The importance of local phase coherence in blur perception seems intuitively sensible from the perspective of visual function.

the accurate localization of image features is critical to a variety of visual capabilities, including various forms of hyperacuity, stereopsis, and motion estimation.


These are linearly mixed to form our patch.

to gain a better understanding of what each mixture component is capturing, we need to look at the eigenvectors and eigenvalues of its corresponding covariance matrix.


Then, when initialized at w 0 = 0, AdaGrad, Adam, and RMSProp all converge to the unique solution w / sign(X T y).

whenever there exists a solution of Xw = y that is proportional to sign(X T y), this is precisely the solution to which all of the adaptive gradient methods converge.


We proceed by studying the more general problem of `1 error for parameter estimation for any loss function L n (•).

consider the general M -estimation problem, where we are given n i.i.d samples Z from some distribution P, and we are interested in estimating some parameter ✓ ⇤ of the distribution P. Let `: R p ⇥ Z 7 !


These methods are well known to achieve linear convergence for strongly convex objectives.

aPG achieves optimal iteration complexities for both non-strongly and strongly convex objectives.


This means that during optimization we are trying to find ¢ functions ¢ R #" ' ¢ 6 8 7 ' ¦ A " ' 5' , 7 ¢ ¤ A¦ ©¦ ¢ , from an D dimensional subspace.

we choose the subspace and perform regularization by allowing only a smaller class of functions.


Our proof for the larger class may be of independent interest.

the following Theorem considers general discrete optimization problems which are linear matrix functionals, and shows sufficient conditions on the matrix for the problem to be monotone and/or submodular.


The proof, which we omit, is a rather straightforward consequence of imposing a sparsity pattern of cardinality k as an additional orthogonality constraint in the variational inequality of the Courant-Fischer "Min-Max" theorem (see [13] for example).

the eigenvalues of a symmetric matrix form upper and lower bounds for the eigenvalues of all its principal submatrices.


Of course, requiring that f (w; θ) is λ-strongly convex for all θ (with respect to w) is enough to ensure the condition.

for a generalized linear function of the form (2) it is enough to require that (z; y) is convex in z and that r(w) is λ-strongly convex (w.r.t.


Furthermore, there is 1 positive symptom in the initial state.

the average maximum number of queriable positive symptoms is only about 2.


Here we provide an alternative route to analyzing the difficulty of obtaining consistent surrogates for such pairwise subset ranking problems using the classification calibration dimension.

we will show that even for a simple setting of such problems, the classification calibration dimension of the underlying loss � is greater than r, and therefore no convex surrogate operating on � T ⊆ R r can be classification calibrated w.r.t.


While the theory developed in the previous section applies to any representation scheme, in this section, for illustrative purposes, we focus on one specific family of approximate densities defined by the firing rate of neurons in a network.

we consider a population of N neurons tasked with encoding a probability density over s. One way to do this, known as a kernel density estimate (KDE) code [1,28], is to associate with each neuron a kernel density f n (s) and then approximate the target density with a convex combination of the kernel densities: where x n denotes the firing rate of neuron n and Z = N n=1 e xn .


We also show, by way of contrast, that certain natural relaxations of this set of properties are satisfied by versions of well-known clustering functions, including those derived from single-linkage and sum-of-pairs.

we fully characterize the set of possible outputs of a clustering function that satisfies the scale-invariance and consistency properties.


Secondly, we use Professor-Forcing (Lamb et al., 2016) to match the sequence of hidden states instead of the output words, which contains the information about outputs and is smoothly distributed.

the input to the discriminator D 1 is the sequence of hidden states of either (1) G(y 1 , z 1 ) teacher-forced by a real example x 1 , or (2) G(y 1 , z 2 ) self-fed by previous soft distributions.


We then derive an algorithm to optimize problem (2) using block coordinate descent.

problem (2) can be viewed as a generalization of predictable discriminative binary codes in [23]: 1) compared with the fully labeled case in [23], Eqn.


The weak learners we use for the local evidence potentials are based on the segmentation fragments proposed in [2].

we create a dictionary of about 2000 image patches U , chosen at random (but overlapping each object), plus a corresponding set of binary (inclass/ out-of-class) image masks, V : see Fig.


To address this, we smooth article scores in segments at each time point through a Bayesian hierarchical model.

if (a it , Q it ), i = 1, • • • , k, are predicted mean and variances of item score at F1 in k different user segments at time t, we derive a new score as follows: where āt is the EMP model score for the item.


Starting from the basic observation that one can construct a kernel-based density estimator fε whose region of support is exactly Ω ε (S), this paper investigates the interplay between the topological information contained in Ω ε (S) and a corresponding density estimate.

we make the following contributions: • Given prior topological information about supp f = Ω, we define a topologically admissible bandwidth interval [ε min , ε max ] and propose and evaluate a topological bandwidth selector • Given no prior topological information, we explain how persistent homology can be of use to determine a topologically admissible bandwidth interval.


This variational renormalization suggests (somewhat ironically) that given a continuous (approximate) solution, it is almost certainly better to discard the loadings and keep only the sparsity pattern with which to solve the smaller unconstrained subproblem for the indicated submatrix A k . This simple procedure (or "fix" as referred to herein) can never decrease the variance and will surely improve any continuous algorithm's performance.

the rather expedient but ad-hoc technique of "simple thresholding" (ST) [1] i.e., setting the n − k smallest absolute value loadings of u n (A) to zero and then normalizing to unit-norm -is therefore not recommended for sparse PCA.


These vectors map features s (t) 1:n to parameters of the ellipsoid.


; θ) directly, NCE estimates the density ratio p m /p n by training a classifier based on logistic regression.

let U = (u 1 , ..., u Tm+Tn ) be the union of X and Y .


STRADS not only supports simple static schedules, but also dynamic, adaptive strategies that take the model state into consideration.

sTRADS Lasso implementation schedules parameter updates by (1) prioritizing coefficients that contribute the most to algorithm convergence, and (2) avoiding the simultaneous update of coefficients whose dimensions are highly inter-dependent.


On the other hand, for problems without pointwise positivity, [16,17] have considered low-rank representations of matrices T , of the form T = V V T where V has more than one column.

[17] shows that the non convex optimization with respect to V leads to the global optimum of the convex problem in T . In order to apply the same technique here, we need to deal with the pointwise nonnegativity.


Specifically, we introduce weights to the pairwise and listwise losses in the following way, It can be proved (see Proposition 1 in [4]) that the above weighted losses are still upper bounds of (1−NDCG) and they are lower bounds of the original pairwise and listwise losses.

the above weighted loss functions are tighter bounds of (1−NDCG) than existing loss functions.


To obtain a fast algorithm (i.e., O(poly(d)), we instead take a mean-field type approximation: where ν(z; β) := β z (1 − β) 1−z .

we approximate a multivariate distribution by the product of its marginals.


We show that a variety of individual-sequence second-order regret guarantees imply fast regret rates for distributions under much milder stochastic assumptions.

we will look at the Bernstein condition (see Bartlett and Mendelson 2006), which is the key to fast rates in the batch setting.


Possible answers were hypothesized in subsequent work.

golub and Jackson proposed an explanation based on computer simulation [9]; they studied a model for generating trees T using a Galton-Watson branching process [3], and they showed that for branching processes near the critical value for extinction, δ-sampling with small values of δ produced large single-child fractions in simulations.


We discuss the properties of conditions Q s,q in Section 3.

in Section 3.1 we show how one can efficiently verify (the strongest from the family Q s,q ) condition Q s,∞ .


That is, for some α * and β * , ) Second, given an example (x, y) ∼ π * , the class label y must be independent of the features f (x) given the labels λ(x).


Define OPT ; £ to be the set of probability measures that minimize the function @ £ jj¡A.

ideally, the target probability measure £ should be one and the only one that minimizes the objective function.


We develop a truncation strategy of these models that is applicable in principle to any backward-simulation-based method, but which is particularly well suited to the PG-AS framework.

as we show in a simulation study, PG-AS can yield an order-of-magnitude improved accuracy relative to PG-BS due to its robustness to the truncation error.


The optimization for MCU inherits the basic form of the optimization for MVU.

it can be cast as a semidefinite program (SDP).


We therefore construct an additional decision module which takes the outputs of the familiarity and recollection modules and maps them into a binary behavioral response (familiar vs. novel).

we use the average of the entropies associated with the activities of neurons in the recollection module and the mean estimate of t from the familiarity module.


Throughout this paper, we assume that we have a generative model, a notion introduced by [Kak03], which allows us to draw random state transitions of the DMDP.

we assume that we can sample from the distribution defined by P s,a for all (s, a) ∈ S × A in O(1) time.


Lemma 2 shows that if the parameter is set to be equal to w * , then the resulting mean squared error E π (w * ) (now treated as a function of the baseline b(s)) is further minimized when b(s) = V π (s).

the variance in the action-value-function estimator is minimized if the baseline is chosen to be the state-value function itself.


To evaluate the clustering performance, we use the some standard performance metrics, including pairwise Precision, pairwise Recall, and pairwise F1 measures [9], which are evaluated base on the pairwise results.

pairwise precision is the ratio of the number of correct pairs placed in the same cluster over the total number of pairs placed in the same cluster, pairwise recall is the ratio of the number of correct pairs placed in the same cluster over the total number of pairs actually placed in the same cluster, and pairwise F1 equals to 2 × precision × recall/(precision + recall).


Let T i ∈ R m×d be the matrix whose columns constitute an orthonormal basis for T xi M. It is easy to show that P i = T i T T i is the unique orthogonal projection from R m onto the tangent space T xi M [11].

for any vector a ∈ R m , we have P i a ∈ T xi M and (a − P i a) ⊥ P i a.


This Markovian assumption is commonly adopted in structured prediction problems such as NLP (Manning and Schütze, 1999).

it holds for feature mappings that are frequently used in conjunction with the CRF, as well as outputs of a recurrent neural network, reset at the begining of each new input (see Appendix B).


It is shown that the methods achieve essentially a sample complexity of O(1/ε) to attain an error of ε under a variant of restricted eigenvalue condition, and the rate has better dependency on the problem dimension than existing methods.

if the smallest magnitude of the non-zero components of the optimal solution is not too small, the rate of our proposed Hybrid algorithm can be boosted to near the minimax optimal sample complexity of full information algorithms.


However, the design of ROCK has been kept fairly simple to prove the relevance of the approach.

the fusion operation could be studied more thoroughly.


it has nonnegative entries, and its row sums are less than or equal to l. Write s for the vector whose (s, a)th element is So(s)7r(als), that is, the probability that we start in state s and take action a.


Proportional hazard (PH) models have become the standard for studying the effect of the covariates on the survival time distributions, e.g., [8].

the PH model assumes a multiplicative effect of the covariates on the hazard function, i.e., where λ(t|x) is the hazard function of a person with covariates x; λ 0 (t) is the so-called baseline hazard function (i.e., when x = 0), which is typically based on the exponential or the Weibull distributions; w is a set of unknown regression parameters, and e w x is the relative hazard function.


1  In this section we characterize the structure of optimal learner strategies.

intuitively, it seems plausible that the learner should not assign higher rejection values to higher probability events under P . one may expect that a reasonable rejection function r(•) would be monotonically decreasing with probability values (i.e., if p j ≤ p k then r j ≥ r k ).


Next we begin by optimizing the dual function given in Lemma 3.1 with respect to the λ parameters.

for a chosen region r we optimize the dual w.r.t.


To ensure that they classify as well as possible, we assign them the optimal labeling over the data they need to classify; we do this by allowing them to make multiple passes over the data.

for each day, we assign labels so that the fixed clusters maximize their accuracy on spam for a given required accuracy on legitimate mail 2 .


• Moreover, notice that the tails for degree-2 functions are exponential and not Gaussian, and this is unavoidable, and that as the degree grows the tails become heavier exponentials, and this is also unavoidable.

the tightness of our bound is justified in the supplementary material.


However, it was recently shown [6] that positive correlations which vary smoothly with space may drastically suppress the information in the mean responses.

the Fisher Information of the system saturates to a finite value as the system size grows.


The intermediary implements a non-anticipative adaptive policy π that maps the history at time t to a reserve price r π t ∈ R + for the second price auction and a payment function p π t : R + → R + that determines the amount to be paid to the seller as a function of the buyers' payments.

the item is sold whenever the highest bid is above the reserve price, or equivalently b f t ≥ r π t . The intermediary's revenue is equal to the buyers' payments of max(r π t , b s t ) and the seller's revenue is given by p π t (max(r π t , b s t )).


over index pairs (i, j)) and our sample S is sampled i.i.d.

from D. Our objective is to get low average error with respect to the distribution D. we measure generalization performance in terms of the weighted sum-squared-error: We first point out that when using the rank for complexity control, i.e.


Finally, the dynamics will be stable iff all the eigenvalues lie within the unit disc.

the matrix C describes the dependence of the high-dimensional neural signals on the lowdimensional latent processes x t . equation 2 determines the firing rate of the neurons.


Our algorithm requires minimal prior knowledge.

it does not require exact knowledge of the intrinsic dimension d, since it can work satisfactorily with d = 1 in many cases.


We believe that this is due to the fact that each query has at most 10 intentshifting events spread uniformly and it is possible that there were fewer events with potentially smaller shifts in intent in those runs.

the standard deviation of the regret is large.


In this section we evaluate coordinate minimization algorithms on a MAP problem, and compare them to state-of-the-art baselines.

we compare the running time of greedy coordinate minimization, stochastic coordinate minimization, full gradient descent, and FISTA -an accelerated gradient method [1] (details on the gradient-based algorithms are provided in the supplementary, Section 3).


We can also replace the center of gravity method with the ellipsoid method, or any other optimization method with a similar "optimization interface" (i.e., any method that is based on separation queries and guarantees similar bounds on the number of iterations required to find a feasible point), as pointed out by Garber (2017).

using the ellipsoid method, we can significantly reduce the computational complexity to depend only polynomially in log T (rather than T ), at the cost of a slightly higher oracle complexity, namely O(d 2 log T ) calls to the oracle per round.


In this paper, we aim to combine these two lines of research and consider a supervised form of LDA.

we wish to incorporate side information such as class labels into LDA, while retaining its favorable unsupervised dimensionality reduction abilities.


The performance of an algorithm π ∈ Π is defined through its regret up to round T : The above MAB problem is very generic, as any kind of structure can be considered.

our problem includes classical, linear, unimodal, dueling, and Lipschitz bandit problems as particular examples, see Section 3 for details.


Since the results of denoising images from a visual standpoint can be more qualitative than quantitative, we have tested using denoising as a preprocessing step done before a classification task.

we used the MNIST database of handwritten digits [19] as benchmark to evaluate the efficacy of our denoising procedures.


Hence, there might still exist a subset of world states where all agents would play badly, regardless of the parametrization.

the parametrization procedure may not be generating the idealized diverse team (see Appendix H).


The results of this section are non-trivial extensions of those of Kearns and Ortiz [8].

we can construct a polynomial-time algorithm to compute all MSNE of a uniform-transfer SC α-IDS game, along the same lines of Kearns and Ortiz [8], by extending their Ordering Lemma (their Lemma 3) and Partial-Ordering Lemma (their Lemma 4).


define embeddings for finding nearest subspaces [13].

they define Euclidean embeddings for affine subspace queries and database points which could be used for NNQH, although they do not specifically apply it to hyperplane-to-point search in their work.


A classical missing data problem is to find a way to make valid inferences about the full data law.

the goal is to exploit assumptions on the mechanism which is responsible for missingness or corruption of data records to transform the problem into another where missingness or corruption were not present at all.


Our work is motivated by an application to protein folding where this presents a major difficulty.

while Nature provides samples of protein configurations near the global minima of free energy functions, protein-folding algorithms, which imitate Nature by minimizing an estimated energy function, necessarily explore regions far from the minimum.


This algorithm output the partition of the graph in an online fashion after a group of columns arrives.

if f (n) = n α with 0 < α < 1, our algorithm requires as little as n β memory with β > max 1 − α, 2 3 .


Here µ 0 , µ 1 , µ 1 ∈ P(Z) are suitable measures obtained from M S (x) and M S (x ) through a coupling and projection operation.

the proof of advanced joint convexity uses ideas from probabilistic couplings, and more specifically the maximal coupling construction (see Theorem 2 and its proof for more details).


We consider a generalization of this problem where some of the entries are unobserved.


Our learning algorithm optimizes this pair of equations with respect to γ, ω, θ using stochastic gradient descent.

the algorithms aim to find a simultaneous solution to min ω ÔLR (ω, γ, θ) and min θ,γ Ô(ω, γ, θ).


Unlike the previous usage of large λ, we use small λ for the IMM procedure.

µ k is first trained by Equation 10 with small λ, and then merged to µ 1:k in our IMM.


For brevity, we only present the main results along with the results of simulations, leaving more detailed analysis to the supplementary material.

we consider input signals where the only source of noise is in the input current i.e.


The original model, f ∼ N (0, Σ θ ) and ( 7) define a joint auxiliary distribution P (f , g | θ) given the hyperparameters.

it is possible to sample from this distribution in the opposite order, by first drawing the auxiliary values from their marginal distribution and then sampling the model's latent values conditioned on the auxiliary values from , where some standard manipulations give: under the auxiliary model the latent variables of interest are drawn from their posterior given the surrogate data g. Again we can describe the sampling process via a draw from a spherical Gaussian: We then condition on the "whitened" variables η and the surrogate data g while updating the hyperparameters θ.


Reconstructing distributions over the permutation group from a limited number of Fourier coefficients has several applications.

there has been some recent work on multi-object tracking (see [4] and [3]), in which they approach the daunting task of maintaining a distribution over the permutation group by approximating it using the first few Fourier coefficients.


This rule has no memory of cue performance other than an ordered list of all cues, and just moves a cue up one position in this list whenever it leads to a correct decision, and down if it leads to an incorrect decision.

a correctly deciding cue swaps positions with its nearest neighbor upwards in the cue order, and an incorrectly deciding cue swaps positions with its nearest neighbor downwards.


Here we show that a sophisticated choice of prior distribution can lead to substantial improvements in active learning.

we develop a method for learning under a class of hierarchical, conditionally Gaussian priors that have been recently developed for RF estimation [8,9].


All we need is a loss function that encourages the predicted depth map to agree with the ground-truth ordinal relations.

consider a training image I and its K queries R = {(i k , j k , r k )}, k = 1, . . . , K, where i k is the location of the first point in the k-th query, j k is the location of the second point in the k-th query, and r k ∈ {+1, −1, 0} is the ground-truth depth relation between i k and j k : closer (+1), further (−1), and equal (0).


Our parametric simplex method offers significant advantages over other competing methods: (1) PSM naturally obtains the complete solution path for all values of the regularization parameter; (2) PSM provides a high precision dual certificate stopping criterion; (3) PSM yields sparse solutions through very few iterations, and the solution sparsity significantly reduces the computational cost per iteration.

we demonstrate the superiority of PSM over various sparse learning approaches, including Dantzig selector for sparse linear regression, LAD-Lasso for sparse robust linear regression, CLIME for sparse precision matrix estimation, sparse differential network estimation, and sparse Linear Programming Discriminant (LPD) analysis.


If (1) there exists a joint action 0 I q 6 such that for all , and (2) there exists at least one joint action 0 such that 0 q ¡ X and 0 q 6 , then agent ¢ chooses its best-response action 0 k such that 0 k q 0 X and p I w R sT h 0 (@ q ¡ X BA 0 (@ q 6 .

0 k is contained in the most recent play of a Nash equilibrium inside 6 .


We can use the definition of the task to write a new form for r(•): We assume for simplicity that the inference process on the context models the maintenance of context information and retrieval of the response rule (though the model could be extended to perceptual encoding of the context as well).

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.


In [5], the feature representation includes quantities describing the joint, marginal and conditional distributions.

the conditional distributions are represented with conditional entropy, mutual information and a quantification of their variability in terms of the spread of the entropy, variance and skewness for different values of the conditioning variable.


Our method: In this work, we propose a method that addresses above mentioned challenges in deployment on tiny devices.

our method is motivated by two observations: a) the actual "signature" of the event forms a small fraction of the data point.


Although the entire development was focused on a single Mallows model, our results extend to a finite mixture of Mallows model.

for a Mallows model with T mixture components, we can compute the choice probability by setting ⇡(i, s, n) = P T t=1 ↵ t • ⇡ t (i, s, n), where ⇡(i, s, n) is the probability term defined in Section 4, ⇡ t (•, •, •) is the probability for mixture component t, and ↵ t > 0 are the mixture weights.


However, marginalizing over the activations Ā couples the discrete musical structure with the superposition process of the component spectrograms in an intractable way.

we instead approximate the joint MAP estimates of M , Ā, α, and σ via iterated conditional modes [9], only marginalizing over the component spectrograms, S. we perform the following optimization via block-coordinate ascent: max M , Ā,α,σ r S (r) P (X (r) , S (r) , A (r) , M (r) |µ, α, σ) • P (α, σ) The updates for each group of variables are described in the following sections: M in Section 3.1, α in Section 3.2, Ā in Section 3.3, and σ in Section 3.4.


Recently, Shalev-Shwartz and Zhang [2013a] analyzed a stochastic version of dual coordinate ascent, abbreviated by SDCA, in which at each round we choose which dual vector to optimize uniformly at random (see also Richtárik and Takáč [2012a]).


Preview: The goal of this stage is to provide a coarse estimate of the location of B(f ).

collect n ≡ n/2 samples at points distributed uniformly over [0, 1] d . Next proceed by using the passive learning algorithm described before, but restrict the estimator to RDPs with leafs at a maximum depth of J = d−1 .


The noise vector Z is used to inject noise into the generator to prompt diversity of generated text.

a 3-layer convolutional neural network (CNN) is employed to encode the source sentence S into a fixed-length hidden vector H 0 .


After discussing some existing literature on nearestneighbor search and vector quantization in Section 2, we discuss our following contributions: • We present performance guarantees for Algorithm 1 in Section 3, linking search performance to vector quantization performance.

we show that for any balanced BSP-tree and a depth l, under some conditions, the worst-case search error incurred by the neighbor candidate returned by Algorithm 1 is proportional to a factor which is where β corresponds to the quantization performance of the tree (smaller β implies smaller quantization error) and d is closely related to the doubling dimension of the dataset (as opposed to the ambient dimension D of the dataset).


This is because high-dimension often also comes with additional structure.

if a distribution produces only roughly d distinct categories in a sample of size n, then we ought to think of d (and not k) as the effective dimension of the problem.


The perceptron algorithm (PERC) and its second-order counterpart (SOP) are reported here as a reference, since they are designed to query all labels.

sOP is a mistake-driven variant of the algorithm analyzed in Theorem 1.


The results in this paper are restricted to Mahalanobis metric, which is an appealing choice for a number of reasons.

learning such metrics is equivalent to learning linear embedding of the data, allowing very efficient methods for metric search.


Finally, we demonstrate experimentally that our method is highly scalable and yields close to optimal solutions in a fraction of the time as compared to existing approaches.

our results show that for even small values of k (k bounds the partition size), our algorithm yields close to optimal MAP solutions, clearly demonstrating the power of our approach.


Posterior reshaping Thompson sampling is a heuristic advocating to draw samples from the posterior, but one might consider changing that heuristic to draw samples from a modified distribution.

sharpening the posterior would have the effect of increasing exploitation while widening it would favor exploration.


The remaining tree T after either of the above pruning operations satisfies: (i) T T p h , (ii) there exists a function f whose tree is T , and (iii) T ∈ C α (see Lemma 10 in Appendix D.2).

we identified a valid tree with a statistical guarantee that is simpler than the original estimate T p h . Intuitively, some of the statistically insignificant features have been removed from T p h . We should point out, however,  (c) Pruning leaves and branches.


This is important as it would be a rather strong requirement in the confounded sample where treatment choices may depend on high dimensional variables [DDF + 17], but it is a weak condition for the experimental data.

if the unconfounded sample arose from an RCT then propensities would be constant and the condition would hold trivially.


In a nutshell, the OHC motile forces, through the microanatomy of the CP, feed forward and backward, in harmony with each other, resulting in bidirectional coupling between BM segments in the longitudinal direction.

due to the opposite action of OHC forces on the BM and the RL, the motion of BM segment i − 1 reinforces that of segment i while the motion of segment i + 1 opposes that of segment i, as described in detail in [4].


That is, such that the actual sample complexity for the learning rule on this specific distribution is governed, up to polylogarithmic factors, by this quantity.

we present the γ-adapted-dimension k γ (D).


In this paper we draw upon and extend the existing bandit literature to solve the advertisement problem in the case of unknown CTR.

first in Section 3 we show that the unbudgeted variant of the problem (Cell V in Figure 2) is an instance of the multi-armed bandit problem.


It is often referred to as the cluster assumption in semisupervised learning.


We revisit fuzzy neural network with a cornerstone notion of generalized hamming distance, which provides a novel and theoretically justified framework to re-interpret many useful neural network techniques in terms of fuzzy logic.

we conjecture and empirically illustrate that, the celebrated batch normalization (BN) technique actually adapts the "normalized" bias such that it approximates the rightful bias induced by the generalized hamming distance.


However, consistent with the past literature on monotonic neural networks, we found it difficult to control the shape constraints on neural networks as flexibly as with the lattice models.

for our shape-constrained neural networks (SCNNs) we could not produce a monotonic response for an input without also constraining it to be convex/concave, and we must select either convex or concave constraints -that is, we cannot impose both for different features.


The running time of the proposed algorithm is is the time required to compute the matrix V k , the top-k right singular vectors of X. Theorem 1 says that one can construct k features with sparsity O(k) and obtain a comparble regression error to that attained by the dense top-k PCA features, up to additive term that is proportional to To construct the features satisfying the guarantees of the above theorem, we first employ the Algorithm DSF-Select (see Table 1 and Section 4.3) to select r columns of X and form the matrix C ∈ R n×r .

now, let Π C,k (Y) denote the best rank-k approximation (with respect to the Frobenius norm) to Y in the column-span of C. Π C,k (Y) is a rank-k matrix that minimizes Y − Π C,k (Y) F over all rank-k matrices in the column-span of C. Efficient algorithms are known for computing Π C,k (X) and have been described in [2].


The motivation behind local receptive fields is computational efficiency.

rather than having each hidden unit connect to the entire input image, each unit is instead connected to a small patch (see figure 2a for an illustration).


Here we use elliptical slice sampling [22].

we sample where p(w n |x n , A, ψ) ∼ N (S N ψAx n , S N ), W = [w 1 . . . w N ], W \n is matrix W without column n, S −1 N = ψA ⊤ A + I, and we have marginalized out f as in (9) with W in place of X.


(1) From the input distribution p we construct a new distribution p ′ that is "close" to p but more discrete.

p ′ is based on a new weight function w ′ that takes values only in a discrete set of geometrically increasing weights.


State-of-the-art deep neural networks have recently been shown to be very unstable to worst-case perturbations of the data (or equivalently, adversarial perturbations) [17].

despite the excellent classification performances of these classifiers, well-sought perturbations of the data can easily cause misclassification, since data points often lie very close to the decision boundary of the classifier.


It is generated by linear combination of dictionary atoms A and an associated unknown number of binary causes z, all corrupted by some additive noise .

we assume that x = Az + where ∼ N (0, σ 2 1) and z ∼ IBP(α).


Thus, for the purposes of this paper, we consider background-variation as just another transformation.

"clutter-transformations" map images of an object on one background to images of the same object on different backgrounds.


MCTEIL outperforms existing methods in terms of the average cumulative return.

mCTEIL shows the best performance for the reacher problem with a smaller number of demonstrations while GAIL often fails to learn the task.


For the synthetic corpus, we use both C code and the Eigen [31] C++ library.

random linear algebra operations are procedurally generated from high-level templates using different parameters, such as data types, operations, and dimensions.


We will answer this question in a combinatorial setting with non-negative monotone submodular cost functions on the edge set cardinality.


If an algorithm always finds a hypothesis ĥ with err(D, ĥ) ≤ err(D, H)+ for > 0, then for any η ∈ (0, 1) there is a distribution D with η = err (D, H) such that the auditing complexity of this algorithm for D is Ω(dη 2 / 2 ).

when η is fixed while → 0, the auditing complexity scales as Ω(d/ 2 ), similar to the passive sample complexity.


We demonstrated on a real dataset (of unusually large size) the explanatory as well as predictive power of our method, as compared to two conventional measures of behavior.

the flexibility of the model allowed us to address an important open question in behavioral psychology, known as lapse.


Four main terms constitute our bound: the approximation error due to the limited hypothesis space (first term), the variance (second and third terms), the distance to the prior (fourth term), and a constant term decaying as O(N 2 ).

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


Our results suggest that learning measurement strategies jointly with computational inference is both useful and possible.

our approach can be used directly to learn other forms of optimized multiplexing patterns-e.g., spatio-temporal multiplexing for video, viewpoint multiplexing in lightfield cameras, etc.


Recently, Ramaswamy & Agarwal [39] introduce the notion of convex calibrated dimension, as the minimal dimensionality of the score vector that is required for consistency.

they showed that for the Hamming loss on T binary variables, this dimension is at most T . In our analysis, we use scores of rank (T + 1), see (35) in App.


For example, it is not always clear what it means to minimize the value of a risk measure or to minimize the worst case expected cumulative cost under an uncertainty set.

the iterated risk measure studied in [13,14,19] is defined recursively, which prevents an intuitive understanding of its meaning.


This is analogous to many active learning algorithms.

bach derives a sampling distribution for active learning under the assumption that the current model gives a good approximation to the conditional probability p(y|x) [1].


We evaluate MHE on large-scale ImageNet-2012 datasets.

we perform experiment using ResNets, and then report the top-1 validation error (center crop) in Table 6.


To bound the sample complexity of the DFS routine, since there are M states per level and the consensus test returns true once elimination has been performed, we know that the DFS does not visit a large fraction of the search tree.

this means DFS is invoked on at most MH nodes in total, so we run elimination at most MH times, and we perform at most MKH consensus tests.


Terms (s 1 + λ * α )1 and s 2 ψ can be viewed as cost shaping.

they effectively transform the costs g(x, a) to g(x, a) + s 1 + λ * α + s 2 ψ(x), so that the constraint T α Φr − Φr − λ * α 1 ≥ 0 can be met.


Suppose now that each player randomizes their play according to the sequence of probability distributions on S i generated by DA with regularizer h i .

suppose that each σ i t is a random variable with the following distribution: Example Consider a zero-sum game G 1 between two players on the unit interval with payoff function u(s 1 , s 2 ) = s 1 s 2 − a 1 s 1 − a 2 s 2 , where a 1 = e−2 e−1 and a 2 = 1 e−1 .


For r = σ B σ , this is equivalent to the backprop for the transformation x−µ σ , but combined with the null-space projection.

batch Renormalization allows us to normalize using moving averages µ, σ in training, and makes it work using the extra projection step in backprop.


We can implement a conditional version of MAF by stacking MADEs that were made conditional using the above strategy.

in a conditional MAF, the vector y becomes an additional input for every layer.


They demonstrated that the relationships between these notions of sample complexity are substantially more delicate even in the most well-studied settings of SCO.

let K be a unit 2 ball and F be the set of all convex sub-differentiable functions with Lipschitz constant relative to 2 bounded by 1 or, equivalently, ∇f (x) 2 ≤ 1 for all x ∈ K. Then, known algorithm for SCO imply that sample complexity of this problem is O(1/ 2 ) and often expressed as 1/ √ n rate of convergence (e.g.


Although we focused on learning coupling between arms, there are other kinds of reward structure learning that may account for a broad variety of human decision making performance.

allowing dependence between the probability of reward at a site and previous actions can produce large changes in decision making behavior.


We now move to discussing safe subgame-solving techniques, that is, ones that ensure that the exploitability of the strategy is no higher than that of the blueprint strategy.

in subgame Resolving [6], a safe strategy is computed for P 2 in the subgame by solving the augmented subgame shown in Figure 3b, producing an equilibrium strategy σ S . This augmented subgame differs from Unsafe subgame solving by giving P 1 the option to "opt out" from entering S and instead receive the EV of playing optimally against P 2 's blueprint strategy in S. the augmented subgame for Resolving differs from unsafe subgame solving as follows.


Since the mixing proportions are shared, the learned decomposition must be consistent with content and link statistics.

this coupling allows the model to take evidence about link structure into account when making predictions about document content and vice versa.


Here, we employ the Cayley transformation [15] to maintain orthogonality for V and U .

we update V by where ∇V is the gradient of the objective w.r.t.


. . , F k . We require that the product of the potentials in these subnetworks maintain the same information as the original MRF.

if we originally have a factor φ i ∈ F and associated factors One method of partitioning that achieves this equality is simply to select, for each potential φ i , one subgraph in which it appears unchanged, and set all of the other φ (l) i to be 1.


This results in 11 binary channels of size 40 × 40.

there is a channel for Ms. Pac-Man, each of the four ghosts, each of the four blue ghosts (these are treated as different objects), the fruit plus one channel with all the pellets (including power pellets).


From this fact we now argue that where H is the history after the misprediction.

the probability mass under I G of the consistent goal set after the misprediction is less than half that of the consistent goal set the misprediction.


As a means to describe the properties of disentangled representations, factorial representations have been motivated by many [1,2,3,22,32,33].

appendix B of [22] shows the existence of the total correlation in a similar objective with a flexible prior and assuming optimality q(z) = p(z).


For example, keeping the same classes, exchanging the class labels ¤ and leads to a new partitioning, which is not structurally different.

label values are only known up to a permutation.


To set these parameters, we used the following parameter optimization procedure: we randomly partitioned each dataset into 4 folds and, for each tuple (λ, β, K) in the set of possible parameters (described below), we ran MDeepBoostSum, with a different assignment of folds to the training set, validation set and test set for each run.

for each run i ∈ {0, 1, 2, 3}, fold i was used for testing, fold i + 1 (mod 4) was used for validation, and the remaining folds were used for training.


To find the ROC curve for our meta-classifier, we plot P D against P F for all 0 ≤ α ≤ 1.

for each y ∈ {0, 1} n we can compute Pr[ℓ(Y) > ℓ(y)|H 0 ], which gives us one value for τ * and a point in ROC space (P F and P D follow directly from L and P ).


The method proposes to integrate the M -estimation into the standard incremental PCA calculation.

each newly coming data point is re-weighted by a pre-defined influence function [11] of its residual to the current estimated subspace.


Then, under Assumption 3.1, it attains r SR α (6) in the sense of Definition 3.1.

(i) lim inf n→∞ βtp (n) − max {0, max a∈A β tp (q n ; a) − α} ≥ 0 , and (ii) lim sup n→∞ βfp (n) ≤ 0, for every strategy of the opponent, almost surely.


In this paper, we extend such result by weakening the assumptions on the regularization term.

the main result of this paper implies that, for a sufficiently large family of regularization functionals, radial nondecreasing functions are the only lower semicontinuous regularization terms that guarantee existence of a representer theorem for any choice of the data.


To generate the embedding q for a query q using Algorithm 1, we (i) represent the query using its DAG dependency graph, (ii) start with the embeddings z v1 , ..., z vn of its anchor nodes, and then (iii) we apply geometric operators, P and I (defined below) to these embeddings to obtain an embedding q of the query.

we introduce two key geometric operators, both of which can be interpreted as manipulating the denotation set associated with a query in the embedding space.


However, even when this distance is large, the difference between two alignments may not be significant if both choices' scores are nearly the same.

if the optimal profile alignment's score is only slightly lower than the optimal IB class alignment's score as computed with the original profiles, either might be correct.


It also meshes well with an updating scheme analogous to that in steps 3-4: updating only when no actual improvement (in terms of constraint violation) is realized by that choice.


When the Gaussian has covariance matrix Σ, the graph is encoded in the sparsity pattern of the precision matrix Ω = Σ −1 .

edge (i, j) is missing if and only if Ω ij = 0.


There are a number of possible sign-function approximations, including hyperbolic and arc tangent, and shifted sigmoid function, the latter of which is the most flexible because of its free parameter β.

3 the sigmoid function has the form f (z) = 1 1+e −βz , where the free parameter β (an inverse temperature) determines how well the curve will approximate the discontinuous function.


Given training data {x (q) , y (q) } N q=1 , where each n (q) } is a set of documents of query q, and each y (q) = {y } is a set of ranking scores associated with the documents of query q, we employ Maximum Likelihood Estimation to estimate the parameters {α, β} of C-CRF.

we calculate the conditional log likelihood of the training data with respect to the C-CRF model, log Pr(y (q) |x (q) ; α, β).


1 , l ′ 2 to be as aligned as possible and compute correlation coefficients.

given the output of step 1, 2 ) } between the transformed subspaces.


Lemma 1 below states that no linear combination of the vectors can tolerate a single Byzantine worker.


Equation 2 is a convex function, and thus has a unique optimum.

6 we have logs of a linear function, which are each concave.


In this paper, we study the limits of MSE recovery of high-dimensional, graph-structured noisy patterns.

we assume that the patterns x are generated from a probabilistic model, either Gaussian graphical model (GGM) or Ising (binary), based on a general graph structure G(V, E), where V denotes the p vertices and E denotes the edges.


That is , boundaries created for the source grammar learning can be used, possibly with some modifications, as one of the boundaries for the target grammar.

the source of savings may not be as high level as FSM state space but some lower level features at the syntactic processing level.


Our main research question is how to design a policy class that can capture the salient properties of how expert agents execute trajectories.

we present a general policy class that utilizes a goal space G to guide its actions to create such trajectory histories.


The 3DCNN baseline uses a 3D CNN to process the whole input directly.

the 3DCNN baseline is similar to existing generative models [44,35].


lemma 4.1 implies that it is 0.5-weakly submodular for every 0  r  |N|.


Therefore, we modify the algorithm to use ordinary finite integers.

instead of a single integer, the buffer is represented with a sequence of 64-bit integers (B 0 , .


The elastic net can be viewed as a trade-off between 1 regularization (the Lasso) and 2 regularization (Ridge regression [9]), depending on the relative values of λ 1 and λ 2 .

when λ 2 = 0, (3) is equivalent to the Lasso.


When using weighted entropy approximations, it makes sense to optimize over both the linearization g and the weights ρ jointly.

let T be some set of weights that yield an entropy approximation H that upper bounds H. Then, if we expand H in problem (3), we obtain minimize Note that inside the supremum, both g and ρ appear only linearly, and there is no summand that has terms from both of them.


In our implementation, we changed the auxiliary reward f in the terminal state.

when the agent encounters a terminal state S ⊥ , it receives an auxiliary reward f (S, S ⊥ ) = γϕ(S ⊥ ) instead of f (S, S ⊥ ) = γϕ(S ⊥ ) − ϕ(S).


Retrace(λ) is an off-policy correction method, so it learns from n-step off-policy data by multiplying each term of the loss by a correction coefficient, the trace, in order to re-weight the data distribution to look more like the on-policy distribution.

at each timestep, Retrace(λ) updates the coefficient for that term by multiplying it by λmin (1, π(as|xs) µ(as|xs) ).


This is a consequence of the well known duality between strong convexity and smoothness [e.g., 21].


In situations where information is only gained after each stage (such as in section 4), we can also train the classifiers "bottom-up."

we can start by only adding classifiers to the last stage.


Another implication is that influence at larger time window T is harder to estimate, since σ(A, T ) will generally be larger and hence require more random labels.

once we know how to estimate the influence σ(A, T ) for any A ⊆ V and time window T efficiently, we can use them in finding the optimal set of C source nodes A * ⊆ V such that the expected number of infected nodes in G is maximized at T . we seek to solve, where set A is the variable.


While the resulting detector is fast and accurate, the process of designing a cascade is not.

vJ did not address the problem of how to automatically determine the optimal cascade configuration, e.g.


( 2) has some nice and important properties.

the following Lemma shows that it is invertible and its Jacobian determinant has closed form.


However, to the best of our knowledge, all existing homotopy analysis either only work for specific algorithms [6,25,31] or solve only special problems [33].

none of them provides all-purpose black-box reductions like we do.


To formulate a family of objective functions which depend on both p(s), and the tuning curves, we first rely on Fisher information, I f (s), which can be written as a function of the tuning curves [1,18]: The Fisher information can be used to express lower bounds on mutual information [16], the variance of an unbiased estimator [18], and perceptual discriminability [19].

the mutual information, I( r; s), is bounded by: where H(s) is the entropy, or amount of information inherent in p(s), which is independent of the neural population.


A well known example is Dantzig Selector, which minimizes a sparsity-inducing `1 norm with an `1 norm constraint.

let X 2 R n⇥d be a design matrix, y 2 R n be a response vector, and ✓ 2 R d be the model parameter.


The performance of algorithm A is measured by the number of matches found by A within the T rounds.

if M t (A) is the number of matches uncovered by A after t rounds of a given run, we would like to obtain lower bounds on M T (A) that hold with high probability over the random generation of boys and girls that log into the system as well as the internal randomization of A.


however, is that Poisson processes do not accurately capture the statistics of neural spike trains [2,9,16,1].

the probability of observing a spike is not a functional of the stimulus only; it is also strongly affected by the recent history of spiking.


Let P k : R m×n → R m×n denote the orthogonal projection on to the set C(k).

it is well known that P k (X) can be computed efficiently by computing the top k singular values and vectors of X.


Let F m,δ,n represent the set of those Boolean functions on {0, 1} n that can be computed by a thresholded RBM network of size m with margin δ.

then, there exists a fixed number K such that, when m 2 ≤ δ2 αn , for any constant α < 1/2, the ratio of the size of the set F m,δ,n to the total number of Boolean functions on {0, 1} n (which is 2 2 n ), rapidly converges to zero with n. While interesting, existential results such as the one above does not give us a clear picture of what a particular hard-to-compute function for RBM networks might look like.


In an extreme case, a particular sub-group may be empty.

it is possible that none of the participants of the treatment or the control group expressed a particular belief regarding their treatment assignment.


Our Contribution (II): We provide new analysis for more general optimization problems beyond general convexity and strong convexity, as well as more general algorithms.

we provide several concrete examples: (1) VGD achieves linear convergence under the Polyak-Łojasiewicz (PL) condition (possibly nonconvex), which matches the state-of-art result in [4]; (2) NAG achieves accelerated linear convergence (with a better constant term) under both general convex and quadratic growth conditions, which matches the state-of-art result in [19]; (3) Coordinate-gradient-type algorithms share the same ODE approximation with gradient-type algorithms, and our analysis involves a more refined infinitesimal analysis; (4) Newton's algorithm achieves linear convergence under the strongly convex and self-concordance conditions.


In the past, such theoretical concerns in optimization played a major role in shrinking the field of deep learning.

many researchers instead favored classical machining learning models (with or without a kernel approach) that require only convex optimization.


By applying the Gaussian RBF kernel, we can derive a closed form of g ik and the gradient as A pleasing feature of this formulation is that it is convex in the argument w, allowing us to apply various convex optimization techniques to solve the problem efficiently.


Despite its simplicity, this model remains among the top performing models in terms of likelihood given to left out patches and also gives excellent performance in image restoration [23,20].

it outperforms BM3D on image denoising and has been successfully used for other image restoration problems such as deblurring [19].


The filter can be learned quickly in a supervised manner, requiring no time intensive grid search or coordinate ascent.

we optimize a smooth binomial log-likelihood loss function with respect to a time series convolution kernel, along with the inverse covariance regularization parameter, using L-BFGS [17].


We demonstrate empirically the effectiveness of our theoretical results in predicting when networks are able to start training.

we note that many popular initializations fail our criteria, whereas correct initialization and architecture allows much deeper networks to be trained.


However, in general this would be a complex matrix optimization problem.

it may require sophisticated optimization tools such as semidefinite programming, which may not scale well with the size of W . Fortunately, as we shall show, problem (2.4) can be efficiently solved by alternately minimizing over D and W . in Section 4 we shall show that Ω f is a function of the singular values of W only.


We compare the NN set-up to random Fourier basis expansions [34], which have been successfully applied to BO [35,36].

let U ∈ R D×P and b ∈ R D be such that U ∼ N (0, I) and {b j } D j=1 ∼ U([0, 2π]).


To make inference tractable, we focus on the large-graph, small-neighborhood limit as n → ∞ and ε n (x) → 0.

we will suppose that there exist scaling constants g n and a deterministic continuous function ε : D → R >0 so that where the final convergence is uniform in x and a.s. in the draw of X .


Similar to other large-scale recommender systems that must address the ICS problem [6], we view recommendation as a binary classification problem as opposed to a regression problem.

for an item t i and user u j , the outcome e ij ∈ {0, 1} indicates whether the user engaged with the item.


We consider learning our model with experience replay [17], a widely used technique in recent stateof-the-art systems [18].

the learning process consists of multiple stages, and at each stage, the agent interacts with the environment using a fixed exploration policy ⇡ b (a t |x S 1:t , x A 1:t , a 1:t 1 ) to collect M episodes of data {w S 1:Ti , w A 1:Ti , a 1:Ti , r 1:Ti } M i=1 and saves them into a replay memory D. (We will discuss the choice of ⇡ b in section 4.)


In this paper, we propose to discover a large initial set of data-driven attributes using a dictionary learning method.

assume that we have a set of N videos in a n-dimensional feature space X = [x 1 , ..., x N ], x i ∈ R n , then a data-driven dictionary is learned by solving the following problem: where are the sparse codes of X, and T specifies the sparsity that each video has fewer than T items in its decomposition.


We observe a similar trend in other settings.

we study how the feature dimensionality, the sample size, and the task number affect the required computation cost (in seconds) for convergence.


We can equivalently think of this as a stochastic power iteration algorithm.

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


We mimic this standardization idea for other distributions as well.

for exponential family distributions, we use transformations of the form (sufficient statistic expected sufficient statistic)=(scale factor).


In fact, optimality of affine policies for simplex uncertainty sets holds for more general formulation than considered in [8].


The ⟨M o ⟩ matrices are updated using the least-mean square algorithm.

matrix M o k is updated when option o k is terminated at time k + 1, i.e., when q k+1 = 1.


Simply put, there are better polynomials than A q for denoising tail singular values.

we can use a lower degree polynomial, allowing us to compute fewer powers of A and thus leading to an algorithm with fewer iterations.


Our improvements are not solely due to the use of a better CNN.

fDA [10] also uses ResNet [7], but Ours a +ResNet outperforms it by 1.8% on test-dev.


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).

4 Results We have fabricated a chip containing the basic synapse circuit as shown in Figure 2 through MOSIS in a commercially-available 1.5 µm, double poly fabrication process.


If it is known that rewards are only received upon transitioning to the terminal state and take values between 0 and 1, it might be appropriate to use a variation of the aforementioned feature based model that applies a sigmoidal function to the linear combination.


Temporal alignment of time series has been an active research topic in many scientific disciplines such as bioinformatics, text analysis, computer graphics, and computer vision.

temporal alignment of human behavior is a fundamental step in many applications such as recognition [1], temporal segmentation [2] and synthesis of human motion [3].


In this paper, we combine recent non-Euclidean gradient methods with element-wise adaptive learning rates, and show their applicability to a variety of models.

our contributions are: i) We demonstrate that the objective function in feedforward neural nets is naturally bounded by the Schatten-∞ norm.


We can monitor how the risk bound changes as the number of examples increases, and perhaps even use the bound to define an early stopping criterion for the training algorithm.

we could stop processing examples when the risk bound becomes lower than a predefined threshold.


An MDP M is communicating if and only if it has a finite diameter.

for any two states s = s , there exists a policy π such that the expected number of steps to reach s from s, T π s→s , is at most D, for some finite D ≥ 0.


It is computationally convenient to compute z U (h) recursively as importance weights, just as in a sequential importance sampling particle filter [11]; this only assumes we have access to the likelihood of the observations (i.e., state transitions).

the weights are initialized as z U m (h t ) = 1 M ∀m and are then updated recursively using the likelihood of the dynamics model for that particle of observations as z U m (has ) ∝ z U m (h)P (s |a, s, P m ) = z U m (h) P m (s, a, s ).


For the purpose of our analysis, we assume a consistent read model.

our analysis assumes that the vector x used for evaluation of gradients is a valid iterate that existed at some point in time.


A particular labelling of variables v is specified by a function f whose domain corresponds to the indices of the random variables and whose range is the index of the label set, i.e.

f : random variable v a takes label l f (a) .


Solving an MDP means to find a policy π * that maximizes the expected long-term reward: π * ∈ arg max π∈Π J π D . For any MDP there exists at least one deterministic optimal policy that simultaneously maximizes V π (s), ∀s ∈ S. For control purposes, it is better to consider action values Q π (s, a), i.e., the value of taking action a in state s and following a policy π thereafter: Furthermore, we define the advantage function: that quantifies the advantage (or disadvantage) of taking action a in state s instead of following policy π.

for each state s, we define the advantage of a policy π over policy π as A π π (s) = A π (a|s)A π (s, a)da and, following [14], we define its expected value w.r.t.


This number is overall bounded (over all external loop cycles) by the number of times we can make a cell of matrix m turn from false to true (which is O(n 2 )) plus the number of times we ignore an element because the matrix cell was already set to true (which is at most O(n) per each V j , as this is the maximum number of descendants of V j and each of them can fall into this category only once, so again there are O(n 2 ) times in total).

each element being removed from a todo list is either ignored (matrix already set to true) or an entry in the matrix of descendants is changed from false to true, and this can only happen O(n 2 ) times.


Formally, the inverse filtering problems considered in this paper are as follows: Finally, we consider the more general setting where the posteriors we obtain are corrupted by noise (due to, e.g., quantization, measurement or model uncertainties).

we consider the case where the following sequence of noisy posteriors is obtained over time: from the sensor system.


Background subtracted images play a fundamental role in making inferences about objects and activities in a scene and, by nature, they have structured spatial sparsity corresponding to the foreground innovations.

compared to the scale of the scene, the foreground innovations are usually not only sparse but also clustered in a distinct way, e.g., corresponding to the silhouettes of humans and vehicles.


The reward distributions are assumed to be exactly generalized extreme value distributions.

[21] assumes that the distributions are exactly Gumbel, P (x) = exp(−(x − m)/s)), and [9], that the distributions are exactly of Gumbel or Fréchet P (x) = exp(−(x − m) α /(sα))).


Most of the research has focused on formulating robust classification problems that can be efficiently solved via convex optimization.

the robust classification method developed in [6] is based on the criterion which is similar to the Fisher discriminant ratio f . With a specific uncertainty model on the means and covariances, the robust classification problem with discrimination criterion g can be cast as a second-order cone program, a special type of convex optimization problem [5].


We presented a new, kernel-based reinforcement learning method that overcomes several important shortcomings of temporal-difference learning in continuous-state domains.

we demonstrated that the new approach always converges to a unique approximation of the optimal policy and that the quality of this approximation improves with the amount of training data.


As such, we extend the ventral stream model to be more biologically realistic.

the V1 neurons that project to the ventral stream now have temporal receptive fields (RFs) [17], not just spatial ones.


1 and ignoring constants, finding the MAP assignment is seen to be equivalent to the following combinatorial optimization problem: where the indicator variable x it = I[z i = t] denotes the assignment of word i to topic t. 2.1 Exact maximization for small number of topics Suppose a document only uses ⌧ ⌧ T topics.

t could be large, but we are guaranteed that the MAP assignment for a document uses at most ⌧ di↵erent topics.


Because stage s depends on the historical path only through the state variables (x, x, i, j, s), C(x, x, i, j, s) is well defined and (x, x, i, j, s) transits in a Markov chain with the next state being (x, x, i, j + 1, s + 1) if stage s does not succeed and being (x + , x+ , i+1, j, s+1) if stage s succeeds, where x+ =SVRG HEB (x, T s , R s , 0.5) and x+ = arg min x∈Ω ∇f In the next, we will use backward induction to derive an upper bound for C(x, x, i, j, s) that only depends on i and j but not on s, x and x.

we want to show that where A i := We start with the base case where i = S 1 .


6 The sign of t i ( ) in positive proximity 7 of 0 is the same as the first (i.e., relative to the lowest degree monomial) non-zero coefficient of the expansion of t i ( ) around 0.

there exists a ¯ > 0 such that t i ( ) has the same sign as the first non-zero derivative of t i evaluated in 0 for all 0 < < ¯ .


So, with the shortcut connection of identity mapping x, the whole module of layers fit F(x) + x for the desired underlying mapping H(x).

the only residual mapping F(x), defined by H(x) − x, is learned with non-linear layers.


. . u L ) ∈ U n denotes the current state of the parents (L = |pa(n)|).

we can express the probability of finding node n in state x after some small time-step h, given that it was in state x at time t with x, x ∈ X n as The CIMs are connected to the joint intensity matrix R of the CTMC via amalgamation -see, for example, [13].


In the ambiguous learning setting [9,10], which is a generalization of semi-supervised learning, the labeler reveals a label set Ŷi ⊆ Y for each training example xi such that ŷi ∈ Ŷi .

for each training example, the learning algorithm is given a set of possibile labels the example can have (semi-supervised learning is the special case where each label set has size 1 or k).


The intuition is that at any given point in time, the mixture frame is explained by very few active elements from the training data.

we need the mixture weight distributions and the speaker priors to be sparse at every time instant.


Let us first define notations that are to be used subsequently: we use a linear decoding function, as: f θ (x) = X T θ, to predict the traces of finger movements y as target variable.

we define y ∈ R Y where Y corresponds to the number of samples in the finger traces.


5 shows how the approximate algorithm is able to recover a qualitatively correct structure that Democrats and Republicans typically vote along their respective party ideologies (note that there might be more than one qualitatively correct structure).

we obtain a structure where no Democrat is sandwiched between two Republicans, or vice-versa.


Our high-level idea is to measure the probability density of test sample on feature spaces of DNNs utilizing the concept of a "generative" (distance-based) classifier.

we assume that pre-trained features can be fitted well by a class-conditional Gaussian distribution since its posterior distribution can be shown to be equivalent to the softmax classifier under Gaussian discriminant analysis (see Section 2.1 for our justification).


Note that (C1) and (C2) are two commonly seen guarantees for matrix approximation problems.

(C2) is stronger in the sense that the spectral of the approximated matrix H(w t ) is well preserved.


The situation is complicated by the fact that decompositions like (3) and ( 5) are not unique.

there is no guarantee that the {M α } induced modules will be amongst the modules featured in (3).


To date, most research in this direction has focused on approximation algorithms for finding the set with the highest probability, sometimes called the maximum a posteriori (MAP) set [Gillenwater et al., 2012, Kathuria and Deshpande, 2017, Zhang and Ou, 2016, Nikolov and Singh, 2016.

the MAP objective has recently 32nd Conference on Neural Information Processing Systems (NeurIPS 2018), Montréal, Canada.


For every neural net, our algorithm produces substantially higher estimates of the adversarial frequency.

our algorithm estimates ρ(f, x * ) with substantially better accuracy compared to the baseline.


For hypothesis spaces H, H ′ , we say H essentially contains H ′ if for any h ′ ∈ H ′ , there is an h ∈ H satisfying e(h) ≤ e(h ′ ) for all D, where e(h) = E D l(y, h(x)).

for any distribution D, the approximation error of H is at most the error of H ′ .


If we denote by L the MAP estimate of L, then it follows that L+ is the solution to the program minimize Note the similarity with Mahoney-Orecchia regularized SDP of (2).

if X = {X : Tr(X) = 1} ∩ X , then the two programs are identical except for the factor of log |X| in the optimization criterion.


Unlike d , however, H drops the dependence on ν, giving (1 − γ)q = Hr.

given H we can easily recover the state-action values of π.


Changing the variational approximation in this manner permits us to return the model into its original form and set α = α 0 .

we first expand p(x, D) to obtain p α (x, D).


Here we address the identifiability of the convolution decomposition of C for k and w estimation.

we briefly study the uniqueness of the form C = K > diag(w)K for a single subunit and multiple subunits respectively.


We study the residual bootstrap (RB) method in the context of high-dimensional linear regression.

we analyze the distributional approximation of linear contrasts c ( β ρ − β), where β ρ is a ridge-regression estimator.


In this paper we study the problem of automatically discovering users' social circles.

given a single user with her personal social network, our goal is to identify her circles, each of which is a subset of her friends.


Finally, our problem is fundamentally different from the sequence transduction method in [15], although it also exploits language models for sequence prediction.

the method in [15] is a fully supervised learning in that it requires supervision at the sequence level; that is, for each input sequence, a corresponding output sequence (of possibly different length) is provided as a label.


Consider two sets of solutions ✓ and ✓ such that Lt1 (✓ sh , ✓ t1 ) < Lt1 ( ✓sh , ✓t1 ) and Lt2 (✓ sh , ✓ t2 ) > Lt2 ( ✓sh , ✓t2 ), for some tasks t 1 and t 2 .

solution ✓ is better for task t 1 whereas ✓ is better for t 2 .


Let G = (V, E) be a pdimensional graph and let G = (V, E) be an estimated graph.

we define precision Precision is the number of correctly estimated edges divided by the total number of edges in the estimated graph; recall is the number of correctly estimated edges divided by the total number of edges in the true graph; the F 1 -score can be viewed as a weighted average of the precision and recall, where an F 1 -score reaches its best value at 1 and worst score at 0.


The bound O n − α 1+α log 3+αβ 2 n δ coincides with O(n − α 1+α log n) (up to a logarithmic factor) in expectation for convex and smooth loss functions [21], and largely improves the bound O(n − α 1+2α log n) in expectation for convex and non-smooth loss functions [21].

if α = 1 we derive the optimal bound O(n − 1 2 log 3+β 2 n δ ) in a general case with neither Bernstein conditions on variances nor capacity assumptions on hypothesis spaces (up to a logarithmic factor).


This paper investigates the complexity of such compositional maps and contributes new theoretical results regarding the advantage of depth for neural networks with piecewise linear activation functions.

our analysis is not specific to a single family of models, and as an example, we employ it for rectifier and maxout networks.


We also provide the first general runtime proofs for dual-tree algorithms on bichromatic problems.

we give the first proofs of worst-case O( ) runtimes for the following all-query problems: • All Nearest-neighbors: For all queries ∈ , find * ( ) ∈ ℛ such that * ( ) = arg min ∈ℛ ( , ).


When n is not too small (n = 50), RUMs with normal distributions fit better than P-L.

for log-likelihood, predictive log-likelihood, and AIC, RUMs with normal distributions outperform P-L with 95% confidence in both datasets.


A distinctive feature in convolutional phase retrieval is that L is not a polynomial.

hence, it may be challenging to posit a Q L dec which "recouples" back to L. in the existing form, we need to tolerate an approximation error as L ̸ = L. By the triangle inequality, ( As discussed above, the sup w∈S L(a, w) can be sharply controlled via its moments bound in (19).


In brief, a Workload Generator produces an HTTP-based workload of dynamically varying intensity that is routed to a blade cluster, i.e., a collection of blade servers contained in a single chassis.

(we use an IBM BladeCenter containing xSeries HS20 blade servers.)


In the setting of 0-1 loss, some basic answers have begun to emerge.

it is possible to demonstrate the Bayes-risk consistency of methods based on minimizing convex surrogates for 0-1 loss, with appropriate regularization.


For a new problem, the input may be encoded differently (e.g., different image size, different pixel ordering, different color representation), but there is a transformation T that maps this problem into the same latent space as the previous problem so that the prior solution can be re-used.

for each problem category i = 1, 2, . . . , N , there is a latent problem space Λ i and a solver S i : Λ i → Y i .


The proposed approach offers new foundations, with promising results and room for improvement.

we believe exciting avenues of research concern the learning of C h from examples and extensions to other areas such as in remote sensing, using application-specific forms of C. Acknowledgments.


To construct directionally selective place field estimates in 2D we took inspiration from recent analyses of 2D phase procession [22] conditioning the responses on the main direction of motion within the place field.

we used our estimation of a traditional 2D place field to define a region of interest (ROI) that covers 90% of the field for each cell (Fig.


We therefore find that for ReLU, p(q ⇤ ) = 1 2 is independent of q ⇤ , whereas for hard-tanh, ) depends on q ⇤ .


We propose a balance-based approach that, like the existing weighting-based methods, also reweights the historical data to make it look as though they were generated by the policy being evaluated or learned and potentially denoises outcomes in a doubly robust fashion, but rather than doing so circuitously via a plug-in approach, we do it directly by finding weights that optimize for balance between the weighted data and the target policy in the given, finite sample.

we formalize balance as a discrepancy between the reweighted historical covariate distribution and that induced by the target policy and prove that it is directly related to the worst-case conditional mean square error (CMSE) of any weighting-based estimator.


This demonstrates that a low rank E but a high rank G give the best performance on this dataset.

requiring a low rank G may hurt the performance of recovering a low rank E. The constructed G by our method is plotted in Figure 4, where columns represent cell line features (i.e., principle components) and rows represent drug features.


However, it is straight-forward to sample from this distribution without recourse to f (x) or p(dx).

the second term can be accessed through the law of total probabilities: where the first term [dp | φ 1:n ] is the stick-breaking construction and the term [φ 1:n | X, θ] can be targeted with a Gibbs sampler.


Neurons in the primate visual system exhibit a sparse distribution of firing rates.

neurons in different visual cortical areas show an approximately exponential distribution of their firing rates in response to stimulation with natural video sequences [1].


Encoding and decoding of the neural data is achieved with a Kalman filter which has a number of advantages over previous linear filtering techniques.

the Kalman filter reconstructions of hand trajectories in off-line experiments are more accurate than previously reported results and the model provides insights into the nature of the neural coding of movement.


We proposed an efficient sampling scheme for learning SPAMs.

we showed that with only a few queries, we can derive uniform approximations to each underlying univariate function of the SPAM.


Two inconvenient facts make it difficult to realize this goal in a computationally efficient manner: 1) model complexity -we typically need a large number of parameters to accurately model a system's response p(r t |{ x t }, {r t−1 }, θ); and 2) stimulus complexity -we are typically interested in neural responses to stimuli x t which are themselves very high-dimensional (e.g., spatiotemporal movies if we are dealing with visual neurons).

it is computationally challenging to 1) update our a posteriori beliefs about the model parameters p( θ|{r t }, { x t }) given new stimulus-response data, and 2) find the optimal stimulus quickly enough to be useful in an online experimental context.


To gain some intuition on the behavior of these interpolationnorms, first note that for any p ≥ 1 and any v ∈ R m it holds that max In other words, the interesting range of t for the Next, we prove a theorem which states that interpolating a p-norm with the ∞-norm is approximately equivalent to restricting that p-norm to the absolutely-largest components of the vector.

the 1 − ∞ interpolation norm with parameter t (with t chosen to be an integer in [1, m]) is precisely equivalent to taking the sum of the absolute values of the t absolutely-greatest elements of the vector.


Therefore, before we begin, we need to automatically augment the simple training outlines with a corresponded labeling.

we want to transform arbitrary outlines into useful training instances with consistent elements as depicted in the pipeline of our LOOPS method (Figure 1, first two boxes).


Indeed, personalization is applied in a variety of fields in order to improve user satisfaction.

consider the case where each player may promote a set of items, where different items may be targeted towards different users, and the size of this set is determined exogenously (e.g., by her budget).


We therefore use a set of time and label specific basis state functions.

we use binary basis state functions f l ,d1,d2,τ indexed by a label l ∈ L, two time offsets 0 ≤ d 1 < d 2 and a threshold τ > 0.


The game theoretic formulation of the binding problem described previously involves a transport mechanism that is specific to individual sites.

proteins are allocated to the proximity of sites based on parameters E ij and occupancies α j associated with individual sites.


Next, we provide a mechanism for bounding the Gaussian width w(Ω R ) of the unit norm ball in terms of the Gaussian width of a suitable cone, obtained by shifting or translating the norm ball.

the result involves taking any point on the boundary of the unit norm ball, considering that as the origin, and constructing a cone using the norm ball.


The results show that our graphembedding approach achieves large improvement over sequence-based models.

our approach improves the state-of-the-art accuracy on HolStep by 7.3%.


In this paper, we design, to the best of our knowledge, the first online learning algorithm for the triggering functions in the nonparametric regime.

we tackle the challenges mentioned above, and the only assumption we make is that the triggering functions f i,j (t)s are positive, have a decreasing tail, and that they belong to an RKHS.


these results we observe that, in general, dimensionality reduction is effective: the accuracy of the four considered methods is similar or better than the Base method, in which complete trajectories are used for classification.

base does not perform well when the trajectories are not smooth (Medflies).


This shift is necessary to verify the assumption that the starting point (now given by Y ) has a separable distribution.

it generates correlated input data X while still allowing for the computation of the entropy of any T . At the start of a neural network training, weight matrices initialized as i.i.d.


Then The second step relies on the relationship between the maximum of a set of values and the value chosen by the soft-argmax, which we refer to as the stable-max.

we define where e v should be thought of as the relative weight assigned to value v i .


Let us imagine that the gambler, with the benefit of hindsight, considers what could have happened had he always bet a constant fraction of his wealth on heads.

a simple exercise shows that his wealth would become (1 ) This is optimized at = G T , which gives a simple expression in terms of KL-divergence for the maximum wealth in hindsight, exp , and the former is well-approximated by exp(O(G 2 /T )) when G is not too large relative to T . with knowledge of the final G, a naïve betting strategy could have earned the gambler exponentially large winnings starting with constant capital.


Similarly, the target domain-specific code v y is learned for target domain Y.

to learn the source and target domain specific codes v x and v y , we should minimize the following loss function: where θ represents the model parameters.


The advantage of modeling by MVB is that the sparsity in f ω 's is sufficient and necessary for the conditional independence in the graph, thus fully specifying the graph structure.

y i , Y j are conditionally independent iff f ω = 0, ω ⊇ {i, j}.


Thus beam search is commonly employed to find a reasonably good y. Beam search is a heuristic search algorithm that maintains the top-scoring partial sequences expanded in a left-to-right fashion.

it keeps a pool of candidates each of which is a partial sequence.


The conditional intensity can thus be derived given by: where δ ap = t ap − t ap−1 with p being defined by arg max{p : t ai < t}.

p the index associated to the closest previous event to t. δ ap is thus the previously observed increment.


The (η, γ)-local separation property also holds when there are at most η paths of length at most γ in G between any two nodes (henceforth, termed as the (η, γ)-local paths property).

there are at most η − 1 overlapping 4 cycles of length smaller than 2γ.


Then the source vector can be recovered with a high probability (close to one) by solving (P 1 ).

s is sufficiently close to the original source vector, and s is close to zero vector.


Linear regression (shown as the dotted lines in Figure 1(a)) gives the function y = 0.0094x + 0.3656 for Diverse (R 2 = 0.9206, p = 0.0024) and y = 0.0050x + 0.3542 for Uniform (R 2 = 0.8712, p = 0.0065).

the linear approximation for the winning rate of Diverse increases roughly twice as fast as the one for Uniform as the number of agents increases.


Theorem 4 implies the following "worst-case" upper bounds on influence, which only depends on |A|: Theorem 6.

the influence of A ⊆ V in an independent cascade model satisfies if λ ∞ < 1, we have Note that when λ ∞ > 1, the bound (8) exceeds n for all large enough n, so the bound is trivial.


We analyze decoder accuracy within each session using a leave-one-out approach.

we test the decoder on each held-out block using the remaining blocks in the same session for training.


When provided with "dirty" graphs, for example an e-mail network or a text data set, NCut has the aggravating tendency to return a super-cluster.

nCut often returns a partition P = (A 1 , .


PLANET for high-dimensional datasets, we measured the training time on a series of synthetic datasets parameterized by p. For each dataset, approximately p 2 features were categorical, while the remaining features were continuous.

from Figure 4, we see that, YGGDRASIL scales much more effectively as p increases, especially for larger D. for D = 15, YGGDRASIL is initially 3× faster than PLANET for p = 500, but is more than 8× faster for p = 4000.


Figure 4(c) shows that averaging over several masks reduces bias significantly.

the bias increases considerably for longer sentences when only a single sample is used, but remains roughly constant when we average multiple samples.


The assumption r k=1 n −α k = o(1) is tantamount to saying that the number of tiny communities cannot be too large (e.g., the number of polylogarithmic-size communities cannot be a power of n).

one needs to have mostly large communities (growing like n ǫ , for some ǫ > 0) for this assumption to be satisfied.


With these goals in mind, we devise an empirical approach to generate the pairs (x ni , y ni ) ∈ N . The main idea is to sample a series of candidate neighborhoods for each instance x ni , evaluate their relative success at predicting the training instance's label, and record the best candidate.

for instance x ni , we first compute its proximity to the M − 1 other training images in the feature space.


Moreover, the distance was inversely proportional to the performance of the solution.

the FQI solution that performed the best, was the closest (in 2 norm) to the DQN solution, and vice versa.


In the sample compression setting, each classifier is described by a subset S i of the training data, called the compression set, and a message string σ that represents the additional information needed to obtain a classifier.

in this setting, there exists a reconstruction function R that outputs a classifier R(σ, S i ) when given an arbitrary compression set S i and a message string σ.


In this paper, we consider latent variable models, where a latent variable can alter the relationships (both structural and parametric) among the observed variables.

we posit the observed data as being generated from a mixture of graphical models, where each mixture component has a potentially different Markov graph structure and parameters.


Using an appropriately constructed feature graph, we can model the case in which the underlying distributions are believed to be Gaussians with known, identical variances but with unknown means.

the case in which there are k disjoint classes of features {C i } k i=1 whose weights are drawn i.i.d.


In this section, we present our main results.

we present the algorithm and the main theorem that bounds its extreme regret.


These afford optimal accuracy and complexity scaling for large node degrees and achieve the CH-divergence limit for logarithmic node degrees.

the SBM can be learned efficiently for any diverging degrees.


This risk-sensitive MDP becomes equivalent to the robust MDP having the objective (2) when the objective of the risk-sensitive MDP is to find the optimal π with respect to an iterated conditional tail expectation (ICTE) [13]: where ICTE (N ) α denotes the ICTE defined for N decision epochs with parameter α.

iCTE (N ) α is defined recursively with conditional tail expectation (CTE) as follows [13]: where we define The right-hand side of (4) evaluates the CTE of this random CTE is also known as conditional value at risk or average value at risk and is formally defined as follows for a random variable Y : where V α ≡ min{y | F Y (y) ≥ α}, and F Y is the cumulative distribution function of Y .


The asymptotic convergence of the Bayes-Sard cubature method is established and the theoretical results are numerically verified.

we report two orders of magnitude reduction in error compared to Bayesian cubature in the context of a high-dimensional financial integral.


The proof uses the PAC-Bayes bound, which states that for all prior distributions P, Pr (VQ: KL(eQlleQ) ~KL(QIIP) A choice of the "posterior" Q completes the proof.

the Q we choose depends upon the direction w, the margin 'Y, and the stochastic error E. Q equals P in every direction perpendicular to w, and a rectified Gaussian tail in the w direction 2 • The distribution of a rectified Gaussian tail is given by R(p,) = 0 for x < p, and R(p,) = F(p,~.


The goal is to safely learn about the dynamics from measurements and adapt the policy for performance, without encountering system failures.

we define the safety constraint on the state divergence that occurs when leaving the region of attraction.


As a result, structured physics knowledge can be embedded into larger systems, allowing them, for example, to match observations by performing precise simulations, while achieves high sample efficiency.

in this paper we demonstrate how to perform backpropagation analytically through a physical simulator defined via a linear complementarity problem.


Due to this equivalence between saliency and discrimination, the principle of discriminant saliency can be easily translated into an optimality criteria for the design of saliency algorithms.

it is naturally formulated as an optimal feature selection problem: optimal features for saliency are the most discriminant features for the one-vs-all classification problem that opposes the class of interest to all remaining classes.


The rich body of work on welfare economics offers several axioms to characterize the set of all welfare functions that pertain to collective rationality or fairness.

any such function, W, must satisfy the following axioms [Sen, 1977;Roberts, 1980]: if everyone is better off under b 0 , then W should strictly prefer it to b.


In the model selection scenario, it is equal to P (D new |G MAP ).

in the model averaging scenario, it is equal to averaging over all the DAG structures, G. G∈G P (D new |G)P (G|D).


Natural candidates for parametrizing the agent's dynamics model are Bayesian neural networks (BNNs) [19], as they maintain a distribution over their weights.

this allows us to view the BNN as an infinite neural network ensemble by integrating out its parameters: we utilize a BNN parametrized by a fully factorized Gaussian distribution [20].


In this work, we use the (µ/ρ+λ)-ES [6].

we have the following transformation and selection schemes: 1.


In general each time that d i=1 u 2 i t∈M∪U x 2 t,i ≤ s u 2 with s small enough, it is possible to show that, with an optimal tuning of r, this bound is better of the Perceptron's one.

using a proof similar to the one in [1], in the conservative version of this algorithm, it is enough to have s < M R 2 2d , and to set r = sM R 2 M R 2 −2sd .


Let E be the set of subsets E of edges between the p nodes, satisfying |E| ≤ q and representing a decomposable model.

then it holds with probability at least 1 − the extended BIC with parameter γ selects the smallest true model.


Condition (8) quantifies the capacity assumption and is related to covering/entropy number conditions (see [25] for further details).

it is known that condition ( 8) is ensured if the eigenvalues (σ i ) i of C satisfy a polynomial decaying condition σ i ∼ i − 1 γ .


These basis functions are used as features in the analysis of attention.

we use 120000 8 × 8 RGB image patches from natural scenes for training.


we consider models in a bounded convex subset 8 of 4 .


In the second, simpler model, that we are also interested in here, there is no side-information, but the agent is given a model that describes the possible relations between the arms' payoffs.

in "linear bandits" [10,8,11,12], each arm a ∈ A is associated with some d-dimensional vector m a ∈ R d known to the agent.


Students "learn" over time via an increase to the concept skill which corresponded to the exercise they answered.

the BKT prediction degraded substantially as the number of hidden concepts increased as it doesn't have a mechanism to learn unlabelled concepts.


We particular study the use of Laplace variance mixtures in sparsity modeling.

moreover, we will see that t plays the role of a tuning hyperparameter.


hence, clause a is issuing a warning to variable i.


If we consider orthogonality as a loose proxy for diversity, methods such Principal Component Analysis and Singular Value Decomposition [15] become relevant.

consider the set S obtained by the LS algorithm when it terminates.


In this section, we state and prove a theorem that can be used to determine when any particular unitary parameterization does not have capacity to represent all unitary matrices.

neither restricted-capacity nor full-capacity unitary matrix optimization require gradient clipping.


PNJGL also leads to the most accurate estimates of Θ 1 and Θ 2 .

the network differences are generated from node perturbations: a few nodes are perturbed across networks, and most or all edges stemming from such nodes differ between networks.


The complete proof of Theorem 2 is given in the supplementary material.

a naive application of Fano's inequality only recovers the bound in (10) with `= p⇡.


1. and Ω = ℜ r+ , leads to MIL versions of the Quadratic-Programming-SVM [3].

the optimization problem reduces to: min where T is the within class scatter matrix, µ j = 1 rj X j e is the mean for class j. X j ∈ ℜ rj×n is a matrix containing the r j representative points on ndimensional space such that the row of X j denoted by b i j = B i j λ i j is the representative point of bag i in class j where i = {1, . . . , r j } and j ∈ {±}.


The collection of all permutations of n objects forms a non-abelian group under composition, called the symmetric group of order n, denoted as S n . Let S n−k denote the subgroup of S n consisting of all permutations whose first k positions are fixed: ( The right coset S n−k π = {σπ|σ ∈ S n−k } is a subset of permutations whose top-k objects are exactly the same as in π.

• All the probabilistic model based methods are better than BordaCount, the heuristic method.


To circumvent these difficulty, we devised a modified algorithm called PMED-Hinge (Algorithm 1) that involves extra exploration.

assuming that each convex optimization yields an optimal value, such an alternate optimization Algorithm 3 Cutting-plane method for obtaining {q i,l } on Line 12 of Algorithm 1 1: Input: the number of iterations S, nominal constraint {θ i }, .


In this setting, the p margin, i.e., how robustly classifiable the data is for * p -bounded classifiers, enables dimension-independent control of the sample complexity.

machine learning models are often susceptible to adversarial perturbations of their inputs.


In many real world applications, this property may be crucial.

( 14) can be re-written as follows The key point of this paper, is to note that the matrix K = K ij = K(x i , x j ), i, j = 1, . . . , N , is the data affinity matrix, and that K(x i , x j ) is a Gaussian RBF kernel function.


The most important features are the length of the time series (Feature 1), the fraction of the time for which the patient is at positive risk (Feature 9), and the maximum risk attained (Feature 14).

intuitively, current risk should depend on previous risk.


A uniform transfer IDS game is one in which the transfer risks emanating from a given player are independent of the transfer destination.

furthermore, it can be verified that this algorithm will in fact be able to compute approximate NE in which some players choose to invest and others not to, even in the absence of any dominant strategies.


We are interested in private robust data analysis, specifically, robust low-rank approximation of a matrix with respect to entrywise `p-norm for p 2 [1, 2), under the constraints of differential privacy.

in addition, we also show that ⇧ is an orthonormal rank-k projection matrix.


For example, the solution to the anagram puzzle RYTEHO is THEORY.

if a row or column of a sub symbolic ordering matrix is close to uniform, the selection of a bigram in that row or column will be somewhat arbitrary.


To deal with this problem, many researchers have developed learning methods for graphical models that depend on efficient approximate inference.

we have implemented LASH with infinite discounting of future rewards, but extending to finite discounting might produce better results.


The major contribution of this paper is to give an affirmative answer to this question.

2011,Mazumder and Hastie 2012Danaher et al.


( 4) to address the labeling ambiguity in multi-instance scenarios.

in addition, the B2B distances often do not truly reflect the semantic similarities [9].


The distinction here is significant, as junction points where two decision boundaries meet might actually have a very large (or infinite) curvature (even in linear classification settings), and the curvature condition in Corollary 1 typically does not hold for this global curvature definition.

hence, for semi-random noise that is mostly random and only mildly adversarial (i.e., the subspace dimension is small), affine classifiers remain vulnerable to such noise.


So we can compute local minimums in successive regions [s l , s l+1 ] (l = 1, . . . , d s − 1) and get the global minimum over region [c ik , e ik ] by comparing all local optima.

for those two problems, we also compare our proposed coordinate descent method described in Table 1 with some off-the-shelf solvers such as the CVX solver [11] with respect to the running time.


This material is based upon work supported in part by the U.S. National Science Foundation Grant 1330008, by the Department of Homeland Security, Science and Technology Directorate, Office of University Programs, under Grant Award 2013-ST-061-ED0001, by ONR Grant 50202168 and US AF contract FA8650-14-C-1728.

nearly all previous approaches require solving a non-convex problem and resort to alternating optimization [25,19] or greedy approximation [11].


Specifically, the natural modification of CAL produces a method that (in the realizable case) makes the same number of label requests as before, except that now it makes zero mistakes, since CAL will request a label if there is any uncertainty about its label.

the following algorithm is essentially taken from [DHM07,Han11], adapted here for this streambased setting.


We showed in Section 3 that SE is more expressive than our proposal.

another, secondary, motivation comes from the recent work of [8], in which the authors learn word embeddings from free text, and some 1-to-1 relationships between entities of different types, such "capital of" between countries and cities, are (coincidentally rather than willingly) represented by the model as translations in the embedding space.


In the following theorem statement, I(•) denotes the indicator function, π(a|x) the probability that the logging policy chooses action a on input x, and V h π our estimator as defined by Equation 2 based on parameter τ . Lemma 3.1.

the techniques reported here lift these restrictions, allowing the learning of a policy for choosing actions given features from historical data where no randomization occurred or was logged.