints are the maximal number of available training example and the maximal computation time.

the accuracy ρ involves the empirical quantity E n ( fn ) − E n (f n ), whereas the optimization error E opt involves its expected counterpart E( fn ) − E(f n ).


We solve this problem using MAP inference via EM with a mean-field variational approximation q(x) to the posterior p(x|y, B) [13], where q(x) The E-step, after observing that for binary x, /q 0 ), q 0 = k/M , the vector c = diag(B T B), and C = B T B − diag(c), i.e.

we first propose its computational function as recovery of high-dimensional sparse olfactory signals from a small number of measurements.


Random search is a natural baseline to compare optimisation methods.

x i ∈ X , y i = f (x i ) + i ∈ R, and i ∼ N (0, η 2 ), the posterior process f |D n is also a GP with mean µ n and covariance and K ∈ R n×n with K i,j = κ(x i , x j ).


All models share a common w. We make a few additional assumptions.

firstly, initialize w with a wide Gaussian profile, then estimate e KA e K H from element-wise division of C mele by f W . Secondly, use SVD to decompose e KA e K H into an orthogonal base set e K and a positive diagonal matrix A, where e K and A contain information about k i 's and ↵'s respectively, hypothesizing that k's are orthogonal to each other and ↵'s are all positive (Assumptions 3 and 5).


Furthermore, in complex modeling tasks, obtaining the large amount of labeled data necessary for training can be impractical.

the (sML+Boost) method performs better than sML but does not perform as well as when feature selection and parameter estimation is done within a unified framework as in sVEB.


The activity of these sub-sets were imagined to be "imaged" in two separate "imaging" sessions (see Section 2.2).

a naive approach would not be able to estimate noise correlations between non-simultaneously observed pairs.


We should stress in particular that whenever we say that the set of OGDA-stable fixed points is a super-set of the GDA-stable fixed points, we will be somewhat abusing notation, since the fixed points of OGDA lie in R 2n+2m while the fixed points of GDA lie in R n+m .

let (x * , y * ) be a local min-max critical point of f and matrix H (see equations ( 5)) computed at (x * , y * ) has all its eigenvalues with real part nonzero (i.e., Assumption 1.8).


Using the auxiliary graph described above, and updating on shortest augmenting paths, one can generalize several maximum flow algorithms to a level-1 algorithm of DSFM.

the oracles are evaluated via the Fujishige-Wolfe minimum norm point algorithm [11,31] for level-0.


We do not observe A(M ) directly; rather, we estimate each entry (A(M )) i by preparing many copies of the state M , measuring the Pauli observable S i on each copy, and averaging the results.

we get where C 4 is some universal constant.


If the true label is Y = 0, then the attempted labeling is much more likely to fail, but because of noise, could succeed.

for a two-component mixture sample, M , and a sample from one of the components, C, it only requires an algorithm to estimate the maximum proportion of C in M . For this purpose, we use the AlphaMax algorithm (Jain et al., 2016), briefly summarized in the Appendix.


NBP [2] solves inference problems on non-Gaussian graphical models by propagating the results of local sampling computations.

sampling is the primary computational burden for both NBP and PoE.


We show the solution attained by minimizing the maximum information (eq.

we constrain each region in the cover (Q ∈ C) to carry at most γ units of information.


Bottou and Bousquet [BB07] show that if is a bound on the sub-optimality of w on S i , then the total error is bounded by H(n i ) + .

finally, we will bound the expected sub-optimality of STRSAGA over its effective sample set T i in Lemma 3.


. . , C m are already generated clusters.

we use the smoothed estimation π ∝ (1 + n is the total number of times that term t happened in the collection H, and V t=1 π t should be normalized to 1.


In the ( + 1)th iteration of CCCP, we need to solve the following problem The Lagrangian is given by where ≥ 0 and ≥ 0.

in the th step, we assume that the first − 1 columns of W have been obtained and we find the th column according to problem (4).


The symmetric matrix A = [A ij ] describing the graph is the edge probability matrix.

the C 0 is always stable in the PFM framework.


Indeed, this curious property appears anytime the variables take the form Y = BG, for any fixed scalar random variable B and Gaussian vector G. It follows that the predictive mean estimates for (10) employing sub-Gaussian priors are identical to the estimates under a Gaussian hypothesis.

our discussion of the stable process regression problem has principally been confined to an exposition of the basic theoretical issues and principles involved, rather than to algorithmic procedures.


By comparing it to a logistic regression, we measure the marginal benefit of the SVA policy to approximately 1 percentage point gain in accuracy.

we obtain new state of the art results on the Penn Treebank and the WikiText-2 word-modeling tasks, using ~20-30% fewer parameters and converging in less than half as many iterations.


Since φ, ψ, and λ have been marginalized out, the only latent variables we have to update are m and z.

we empirically found that the model shrinkage of the EPM does not typically work appropriately and leads to an overfitted solution.


The computational complexity of our algorithm grows as a low order polynomial in the ambient dimension d of the input, but exponentially in its rank r. Despite the unfavorable dependence on the rank, it is unlikely that a substantial improvement can be achieved in general [21].

. . , v d , corresponding to the d variables, i.e., the d rows of X.


The idea is simple: instead of choosing a (potentially different) expert at each stage of the game, the number of stages an expert is followed, each time it is selected, increases gradually.

(b) When lim sup i→∞ M e (i) < V , there is a phase I such that for all i ≥ I, M e (i) < M Ē (i), so that expert e is played only on exploration phases, and a large deviations argument establishes that (3) holds.


Such an edge is not discriminative and its influence should be decreased.

when the noise is small enough, the optimal matching is the desired permutation p * = {11 ′ , 22 ′ , 33 ′ }, with an initial score of 8 for σ = 0.


In theory, this worst-case quantizer is completely insensitive to variations in sampling density, since the optimal error e * ∞ (k|µ) is the same for all µ with the same support.

this can have serious implications in practice, as it may result in lowdimensional representations that lose essential features of the data.


On the other hand, from the computational point of view, our procedure is quite comparable with the direct stochastic gradient descent.

at each iteration i, a new data point (X i , Y i ) is observed and there are two updates: one is the value ζ i as the result of the stochastic gradient descent in the dual space, the other is the update of the parameter θ i which is the "mirror image" of ζ i .


Thus, we need to start the path at λ = Ω * (X y), corresponding to the empty solution 0, and then decrease λ.

for the sequence µ i , we use a decreasing sequence converging to ten times the machine precision.


(2016) and  discuss the topic in detail.

observe that Pr (j * > j) ≤ Pr The proof is based on the following lemma: Lemma 4.3.


DAG models can be used to encode causal relations in terms of a directed acyclic graph (DAG) G, where each node is associated to a random variable and the arrows represent their causal influences on one another.

at each step we only need to update this list locally; so the computational complexity of the algorithm is not drastically impacted by this procedure.


It does not show that the addition of an adversary can increase the sample complexity and whether this is possible remains an open question.

if H achieves k classification patterns on y, then F achieves k error patterns on (y, c) for any choice of c. σ(H, i) = σ (F, i).


MiME explicitly captures the hierarchy between Dx codes and treatment codes depicted in Figure 1.

implementation and training configurations are described in Appendix C. We also performed sequential disease prediction (SDP) (predicting all diagnoses of the next visit at every timestep) where MiME demonstrated superior performance over all baseline models.


The proposed approach could be easily extended to other problems such as density estimation or classification.

when humans address a new learning problem, they often use knowledge acquired while learning different but related tasks in the past.


. . , r D ] to denote the reward function.


A tensor is a higher order generalization of a vector (first order tensor) and a matrix (second order tensor).

in many practical applications such as face recognition and image/video denoising, a portion of the observation tensor Y might be contaminated by gross error due to illumination, occlusion or pepper/salt noise.


It does so by computing messages in a message-passing algorithm using Monte Carlo sampling, freeing us from having to implement hand-crafted message update operators.

in addition to the difficulty of computing messages for the multidimensional yield factor, inference in the model is challenging as it includes multiple Gaussian processes, separate t opt and y max variables for each location, many copies of the yield factor, and its graph is loopy.


Instead of assuming that p(x) has a simple, parametric form, we will use a more modest assumption, that p(x) has a product form.

3) by examining the clusterings suggested by the full data and a small subsample.


The connection between whitening and LDA is well known [15].

this is a powerful result we will exploit further.


We assume that each component of y i,j is a scalar measurement of a given biomarker and belongs to a geodesically complete one-dimensional manifold (M, g).

mathematically, this writes η wi (γ • ψ i , s) = η wi (γ, ψ i (s)).


Assume we are given a dataset of n observations a = [a 1 , .

in fact, except for very specific cases, it is impossible to balance these measures of fairness [3,10,20].


We have already introduced the Lagrangian (9) for the Gaussian MRF.

lBP often fails to converge for networks with tight loops [1] such as the 3×3 lattice of Figure 1(a).


To address such a problem, a popular approach is to assume the covariance matrix of the tensor normal distribution is separable in the sense that it is the Kronecker product of small covariance matrices, each of which corresponds to one way of the tensor.

we define kAk 1,off := P i6 =j |A i,j | as its off-diagonal `1 norm and |||A||| 1 := max i P j |A i,j | as the maximum absolute row sum.


In this section, we extend this definition of sleeping regret to sleeping transductive regret, that is the difference between the learner's cumulative expected loss and the cumulative expected loss of any transduction of the learner's actions among a family of finite-state transducers, where the weights of the transductions are normalized over the set of awake experts.

this is because the true losses assigned to each column of the stochastic matrix are the same, and the rescaling based on the distribution p t is uniform over each row.


VQ type algorithms can also be more computationally efficient since they require the calculation of distances, or distortion, between the data and the centroid models only, not between every pair of data points.

when varying the temperature T = /3-1, the information bottleneck algorithms explore the structure of the data in various resolutions.


For any y j consistent with y, we have θ p (x, y j ) ≥ θ p (x, y).

in total we test on 901 individual frames.


Finite PM games restrict both the learner's and adversary's action spaces to be finite, with a very general feedback model.

the learner might not get to know either θ(t) (as in a full information game) or r(x(t), θ(t)) (as in a bandit game).


Since:F:::; Ltlnp(y(t)), this procedure maximizes a lower bound on the log-probability of the data.

the noise model can be learned from the test utterance and then used to de noise the test utterance.


Large corpora of speech data available in recent years allow experimentation with long term statistics of phone patterns, word patterns, etc.

for this paper, we concentrate on the use of phone sequences [6].


Another thorny issue in applying standard MAB frameworks in practice is the assumption on a constant set of arms that are available indefinitely.

let q = |M ue,t | be the size of under-explored arms.


It follows from Lemma 3 and Lemma 1 that, if u i = 0, then x * i = 0.

for example, with the grouping by pathways, FoGLasso is about 25 and 70 times faster than SLasso for 1000 and 2000 genes, respectively; and 3) the efficiency on edges is inferior to that on pathways, due to the larger number of overlapping groups.


The second component is a deep Convolutional Neural Network (CNN) that generates the representation of an image.

in this paper, we use the GoogleNet [36].


Substituting yields Note that 1) ρ is the empirical distribution over the observations, and so converges almost surely (a.s.) to the true generating distribution, and 2) the convergence properties of P n are determined by the quantity between the square brackets in (2).

the results of a   This paper has introduced the problem of dynamic coherence and analyzed it when the dynamics are induced by Bayes' rule.


where W is the adjacency matrix, finding the minimum bisection of G is equivalent to finding a partition of G that minimizes the SRcut cost function with weights β = e and the regularization parameter α > d * where Proof: Without loss of generality, we assume that N is even (if not, we can always add an isolated vertex).

the corresponding SRcut value is then computed.


The ith input sample is given as x i = (s i , t i , w i ), which is a combination of task index (s i , t i ) and input feature w i .

first, we assume that the distribution P (X) of the input feature x ∈ X is a product measure of P k (X) on each X k . P X (dX This is typically assumed in the analysis of linear tensor estimation methods [13,6,3,21,1,36,27,37].


In the era of big data, searching for the desired information has become an important topic in such a vast ocean of data.

dCC which is used to solve the discrete optimization by DSDH, can only be applied to the standard binary quadratic program (BQP) problem with limited applications, while HashNet is still distracted by quantization error as β cannot increase infinitely.


As discussed in [15], ACCPM has an overall complexity is O(n 4 log(1/ε) 2 ) for finding an ε-optimal solution.

the convergence of this optimal method was shown in [18]: where α * is one of the optimal solutions.


this algorithm has high computational complexity and memory requirements and so cannot be used for solving large scale problems.


Normally this would be an easy bug to find, because one wouldn't have to look very far beyond the crashing point at the top of the stack.

for further code optimization, we analyze each contiguous acyclic code region (loops-and recursion-free) at compile time and count the maximum number of assertions on any path through that region.


[20] established a 1/n rate in low-noise conditions, i.e., when the expected loss of the best hypothesis is of order 1/n.

this establishes the lower bound 0 ≤ h(x 1 ) − h(x 2 ).


When all blocks have size one, or equivalently when all kernel matrices have rank one, then the path is provably linear in 1/λ between each kink [4] and is thus easy to follow.

the path is obtained by using numerical continuation techniques, and involves a running time complexity that is a constant times the complexity of solving the problem for one value of the regularization parameter.


We labelled a subset of 100 out of the total of 698 data-points with the three mentioned degrees of freedom in the following way: After standardizing the pose and lighting parameters so that they were centered and had unit variance, we constructed three corresponding similarity matrices (P Pose1 , P Pose2 , P Lighting ) for a randomly chosen subset of 100 points using Eq.

both these difficulties can be alleviated by allowing the user to provide more information than just the raw data points or a single set of pairwise similarities between data points.


The first is that F is independent of θ conditionally on ( Qm t , x t , a t ) (by assumption).

it ensures the three following properties that are very natural when thinking about safe interruptibility: • Interruptions do not prevent exploration.


Further, to speed up the training for BAE-cr we merged each 5 adjacent sentence pairs into a single training instance, as described in Section 2.1.

bAE-cr often outperforms the approach of Klementiev et al.


In practice, this low dimensionality is tuned by ad hoc methods such as cross-validation.

we briefly review Nesterov's approach [17] in the setting of a general min-max problem using smoothing techiniques.


To remedy this, some intuitive smoothing methods are proposed.

we can find the maximum of entropy for every segment According to Equation 2 and the definition of segmentation, the entropy of feasible paths satisfying a specific segmentation sequence can be disassembled into the summation of the entropy of segments.


Using a trainable p(a) allows the model to learn that some memory entries are more useful for generating new targets than others.

an alternative approach to generative few-shot learning proposed in [23] uses a hierarchical VAE to model a large number of small related datasets jointly.


For machine learning approaches to these predictions, the diversity and high dimensionality of the structures involved mandate very large training sets.

it is sufficient for controlled comparison of learning methods.


Let t-rankpYq " r and rankpY k q " r max .

relational and graph-structured data has become ubiquitous in many fields of application such as social network analysis, bioinformatics, and artificial intelligence.


The goal is to adapt σ t such that the steps of the algorithm become uncorrelated.

as the CMA-ES is a randomized algorithm, we cannot assume convergence of C t . in simplified algorithms the expectation of C t converges [Beyer, 2014].


MSRA initialization [16] is used for the convolution parameters and the initial gradient step for each iteration is set to be 0.02.

in this section, we will focus on this family of inference algorithms and show that they are a particular type of recurrent net.


By construction, spatial approaches provide filter localization via the finite size of the kernel.

all FCk, Ck and GCk layers are followed by a ReLU activation max(x, 0).


LORD avoids both extremes and controls FDR while having reasonable power.

theorem 1 (Online mFDR control for MAB-LORD).


[35] added a crowd layer after the output layer for noisy labels from multiple annotators.

that being said, it is worth noting that, in each mini-batch of data, each network views its small-loss instances (like self-paced MentorNet) as the useful knowledge, and teaches such useful instances to its peer network for updating the parameters.


In particular, several general characterizations have been developed for describing when active learning can in principle have an advantage over the classic passive supervised learning paradigm, and by how much.

in this section we outline our reduction from active learning to passive learning of homogeneous linear separators based on the analysis of Balcan and Long [8].


Given v ∈ V , we denote its degree by d(v) and the set of adjacent vertices N(v) := {u | (v, u) ∈ E}.

finally, we provide an experimental evaluation of our property tester on approximate nearest neighbor (ANN) indices computed by various ANN algorithms.


Suppose we are given a dataset of labeled sequential data points Z = [(X 1 , y 1 ), .

for example, the GesurePod device [26] requires the buffer to be refreshed every 100 ms and hence predictions must be completed in 100 ms using just 32KB of RAM.


We also obtain a valid approximation, of course, without selection (I = {1,. . . ,H}) but MCMC samplers in very high dimensional spaces  ); compute M-step with arguments f (� s) as in ( 3) and (4); until (until Θ have converged); Illustration of general application.

2) and they show that spike-and-slab models may be very suitable generalized V1 models.


We consider the scenario when websites such as IFTTT.com release new channels and functions.

for each description, we focus on predicting the channel and function for trigger and action respectively.


For example, the choice: results in the AIS algorithm, with weights w n ∝ fn(xn−1) fn−1(xn−1) .

to obtain a good estimate, MCMC requires that the process "visit" each of the target distribution's basins of energy with a frequency representative of their probability.


To simplify the description, we assume that the visible and hidden variables of the RBM are binary.

the set of data vectors that a particular mixture component has high responsibilities for should have the same class label.


To the best of our knowledge, this is the first work that combines contextual bandits with the social graph information.

an analysis of LinUCB was provided in the subsequent work [9].


However when γ is large, for computational reasons we can use the technique presented in [7] to limit the number of datapoints spanning this new space.

further-although this is not the main focus of our paper-on traditional benchmarks for MIL, our algorithm is again shown to be competitive with the current state-of-the-art.


Figure 1 (d) and (h) show that both models achieve the desired mean population sparsity.

the benefit of using RBMs as building blocks for a DBN is that they often provide a good initialization for feed-forward neural networks, and they can effectively utilize large amounts of unlabeled data, which has led to success in a variety of application domains [3].


Consequently, we evaluate the performance of an estimate θ using log-loss on a held-out dataset.

let θ denote the vector output by any of our procedures after inference (so in the BAVGM case, for example, this is the vector θ = θ BAVGM = (θ 1 − rθ 2 )/(1 − r)).


In this paper, we instead propose a novel combination of unsupervised joint alignment with unsupervised feature learning.

using a CDBN representation learned with a group sparsity penalty, leading to learned filters with topographic organization, consistently gives a higher accuracy of one to two percentage points.


Last but not least, contrary to conventional sequential updating, we choose to update the terms ti in parallel.

our representation allows the specification of both spatio-temporal as well as sparsity constraints.


Our results indicate that by leveraging the network interaction structure, it is possible to tolerate noise with variance that increases with the size of the network whereas without exploiting dependencies in the node measurements, the noise variance needs to decrease as the network size grows to accommodate for multiple hypothesis testing effects.

by Markov's inequality, for t > 0,  Note that x contained within the ellipsoid x T Lx ≤ δp, x ∈ {0, 1} p implies that x is feasible, so a solution to the optimization upper bounds sup x:x T Lx≤δp p i=k+1 (u T i x) 2 .


We see that the RBP-RM achieves competitive performance against the other methods.

a stochastic partition process generates a partition on a multi-dimensional array, which serves as a prior for the underlying communities in the relational data (e.g.


In this problem, the data D contain N independent tuples consisting of a time series S i and a label y i .

there are several choices for R that satisfy Σ = RR .


The proposed algorithm solves this problem based on the proximal gradient method [23].

the workers compute both gradients and coordinate-specific learning rates, e.g., the diagonal part of the second derivative, on this block.


That is, R D II provides less power than R S II .

a decorrelation of neural activity has been proposed to be beneficial for discarding statistical redundancies in the input signals.


We reduced the variance of this approximation by selecting additional queries for each evidence configuration.

this ruled out most traditional benchmarks, for which ACs can already perform exact inference [9].


For rotation matrices it is computed as the Frobenius norm of the difference between ZT Z and Gaussian noise variance Mean 3D error [mm] GP GP + trsf Cstr GP [12] Cstr GP [12]    Gaussian noise variance Mean 3D error [mm] GP GP + trsf Cstr GP [12] Cstr GP [12]   Note that the global transformations estimated with the PnP method yield poor reconstructions.

note, however, that other types of image information, such as silhouettes or texture, could also be employed.


The positions of these objects can be varied so long as the robot sees the red object on the left side of its field of view, the green object in the middle, and the blue object on the right at the start of every trial of behavioral sequences.

no a priori knowledge about the meanings of words is pre-programmed.


A potential sublety in interpreting these results is the small absolute values of the Rand error for all of these techniques.

the improvement is substantially less than achieved by LASH.


To conclude and summarize, from a statistical performance point of view, what we can expect from a regularized estimator s (i.e.

the KPCA step was useless or even counterproductive.


The algorithm is relatively expensive to execute compared, say, with the contamination-free RVM.

the inference scheme makes use of "hallucination" to fill in parts of the object that are unobserved due to occlusion.


High-performance algorithms and implementations are critical to efficiently solving these problems.

consider the case where all blocks are updated in parallel as in the thread-greedy coordinate descent algorithm of Scherrer et al.


The online classification algorithms discussed above keep enlarging C t -once an example is added to C t it will never be deleted.

examples of such algorithms include the Relaxed Online Maximum Margin Algorithm (ROMMA) [4], the Approximate Maximal Margin Classification Algorithm (ALMA) [2], and the Margin Infused Relaxed Algorithm (MIRA) [1] which can be used in conjunction with kernel functions.


We would like to thank Sam Roweis for advice on Hidden Markov models and Maria Minkoff for help with the manuscript.

hidden-state switching seems to occur more frequently in the combined model.


the fact that the second order term has a worse complexity than the first order term is in contrast to Boltzmann machines, in which the TAP approximation has the same complexity as the standard mean field approximation.


For networks with other activation functions, CROWN-general is our proposed method.

all functions are convex on one side (y < 0) and concave on the other side (y > 0), thus the same rules can be used to find h Bounding ReLU.


It is known that these two coincide up to a change of the regularization coefficient.

we show that (i) as a direct result of feature-wise independence of the uncertainty set, a slight change of a feature that was originally assigned zero weight still gets zero weight (Theorem 4); (ii) using Theorem 4, we show that "nearly" orthogonal features get zero weight (Corollary 1); and (iii) "nearly" linearly dependent features get zero weight (Theorem 5).


A solution is to downsample the binary code to a very low dimension, or by slowing down the training process.

this AE takes as input states s and contains one special dense layer comprised of D sigmoid functions.


We randomly draw p-subsets from the data and use it to fit a hypothesis of the model, where p is the number of parameters that define the model.

instead of ranking these hypotheses we encapsulate them in a novel Mercer kernel.


Rather, if such a structure exists, it can only be discovered after the model has been successfully built and learned.

in general, the computation of each auxiliary variable is multiplied by an identity function that enforces the consistency between the observations and the required constraints associated with the computation of that variable.


To allow for an analytic calculation of the loss L(β, X, P), we assume that the distribution P is a d-dimensional mixture of Gaussians [1,8].

for anisotropic Gaussian, the level sets are concentric ellipsoids, which makes the effect dependent on the direction of shrinkage.


Table 1 shows the CER and WER performance of the RNN models trained with the WSJ SI-284 training set.

we needed to try many different RNN structures, thus each training should not take much time.


After each word, the incremental posterior over partial structures T can be read off the particle structures and weights.

it is well documented (e.g., [24]) that locally ambiguous sentences such as Example 1 are read more slowly at the disambiguating region when compared with unambiguous counterparts (c.f.


assign either everyone or nobody to the positive class).

we show that DLPs are suboptimal for trading off accuracy and impact parity.


We use a subset that consists of 22,395 records of patients over age 15 and stayed in ICUs between 2001 and 2012, among which 2,624 patients are diagnosed of sepsis.

we utilize variational inference, which is an approximation method that has been shown to be successful in many applications of neural networks [16,23], along with reprameterization tricks for pathwise backpropagation [15,8].


Skip connection has been empirically demonstrated important to obtain state-of-the-art results [He et al., 2016a,b, Huang et al., 2017a, while its functionality has various interpretations.

these two layer-wise learning rate strategies do not have explanation of why the rate is set in that way.


Each bar had a gaussian cross-section, with maximum amplitude drawn from a standard normal distribution of width 1.2 pixels.

using a simple approximation for the decoding distribution, q(y|r) (e.g.


The internal reward features are capable of representing arbitrary policies (and thus we also implemented classical policy gradient with these features using OLPOMDP [2] but found it to be far slower than the use of PGRD with UCT and hence don't present those results here).

in a departure from the original definition of the routing domain, we parameterize the transition function to allow a comparison of agents' performance when transition functions change.


To ensure a valid probability density, each kernel must integrate to one; i.e., ´φi (s) ds = 1, ∀i, and similarly for ψ and ϕ.

this paper presents two key contributions to continuous-state policy evaluation.


with virtual support vectors (Decoste and Scholkopf, 2002).

the USPS data set was used to perform a classification experiment.


We focus on a graphical variant defined as follows: There exist some graph G whose vertex set is the set of arm K and an arbitrary edge set E. For every sub-optimal arm x there exist some neighbor y in the graph such that µ(x) < µ(y).

indeed, one cannot discover the best arm without verifying that it is superior to the others, and the set Y provides the best strategy to do so.


v int increases with the SFA amplitude m (Fig.

we have the following two observations: • Perfect tracking.


Therefore, MDA is faster than the gradient descent method by a factor O((n/ ln n) 1/2 ).

bADMM generalizes ADMM similar to how MDA generalizes gradient descent and how PMD generalizes proximal methods.


In the context of regression, L 2 boost, proposed by Buhlmann et al [4] produces a path of ensemble models which progressively minimize the sum of squares of the residual.

where b is a scalar quantity determined by the experimenter, and related to the parameters of the measurement (the magnitude of diffusion sensitization applied in the MRI instrument).


First we notice that the renormalization step remains valid if the greatest common divisor of the elements of β * is 1.

in the first reference the authors propose a mixed linear/integer model of the form Y = Ax + Bz + W where z is an integer valued vector corresponding to integer multiples of certain wavelength.


Early work assumed stringent matrix incoherence conditions for low-rank completion to preclude such matrices [7,18,19], while more recent work [11,26], relax these assumptions to a more intuitive restriction of the spikiness ratio, defined in (3).

theorem 2 (Partial Gaussian Complexity).


The aim is to visualize the positions in which STRAWe terminates macro-actions and re-plans.

this is the same architecture as in [17,18], the only difference is that in pre-processing stage we keep colour channels.


The second work [17] optimizes a rank sensitive loss function (Discounted Cumulative Gain).

if the number of non-leaf nodes of the tree reaches threshold T , no more nodes can be expanded and thus j cannot create children.


Although the field of robust regression is well established, it has not considered computational complexity analysis to be one of its central concerns.

it is clear that all methods based on convex losses (L2, L1, Huber) suffer significantly from the added outliers.


Initial results show that in field L, temporal patterns give at least % extra information.

2, we find that the dependence of our estimate on sample size is simple and regular; specifically, we find This is what we expect for any entropy estimate if the distribution is well sampled, and if we make stronger assumptions about the sampling process (independence of trials etc.)


We now compare algorithms for clustering N = 60000 MNIST images of handwritten digits 0-9.

in practice merge moves reliably reject poor births and restore original configurations.


For example, metric learning [6,9,14] maps faces to some feature representation such that faces of the same identity are close to each other while those of different identities stay apart.

these features come from the six identities with the largest numbers of face images in LFW, and are marked by different colors.


The mean computation time over 100 trials is described in the bottom row of the table, where the value is normalized so that the computation time of uLSIF is one.

defining the importance over two sets of samples, we can see that the importance values for regular samples are close to one, while those for outliers tend to be significantly deviated from one.


The core consists of a three-layer, 2d convolutional neural network (CNN), applied separately to each frame, followed by a convolutional Gated Recurrent Unit (GRU) [14].

we also demonstrate that the nonlinear feature representation learned on natural movies can transfer well to the noise domain by fine-tuning the last layer's weights, while the converse is not true (i. e. generalization from noise to movies).


As in the naive approach, approximated MV-sets in our method are represented as dense sets captured by separating hyperplanes in a reproducing kernel Hilbert space.

let SV oj be the set of SVs lying strictly outside C j , and SV bj be the set of SVs lying exactly on the boundary of C j .


In this section, we formulate the low-dimensional principal component discovering problem as a conditional likelihood maximization problem based on exponential family model representations, which can be reformulated into an equivalent nondifferentiable convex optimization problem.

in this section, we deploy a bundle method to solve this nondifferentiable min-max optimization.


Unlike the shape context descriptor, the RDF feature vector is neither scale nor translation invariant.

we represent the body using a parameterized triangulated mesh model that is learned from a database of human range scans.


Let I j = I j (e), (j = 1, 2, . . .) be the phase numbers in which e is followed.

the column player may be very patient and cooperative, willing to wait for the row player to become cooperative, but eventually becoming non-cooperative if the row player does not seem to cooperate.


In addition, H matrices enable a significant space advantage: since the fast Walsh-Hadamard transform can be computed without explicitly storing H, only O(n) space is required to store the diagonal elements of (D i ) k i=1 .

we consider the variant S-Hybrid random matrix below, where D (U ) k is a diagonal matrix with iid Unif(S 1 ) random variables on the diagonal, independent of (D (R) i ) k−1 i=1 , and S 1 is the unit circle of C. We use the real part of the Hermitian product between projections as a dot-product estimator; recalling the definitions of §2, we use: Remarkably, this complex variant yields exactly half the MSE of the OJLT estimator.