One could straightforwardly instead use, for example, either a mixture of Gaussians, or, normalizing flows (Rezende & Mohamed, 2015;Kingma et al., 2016), to parametrize each inference network factor in order to improve expressivity, at the cost of additional implementational complexity.

if one were to use a provably universal density estimator to parameterize each inference network factor, such as that introduced in Huang et al.


In one variant, we do not use the foreground-background prior, which is termed no background-foreground prior.

instead of using Equation 9, we use Equation 4.


We also found that one translation was usually harder than the other.

the translation that required adding more details to the image was usually harder (e.g.


By properly tuning the elimination thresholds ε r of Algorithm 3 in accordance with the target accuracy ε, we can establish an explicit trade-off between the number of communication rounds and the number of arm pulls each player needs.

we can design a multi-player algorithm that terminates after at most R communication rounds, for any given parameter R > 0.


Common techniques include global eigenmodes for linearized dynamics (see, e.g., [3]), discrete Fourier transforms, POD for nonlinear dynamics [30,12], and balancing modes for linear systems [24] as well as multiple variants of these techniques, such as those using shift modes [22] in conjunction with POD modes.

pOD, which is in principle equivalent to principal component analysis, has been extensively applied to the analysis of physical phenomena [5,22] even though it suffers from numerous known issues, including the possibility of principal directions in a set of data may not necessarily correspond to the dynamically important ones.


Next, we explore different posterior distributions from computational perspectives.

we show how to learn the posterior model so to ensure the computational efficiency of its MAP predictor.


Essentially, after a pattern presentation the complete time course of the membrane potential during the presentation is examined, and if classification was erroneous, the synaptic weights which contributed most to the absolute maximum of the potential are changed.

the neurons would have to able to retrospectivly disentangle contributions to their membrane potential at a certain time in the past.


In the following, we will formally derive the mean estimation bias b(θ) of the proposed encodingdecoding framework.

we will study the conditions for which the bias is repulsive i.e.


We note that when the matrix U is not learned and we set U = I d×d , problem (2.4) computes a common set of variables across the tasks.

we have the following convex optimization problem We shall return to problem (2.5) in Section 4 where we present an algorithm for solving it.


For the calcium imaging, we use a standard model [7], where the concentration of fluorescent Calcium has a fast initial rise upon an action potential followed by a slow exponential decay.

we let z k i = [Ca 2+ ] k be the concentration of fluorescent Calcium in neuron i in time bin k and assume it evolves as first-order auto-regressive AR(1) model, where α CA is the Calcium time constant.


Thus, in all three cases, the claim is established.

we have X ∈ X c . This, together with for ǫ > 0 sufficiently small, which contradicts the fact that Xk is the projection of X k onto X c . This completes the proof of Lemma 4.1(c).


We state these technical bounds in Appendix E. 3 The wave-filtering algorithm Our online algorithm (Algorithm 1) runs online projected gradient descent [Zin03] on the squared loss Here, each M t is a matrix specifying a linear map from featurized inputs Xt to predictions ŷt .

after choosing a certain bank of k filters {φ j }, Xt ∈ R nk+2n+m consists of convolutions of the input time series with each φ j (scaled by certain constants), along with x t−1 , x t , and y t−1 .


The role of inhibition and the role of the excitation/inhibition balance in the emergence of synchronized patterns will be studied.

the impact on the phase diagram of individual parameter variations will be analyzed.


Neurophysiological findings support the existence of remembering memories and their involvement in credit assignment and learning in biological systems.

hippocampal recordings in rats indicate that brief sequences of prior experience are replayed both in the awake resting state and during sleep, both of which conditions are linked to memory consolidation and learning (Foster & Wilson, 2006;Davidson et al., 2009;Gupta et al., 2010;Ambrose et al., 2016).


The guarantees of our algorithms hold for all adversaries that stay within the noise budget, given that the input signals are sparse in the Fourier or related domains.

our defenses do not require prior knowledge of the adversary's attack strategy.


We cropped out patches of different sizes, in order to simulate different amounts of visual data that may be processed by the toddler's learning system.

we started with crops of 30 width (roughly corresponding to the area with high acuity) and increased the size in 10 increments up to 70 (the field of view of the head camera); examples are shown in Figures 2a and 2b.


Approaches that combine deep learning and RL have made significant advances [21,22,11].

dQN [21] combined Q-learning [36] with a convolutional neural network (CNN) and achieved state-of-the-art performance on many Atari games.


Some of the recent progress on the theoretical foundations of online learning has been motivated by the parallel developments in the realm of statistical learning.

this motivation has led to martingale extensions of empirical process theory, which were shown to be the "right" notions for online learnability.


An algorithm for the committing bandit problem is a combination of an allocation and a recommendation policy.

the algorithm has to decide which arm to pull during the first N slots, and then choose an arm to commit to during the remaining T − N slots.


Given matrices A, B, C 2 C m⇥k , the tensor product Another view of tensor is that it defines a multi-linear mapping.

for given dimension m C is defined as: for a 2 C m , we use V (I, I, a) to denote the projection of tensor V along the 3rd dimension.


For a point x ∈ S, we write ASSIGN(x) to denote the candidate center to which x is assigned at a given moment of the execution.


1 We leverage the geometry of this cone to determine subspace membership.

figure 1(b) considers a point x ′ ∈ R 1 different from x.


In this paper, we propose strategies that indicate that such advances can indeed be made.

we investigate the greedy coordinate descent algorithm, and note that performing the greedy step efficiently weakens the costly dependence on the problem size provided the solution is sparse.


The feature space is defined by the relationship Ф(x i ) T Ф(x j )=k(x i, , x j ).

inner product of mapped data is determined to by a kernel function k(.,.)


We would like to minimize the entropies of both the speaker dependent mixture weight distributions (given by P t (z|s)) and the source priors (given by P t (s)) at every frame.

we want to minimize H(z|s) and H(s) at every time frame.


Also, we constrain the normal predictions to have unit length.

the definition of unary and pairwise in our model are presented as follows.


. . , G Bn ) is the distribution over TREE A (T B1 , .

. . , T Bn ) satisfying: TREEDIST A (G 1 , .


We use the K-method to interpolate between the 1-norm and the ∞-norm, and to interpolate between the 2-norm and the ∞-norm.

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 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.


To efficiently compute terms of this type, we define Like the forward and backward matrices, α ⋆ (i, j) and β ⋆ (i, j) may be calculated via dynamic programming.

we have the base cases α ⋆ (i, 1) = 1{i = y ⋆ 1 } • α(i, 1) • Q ′ 1 (w) and β ⋆ (i, L) = 0.


These are the properties we need for correctness, and the applicability of the CLT combined with the proven base case completes the inductive proof.

the variance with recursive approximation is the exact variance σ 2 f plus the average of the variances σ 2 i of the approximated f i .


We provide in Theorem 3.2 a bound of the form R T (✓) 6 Õ(D(✓, ⇥ 0 )/ p T ) for a pseudo-metric D and any ✓ 2 B 1 .

we say that this bound is accelerable as the rate may decrease if D(✓, ⇥ 0 ) decreases with T . it yields an oracle bound of the form R T (✓) 6 O(k✓k 1 / p T ).


The minimax value is bounded as More generally, for any measurable function The following corollary provides a natural "centered" version of the distribution-dependent Rademacher complexity.

the complexity can be measured by relative shifts in the adversarial moves.


In contrast, a flower's beauty is greatest from up close, but can also be experienced from a range of distances and perspectives.

ρ g and δ g determine the scale and shape of the state reward function, with r i (S) = max(ρ g (1 − distance(S, i, G)/δ g ), 0), where distance(S, i, G) is the geodesic distance between agent i and the goal.


For the rest of the paper, unless noted otherwise, we use per-action regret as our performance measure.

per-action regret with respect to V ∈ D is defined as: (1) our notion of regret considers only the rounds in which V is awake.


This view of a feedforward network suggests variations in which other kinds of density models are used in place of Gaussians in the input space.

instead of performing pairwise comparisons between Gaussians, the units in the first hidden layer can perform pairwise comparisons between the densities of an input sequence under M different HMM's.


While the possibility of a reduced computational budget is readily apparent when a ceiling is imposed on the number of layers, our work primarily focuses on estimation accuracy.

it is well-known that when a signal dictionary has coherent columns, as quantified by a large RIP constant, then most tractable iterative algorithms are unable to find maximally sparse representations.


We therefore evaluate our algorithm by using the first convolutional layers of the vanilla topologies as "feature extractors" (mostly below 50% of the vanilla network size) and then learning a deep structure, "learned head", from their output.

the deepest layers of the vanilla network, "vanilla head", is removed and replaced by a structure which is learned, in an unsupervised manner, by our algorithm 2 .


This is shown in Figure 5, which compares D-EM to the EM implementations of the GENIE/SMILE and SAMIAM systems, 3 both of which were represented in previous inference evaluations [4].

we ran these systems on a chain network X 0 → • • • → X 100 , where each variable has 10 states, and using datasets with alternating observed and hidden variables.


We will view Π(s, g) as the set of actions that the agent considers acceptable (or equally good) in state s for goal g. The agent policy π always selects a i after its helper action h i whenever a i is acceptable.

π((s, h i ), g) = a i whenever a i ∈ Π(s, g).


Streeter and Golovin [26] study an online submodular maximization problem in the oblivious adversary model.

their result can cover the stochastic K-MAX bandit problem as a special case, and an O(K √ mT log m) upper bound on the (1 − 1/e)-regret can be shown.


However, unlike condition E G , condition E vol ∩ E bal is not directly satisfied under that regime.


Hence, under minimax criterion, we are looking for a decision rule δ * which minimizes the worst case misclassification rate.

the robust decision rule is given by where D is the set of all randomized decision rules.


X and symmetric linearly independent A i (otherwise, consider optimization over a larger matrix W X X Z with A operating symmetrically on the off-diagonal blocks).

this setting covers problems including matrix completion (where A i are indicators, [5]), matrix reconstruction from linear measurements [15] and multi-task training (where each column of X is a predictor for a different task and A i have a single non-zero column, [2,1]).


These problems are modeled as cost-based MDPs.

a cost function c(s, a) is used instead of the reward function R(s, a), and the min operator is used in the Bellman equation instead of the max operator.


where C M (G) is the set of all M -covers of G. Theorem 2.2 claims that the optimal value of the MAP LP is equal to the supremum over all MAP assignments over all graph covers, appropriately scaled.

the proof of this result shows that, under mild conditions, there exists an M -cover H of G and an assignment x H such that In this section, we will describe how to extend the previous results from discrete to continuous MRFs (i.e., X = R) using graph covers.


• Our method does not force the network to adapt to specific (given) quantization outputs (e.g., integers) but learns the quantization levels jointly with the weights, enabling application to a wider set of problems.

we explore vector quantization for the first time in the context of learned compression and demonstrate its benefits over scalar quantization.


This embedding simultaneously represents not only the relations between objects and classes, but also the relations within the set of objects and within the set of classes -each defined in terms of relations to points in the other set.

objects that tend to be associated with the same classes should be embedded nearby, as should classes that tend to have the same objects associated with them.


Our approach is to simultaneously estimate the rigid motion and learn the shape PDF.

we estimate R, D, θ, and σ 2 to maximize ∝ p(P|R, D, S, σ 2 )p(S|θ)dS The key idea is that we can estimate shape and motion while learning the parameters of the PDF p(S|θ) over shapes.


Semi-supervised and unsupervised domain adaptation: The proposed approach can be easily extended to take advantage of additional unlabeled data to improve the estimation of our model.

extra unlabeled target task data can be used to refine the factors in the R-Vine decomposition of p t which do not depend on y.


It would be worthwhile to consider how the model presented here could be implemented with such a neural mechanism.

one might expect that the sudden change in posterior probabilities over the hypotheses associated with the decision task would be reflected in sudden changes in response pattern in such populations [16].


A detailed proof is provided in Appendix C. The main tool of the proof of this rather surprising result is Lindsay's (1983) geometric analysis of the likelihood of nonparametric mixtures, based on Minkovski's theorem.

lindsay's (1983) Theorem 3.1 ensures that, when the trace of the likelihood curve is compact, the likelihood function is maximised for a finite mixture.


The observation that recent memories are more likely to be lost than old memories in these cases has generally been interpreted as evidence that the role of these medial temporal lobe structures in the storage and/orretrieval of declarative memories is only temporary.

several investigators have advocated the general idea that, in the course of a relatively long time period (from several days in rats up to decades in humans), memories are reorganized (or consolidated) so that memories whose successful recall initially depends on the hippocampus gradually become independent of this structure (see Refs.


We modify this benchmark by introducing soft constraints defining a weighted distribution over valid traces, indicating traces that meet certain criteria should be sampled more often.


The other important difference between ELBO and RELBO is the residual term which is expressed through E s [log p] E s [log q t ].

maximizing this term amounts to looking for a density with low cross entropy with the joint p and high cross entropy with the current iterate q t . the next component s t needs to be as close as possible to the target p but also sufficiently different from the current approximation q t . Indeed, s t should capture the aspects of the posterior that the current mixture could not approximate yet.


We consider the stepsize η needed to reach L min (under idealized assumptions) by satisfying We linearize L (around θ) and then, after denoting g = ∇ θ L, we solve for η: First of all, note the clear separation between g, the estimator of the gradient of L and v, the proposed update step.

moreover, it is easily seen that the final update step ηv is independent of the magnitude of v. the adaptation method only takes into account the "direction" of the proposed update.


The former is standard recognition accuracy, while the latter gives a more nuanced view of the "semantic magnitude" of the classifiers' errors.

we calculate the semantic similarity between classes (nodes) i and j using the metric defined in [36], which counts the number of nodes shared by their two parent branches, divided by the length of the longest of the two branches.


We first define an initial grammar that generates the exact set of training samples.

for each training sample x i ∈ X, there is an Or-rule S → A i in the initial grammar where S is the start symbol and A i is an And-node, and the probability of the rule is 1 X where X is the number of training samples; for each x i there is also an And-rule A i → a i1 a i2 .


However, the above infimum may not exist for a general configuration.

there might be a sample x ′ ̸ ∈ S(x) for which d β (x, x ′ ) ∈ W N (x) for all values of β ≥ 0.


These previous studies use dimensionality reduction methods that do not explicitly account for multiple populations of neurons.

these methods are invariant to permutations of the ordering of the neurons (i.e., the observed dimensions).


It is interesting to note that the quantity tr(T + − G + ) is related to the total resistance.

we have by equation (3.2) that tr(T . As noted in [10], the total resistance is a convex function of the graph Laplacian.


We observe that 20 Newsgroups and Sentiment Analysis datasets have predominantly marginal probability differences.

the frequency of a particular word varies from one category of documents to another.


if (v, P ) is a valid parent set choice for G with some P ⊇ P ∪ {v } then if (v, P ) is valid parent set choice for G and s(v, P ) > s(v, P ) for all P ∈ C then CMSL solution (i.e., under the current branch).

before the actual branch and bound, we precompute a DP table which stores, for each subset of vertices V ⊂ V of the problem instance, the score of the so-called BN extensions of V , i.e., the optimal BN structures over U = V \ V where we additionally allow the vertices in U to also take parents from V . This guarantees that the BN extensions are compatible with the vertex order in the current branch of the branch-and-bound search tree, and thereby the sum of the score of the current partial CMSL solution over V and the score of the optimal BN extensions of V is a valid upper bound.


First, their algorithm finds the smallest representation required to solve a problem, whereas our definition directly analyses the actual representations learned in practice.

they consider a strongly regularized auxilliary problem, whereas we examine given solutions directly.


Attribute preservation reasons that no changes of an attribute lead to no changes of its witness neurons.

it retains the attribute of the base image by copying it to other images.


The mixture random variable l, which is used to identify the Bayes nets, can take values from 1 to |E|, the number of edges in the graph, with uniform probability.

if k = |E|, then In what follows, we will also use the variable l to denote the corresponding edge in the MRF.


Similarly, the presented bound for r ∞ also implies sparsity, though it is the sparsity of w k − w. In fact, this is directly related with the sparsity of w k , considering that the classifiers can be postprocessed to subtract their average simultaneously whilst the classification decision won't change for any possible input.

theorem 3.2 also partially suits linear DNN-based classifications.


We propose an adaptive CNN (ACNN) that uses side information (e.g., the perspective weight) as an auxiliary input to adapt the CNN to different scene contexts (e.g., appearance changes from high/low angle perspectives, and scale changes due to distance).

we consider the filter weights in each convolutional layer as points on a low-dimensional manifold, which is modeled using a sub-network where the side information is the input and the filter weights are the outputs.


The intractability results for the feasibility of satisfying the together and apart constraints are different from those for constrained clustering [1].

finding a feasible description just for one cluster under apart constraints is intractable (see supplementary material) where as clustering under apart constraints is only intractable for any fixed k ≥ 3 [7].


for each ψik we compute Q \ ψik as in step 2-(a) of EP.


After finding an -approximate minimizer σ A in the learning step as above, Observation 5 tells us that the prediction g(σ A ) has loss ≤ V + 2 .

note that there is no algorithmic dependence on n in either step in a statistical learning setting.


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

we relate polynomial time solvability of a SAT subset to a notion of margin between sentences mapped by a feature function into a Hilbert space.


The Triad model is a type of transitivity template, as discussed in Section 4.

we introduce cliques over sets of three candidate links that form a triangle in the link graph.


As a result, N outputs are computed exactly while (V − N ) outputs are only an approximation based on the preview outputs.

only the selected indices use the full window for output vector computation.


The present work is a non-trivial generalization of their work that leads to improved convergence for a much broader family of non-smooth optimization problems.

their result is just a special case of our result when the constant θ that captures the local sharpness is one for problems whose epigraph is a polytope.


The characterization of the Bayes classifier for the family of performance metrics (4) given in Theorem 2 enables the design of practical classification algorithms with strong theoretical properties.

the algorithms that we propose are intuitive and easy to implement.


Third, we show how to further improve the complexity of our refinement procedure by exploiting the exchangeability property of successive refinements.

we show that the exchangeable refinements can be arranged on a lattice, which can then be searched via a heuristic search procedure to yield an efficient any-time, any-space algorithm for MAP inference.


A less well-known fact is that the locations of the optimal centroid configuration of k-means converges to a limit distribution closely related to the underlying density [9,18].

given a discrete set of centroids α k , to construct the corresponding discrete measure, where δ a is Dirac measure centered at a.


Each column of M defines a partition of Y into two disjoint sets.

binary learning algorithms are used to construct classifiers, one for each column t of M. the set of examples induced by column t of M is (Xl, Mt,yJ, .


However, when it comes to the reachability, MCTEIL outperforms other methods when they use the same number of mixtures.

mCTEIL can learn all modes in demonstrations at the end of learning while soft GAIL and info GAIL suffer from collapsing modes.


In this paper, we carefully studied the receptive fields in deep CNNs, and established a few surprising results about the effective receptive field size.

we have shown that the distribution of impact within the receptive field is asymptotically Gaussian, and the effective receptive field only takes up a fraction of the full theoretical receptive field.


On the other hand, notice that by definition of ξ t−1 , w(e) ≤ U t (e), ∀e ∈ E under event ξ t−1 .

using the monotonicity of f in the probability weight, and the fact that ORACLE is an (α, γ)-approximation algorithm, we have The next observation is that, from the linearity of expectation, the gap f (S t , U t ) − f (S t , w) decomposes over nodes v ∈ V \ S t . for any source node set S ⊆ V, any probability weight function w : E → [0, 1], and any node v ∈ V, we define f (S, w, v) as the probability that node v is influenced if the source node set is S and the probability weight is w. Hence, we have  In the appendix, we show that under any weight function, the diffusion process from the source node set S t to the target node v can be modeled as a Markov chain.


In an attempt to equalize that factor, we also ran an experiment where the Local method was allowed to check more candidate k values than our method.

it could generate as many (proximity-based) candidate neighborhoods at test time as would fit in the run-time required by our approach, where k ranges from 20 up to 6,000 in increments of 10.


Each edge (u, v) ∈ E G (T , T ) whose label has not been previously queried is then part of the test set, and its label will be predicted as Ŷu,v ← π T (u, i ) 11).

using the path obtained by concatenating Path T (u, i ) to edge (i , i ) to Path T (i , v).


In one mechanism, neural firing elevates the intracellular calcium level of a neuron, which induces an inward potassium current and subsequently hyperpolarizes the neuronal membrane potential [11].

strong neuronal response induces a negative feedback to counterbalance itself.


( 4) enforces winner-take-all competition between the groups of neurons.

the only sets of neurons that can be coactivated at a stable steady state are the groups and their subsets.


Equipped with this new tool, we prove a series of theorems for missing data recovery and matrix completion.

we prove that the exact solutions that identify the target matrix are included as critical points by the commonly used nonconvex programs.


For the noisy ERM algorithm in (33), choosing N i to be an exponential random variable with mean b i , we have where i o = arg min i L µ (w i ).

choosing b i = i 1.1 /n 1/3 , we have Without adding noise, the ERM algorithm applied to the above case when Compared with (35), we see that performing noisy ERM may be beneficial when we have high-quality prior knowledge of w o and when k is large.


We follow the authors' experimental settings.

for hyperparameter selection we started with the values of hyperparameters suggested by the authors and explored various values of the learning rate as well as the variance of the prior over the correction factor (λ v in [20]).


However, this confidence parameter appears in the analysis of the number of queries, so that we have a natural trade-off between the number of mistakes and the number of label requests.

under Assumptions 2 and 5, this procedure achieves an expected excess number of mistakes MT − M * T ≤ ⌊log(T )⌋ i=1 δ i 2 i , where ǫ T = T − α (α+2)(m+1) .


A hidden underlying assumption is that errors are confined to the output y.

the input data are not corrupted with noise; or even when noise is present in the data, its effect is ignored in the learning formulation.


We implement the LSH scheme, referring to the manual [39].

we implement the reuse of the h-functions, such that the number of actually evaluated h-functions is (k/2 • √ 2L), in contrast to (k • L).


Furthermore, let L be a continuous convex loss function satisfying some minor regularity conditions.

then it was shown for universal RKHS's and stritly positive nullsequences (λ n ) satisfying a regularity condition that the following statements hold for all ε > 0 and n → ∞: this result holds for L1-SVM's.


We note that unlike traditional approaches to novelty detection, which must use generative models or one-class classifiers in the absence of appropriate discriminative data, our dependence on object hierarchy provides discriminative data as a by-product.

after the recognition by a parent-node classifier, we may use classifiers trained to discriminate between its children to implement a discriminative novelty detection algorithm.


Since x 1 and x 2 are conditionally independent given the latent content variable z, (2) This suggests us learning an auto-encoder model.

a style transfer from x 2 to x 1 involves two steps-an encoding step that infers x 2 's content z ∼ p(z|x 2 , y 2 ), and a decoding step which generates the transferred counterpart from p(x 1 |y 1 , z).


Finally, we also point out that our measure of redundancy is rather crude.

it tends to saturate at very high or very low levels.


Note our techniques here are different from those used for the decreasing-step-size SGLD [5], which interestingly result in similar convergence patterns.

by adapting the same techniques used in the previous sections, we establish conditions on the step size sequence to ensure asymptotic convergence, and develop theory on their finite-time ergodic error as well.


KMUCB's estimation procedure leverages information across threshold values, where observations from higher thresholds are utilized to estimate mean payoffs for lower thresholds; information does not flow in the other direction, however, as a result of the censoring assumption.

for a given threshold index j, KMUCB tracks the arm elimination process as follows: for any threshold values below j, KMUCB believes that we have determined the best arm, and plays that arm constantly.


These results show that O(n) random features are needed for O(1/ √ n) learning bounds and choosing less random features leads to worse bounds.

these results suggest that that computational gains come at the expense of learning accuracy.


We assume that D is endowed with a kernel function k(•, •), and f has a bounded norm in the corresponding Reproducing Kernel Hilbert Space (RKHS) H k (D).

we assume that and kf k k is the RKHS norm in H k (D).


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

we define C class-conditional Gaussian distributions with a tied covariance ⌃: , where µ c is the mean of multivariate Gaussian distribution of class c 2 {1, ..., C}.


(K2) The kernel function K and its partial derivative satisfies condition K 1 in [16].

let We require that K satisfies for some positive number A, v, where N (T, d, ) denotes the -covering number of the metric space (T, d) and F is the envelope function of K and the supreme is taken over the whole R d . The A and v are usually called the VC characteristics of K. The norm F L2(P ) = sup P |F (x)| 2 dP (x).


Let letter j be reserved for index of the machine and k for the sample and letter i for the dimension.

x(j,k) i is the ith-coordinate of kth sample of machine j.


We have found that this approach leads to good empirical performance.

instead of using the weights α i,x we use the weights αi,x = P (x = When the posterior over f is represented as a GP, as in our experiments, the joint distribution over experimental outcomes in S i = {x i,1 , .


In this section, we report the main theoretical results of the paper.

we derive a performance bound for LSTD-RP in the Markov design setting, i.e., when the LSTD-RP solution is compared to the true value function only at the states belonging to the trajectory used by the algorithm (see Section 4 in [11] for a more detailed discussion).


The active set of a matrix A is defined as This set comes from the definition of the sub-gradient of (3).

as A (k) approaches the solution A * , Active(A (k) ) approaches (i, j) : A * ij = 0 .


A function φ : R → R is (M, δ, θ)-quasiperiodic if there exists a function φ : R → R which is periodic with period θ such that |φ(x) − φ(x)| < δ for all x ∈ [−M, M ].

any periodic function with period θ is (M, δ, θ)-quasiperiodic for all M, δ > 0.


In this paper we present a counterpoint to these pessimistic conclusions.

we present a general model for bounding any convex loss function, via a process of "loss clipping", that ensures bounded sensitivity to outliers.


Adaptor grammars extend PCFGs by inserting an additional component called an adaptor into the PCFG recursion (Equation 1).

an adaptor C is a function from a distribution G to a distribution over distributions with the same support as G. An adaptor grammar is a sextuple (N, W, R, S, θ, C) where (N, W, R, S, θ) is a PCFG and the adaptor vector C is a vector of (parameters specifying) adaptors indexed by N . C A maps a distribution over trees T A to another distribution over T A , for each A ∈ N . An adaptor grammar associates each symbol with two distributions G A and H A over T A .


( 5) by matrix inverse is a consistent algorithm if (T , H) are core w.r.t.

f and The proof can be found in Appendix C. While Theorem 1 guarantees consistency, we have not yet illustrated the benefits of using f . we want to characterize the sizes of the minimal core tests/histories, as they determine the number of model parameters.


To understand the applicability of Theorem 1, consider a concrete example with r = 2; let the corresponding weights w (1) and w (2) be generated by choosing each weight uniformly from [1,2].

the rank order for each component is a uniformly random permutation.


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

if applied twice to the same instance, h S may output different target values.


The two coordinate systems are closely related through the Fisher information matrices (FIMs) If we take the natural parameters or the expectation parameters as a coordinate system for an exponential family, a flat structure can be realized [1].

θ is called a 1-affine coordinate system, and the space spanned by θ is called 1-flat.


Moreover, note that the weighted averages of the m si in (10) and the Csi in (11), with weights given by ( 9), can be written as unweighted averages of the corresponding products π si m si and π si Csi .

each local estimate can be written as the ratio of two local estimates that converge to the correct values at the same exponential rate (as shown in the previous section).


Suppose P (X i = j) = p j ∀j and X i 's are independent.

the prior distribution of the labels is given by the vector p ≡ (p 0 , .


For fixed truncation levels L * and K * , the algorithm for posterior computation alternates between a simple and efficient simulation smoother step [24] to update the state space formulation of the nGP, and standard Gibbs sampling steps for updating the parametric components of the model.

considering the observations (y i , t i ) for i = 1, ..., T : A.


Since u i and v i play exactly the same role, it is also easy to see that the term approximation is always symmetric in u i and v i .

let us suppose that q (s i , u i , v i ) and consequently q \i (s i , u i , v i ) factorizes into independent terms for s i , u i , and v i , e.g., we can write By initializing ti (s i , u i , v i ) = 1, we have q(z) ∝ t 0 (z) and the factorization of q \i (s i , u i , v i ) follows directly from the factorization of t 0 (z) into independent terms for s, u, and v. for the first EP step, the factorization can be guaranteed.


Bayesian updating provides a principled and coherent approach to inference for probabilistic models [23], but is predicated on the model class being true.

for an observation x and a generative model F θ (x) parametrized by a finite-dimensional parameter θ ∈ Θ, then for some parameter value θ 0 ∈ Θ it is that x ∼ F θ0 (x).


Our LIRPG algorithm is also compatible with such actor-critic architectures.

for our experiments on Atari games we used a reasonably state of the art advantage actor-critic (A2C) architecture, and for our experiments on Mujoco domains we used a similarly reasonably state of the art proximal policy optimization (PPO) architecture.


Unfortunately, we show that it is not possible to obtain a algorithm where the degree of the polynomial does not depend on k even when the maximum parent set size is limited to 2, that is, there is no algorithm with running time g(k) poly(n) for any function g, unless the widely believed complexity assumption FPT = W [1] fails.

we show that Bayesian network structure learning with bounded vertex cover number is W [1]-hard when restricted to instances with parent set size 2, implying the above claim.


Nevertheless, there are still challenging technical problems during the training process of cascade detectors.

determining the optimal target detection rate for each stage of the cascade remains an unsolved issue.


4 (left) also gives results when the weights of the random RNNs are untied across layers in the tree (TNN).

different random weights are used at each depth of the tree.


R with the properties: ] and all integer m 0.

there exist constants a m,p 0, such that, for every f 2 W m p (⌦), we have (c) E continuously maps B ↵ p,q (⌦) into B ↵ p,q R d for all p 2 (1, 1), q 2 (0, 1] and all ↵ > 0.


As for the computation of the distribution of words given the hidden units, our feed-forward neural network approach leaves us free to use other conditionals than the V -way multinomial logistic regression implied by the Replicated Softmax.

we instead opt for a hierarchy of binary logistic regressions, organized in a binary tree where each leaf corresponds to a word of the vocabulary.


Since our boosting procedure does not change the distribution over unlabeled examples, it offers two advantages: (1) Agnostic weak learning may be defined with respect to a single distribution µ over unlabeled examples, and (2) The weak learning algorithms may be active (or use membership queries).

the agnostic weak learning hypothesis for C and µ is that for any f : given examples from D = µ, f , the learner will output a γ-optimal classifier for C. The advantages of this new definition are: (a) it is not with respect to every distribution on unlabeled examples (the algorithm may only have guarantees for certain distributions), and (b) it is more realistic as it does not assume noiseless data.


Since is an upper bound surrogate of the 0-1 loss, the optimal -risk E * is larger than the Bayes error R * , i.e., E * ≥ R * .

if the individual loss is the hinge loss then E * = 2R * .


Comparing this result to the known label complexity of CAL, which is (from [7]) we see that the major factor, namely the O (θ(ǫ) (d log(θ(ǫ)) + log(log(1/ǫ)/δ))) factor, is now inside the argument to the cost function c(•).

when this cost function is sublinear, we expect this bound to be significantly smaller than the cost required by the original fully-sequential CAL algorithm, which uses batches of size 1, so that there is a significant advantage to using this batch-mode active learning algorithm.


The training of Post progresses in a distributed fashion, with a parameter server maintaining the parameters of softmax placement distributions and 12 workers.

at each iteration of learning, the parameter server samples the distributions to obtain 12 placements, each to be evaluated at a worker.


It is essentially a Gauss-Seidel iteration for solving a set of normal equations in a function space.

we denote the estimates on the jth variable X j to be m j ≡ ( m j (X 1 j ), .


For s ≥ 0, define the moment generating function ϕ ].

then we have if Group-privacy Profiles Recall the kth group privacy profile of a mechanism M is defined as A standard group privacy analysis 5 immediately yields δ M,k (ε) ≤ (e ε − 1)δ M (ε/k)/(e ε/k − 1).


We have shown that dynamic Bayesian networks (DBNs) can be used to model the transitions between brain-and muscle-states as a subject performs a motor task.

a two-level hierarchical network was proposed for simultaneously estimating higher-level brain state and lower-level EEG and EMG states in a left/right hand movement task.


In this work, we propose a novel Dual-Agent Generative Adversarial Network (DA-GAN) for profile view synthesis, where the dual agents focus on discriminating the realism of synthetic profile face images from a simulator using unlabled real data and perceiving the identity information, respectively.

the generator needs to play against a real-fake discriminator as well as an identity discriminator simultaneously to generate high-quality faces that are really useful for unconstrained face recognition.


Our experimental results confirm that the proposed algorithms are significantly faster than other competitors under large-scale real-world instances.

for learning Gaussian process under Szeged humid dataset, our generic method runs up to six times faster than the state-of-art method [7] specialized for the purpose.


According to Theorem 4 of Zhao and Yu (2006) 2) , when samples follow the sparse model as in Assumptions 1-4 and λ ∼ = d −τ for 1/4 ≤ τ ≤ 1/2, the representation φ D (x) reconstructs the true sparse representation a of sample x with a small error.

when τ = 1/4 (i.e., λ ∼ = d −1/4 ) in Theorem 3, the failure probability δ t,λ ∼ = e − √ d on the margin is guaranteed to become sub-exponentially small with respect to dimension d and is negligible for the high-dimensional case.


While the subspace estimates are derived from the available samples only, or their embedding, the learning problem is concerned with the quality of the computed subspace as an estimate of S ρ (the true span of the support of ρ).

it may be of interest to understand the quality of these estimates, as a function of the algorithm's parameters (typically the dimensionality of the estimated subspace).


Another important measure of computation is storage, or the space used by a procedure.

we may wish to limit the number of bits used to represent our estimator f . The question then becomes, how does the excess risk depend on the budget B n imposed on the number of bits C( f ) used to encode the estimator?


In order to be able to deal with an infinite number of sources, we place a BNP prior over the binary matrix S that contains all variables s tm .

we assume that S ∼ mIBP(α, β 0 , β 1 ), i.e., S is distributed as a mIBP [23] with parameters α, β 0 and β 1 .


3 Starting from this edge label assignment, which is consistent with the two-clustering associated with the USPS labels, we generated a p-stochastic label assignment by flipping the labels of a random subset of the edges.

we used the three following synthetic datasets: DELTA0: No flippings (p = 0), 1,000 nodes and 9,138 edges; DELTA100: 100 randomly chosen labels of DELTA0 are flipped; DELTA250: 250 randomly chosen labels of DELTA0 are flipped.


The core idea of Greedy-MIPS is to iteratively traverse (j, t) entries of Z in a greedy sequence and collect newly observed indices j into C(w) until |C(w)| = B.

if r = ⇡(j, t|w), then (j, t) entry is visited at the r-th iterate.


In a lot of applications, e.g., influence maximization in social networks [15], community detection in graphs [13], etc., we are interested in selecting a small subset of vertices from a massive graph that "cover" in some sense a large fraction of the graph.

in section 6, we consider two fundamental set cover problems: Dominating Set and Vertex Cover problems.


Our work borrows ideas from the work of Warmuth and colleagues [11].

gentile and Warmuth [6] generalized and adapted techniques from [11] to the hinge loss which is closely related to the losses defined in Eqs.


Proposition 3.4 (Non-Convex Analysis -Parameterized Surrogates).

let us make the same assumptions as in Proposition 3.3, and let us assume that the functions ḡn are parameterized by some variables κ n living in a compact set K of R d . ḡn can be written as g κn , with κ n in K. Suppose there exists a constant K > 0 such that |g κ (θ) − g κ ′ (θ)| ≤ K κ − κ ′ 2 for all θ in Θ and κ, κ ′ in K. Then, every limit point θ ∞ of the sequence (θ n ) n≥1 is a stationary point of f -that is, for all θ in Θ, Finally, we show that our non-convex convergence analysis can be extended beyond first-order surrogate functions-that is, when g n does not satisfy exactly Definition 2.1.


In contrast, classical optimization analysis only yields upper bounds on the optimization error, which are unlikely to be tight in the presence of highly nonconvex geometry, especially around the stationary points that have negative curvatures along certain directions.

we identify three consecutive phases of the global dynamics of SGD, which is illustrated in Figure 1.


From the above theorem, the sequence {f (α k ) : k ∈ N} is monotonically increasing and the iteration complexity of SPGM is O(L/ε) for finding an ε-optimal solution.

in [18,17], Nesterov proposed an efficient smooth optimization method for solving convex programming problems of the form min where g is a convex function with Lipschitz continuous gradient, and U is a closed convex set in R n . suppose there exists L > 0 such that ∇g(x) − ∇g(x The smooth optimization approach needs to introduce a proxy-function d(x) associated with the set U .


We say that the probability distribution of X G is a Fiedler random field if it factorizes as where Z(θ) is the partition function.

a FRF is a Gibbs-Boltzmann distribution over graphs, with potential functions defined for each node pair {u, v} along with some neighboring subgraph G uv .


Note that we have tacitly assumed 2) is also known as the atomic norm with the set of atoms S F [20].

it will be useful to recall that the polar of a gauge Ω is defined by [19, §15]: the polar of a norm is its dual norm.


We also showed evidence (theoretical and empirical) that our adaptive sampling algorithms are better than sequentially sampling all the columns at once.

our theoretical bounds give a result which is tighter for matrices whose singular values decay rapidly.


Infants in the "no obstacle" group looked equally at both test stimuli.

infants in the "obstacle" condition appeared to interpret the sprite as moving in a rational goal-directed fashion, with the other object as its goal.


We study a class of large-scale, nonsmooth, and nonconvex optimization problems.

we focus on nonconvex problems with composite objectives.


Here, we point out that the target function Y has disappeared in the loss L previous (W ) (i.e., the loss value does not depend on the target function).

whatever the data points of Y are, their loss values are the same.


In this section, we give a specific accelerated scheme for a type of conic geometric optimization problems [25], e.g., the matrix Karcher mean problem.

the loss function of the Karcher mean problem for a set of N symmetric positive definite (SPD) matrices {W i } N i=1 is defined as where X ∈ P := {Z ∈ R d×d , s.t., Z = Z T 0}.


The other half of the lower bound is somewhat more difficult and we rely on the lower bound techniques of [DK16].

for n > 0, and 1/10 > > n −1/4 and for N sufficiently large, we produce a pair of distributions D and D over positive measures on [N ], so that: 1.


Based on this observation the basic idea in [7] is to consider both steps separately.

it turned out that the sets of ε-approximate minimizers and the set of exact minimizers M L,Q,x (0 + ) := ε>0 M L,Q,x (ε) play a crucial role.


Second, to address the challenge of sparse rewards, M-Walk exploits the fact that the MDP transition model is known and deterministic.

2 it combines Monte Carlo Tree Search (MCTS) with the RNN to generate trajectories that obtain significantly more positive rewards than using the RNN policy alone.


Define the regularized estimator as follows: θλ The goal of this paper is to choose good values of λ and analyze the subsequent impact on performance.

we wish to minimize the relative risk: which is the difference in risk (averaged over the training data) between the regularized and unregularized estimators; L n (λ) < 0 is desirable.


This paper is motivated by this scenario.


Such problems can be viewed as POMDPs with belief-dependent rewards [3] and their applications include active sensing [7], attention mechanisms for multiple-object tracking [22], as well as online summarisation of massive data from time-series [4].

we discuss the restless bandit [24] associated with the discrete-time Kalman filter [19].


The proofs of these bounds essentially follow from a very recent analysis of Thompson sampling, and the implied regret bounds are the same as those established for Thompson sampling.

since Ψ * t ≤ Ψ t (π TS ) where π TS is the Thompson sampling policy, it is enough to bound Ψ t (π TS ).


the AUC of our proposed method is 40.0% (22.1%), which is better than 32.7% (15.6%) of the softmax classifier and 32.9% (17.1%) of the Euclidean distance classifier after all new classes are added in the first (second) experiment.


Experiments show that our method outperforms strong baselines on three IWSLT tasks and two WMT tasks.

we achieve 34.43 and 29.01 BLEU score on WMT16 English-Romanian and WMT14 English-German tasks.


Agents are assumed to be rational and aim to maximize their expected scores.

if an agent i believes X is drawn from some distribution p, she will choose to report r i 2 argmax r2R E X⇠p [S(r, X)].


Then we start from ⌘ t = 1 and use backtracking line search to find the optimal ⌘ t 2 (0, 1] such that the Armijo condition [1] holds.

given a constant µ 2 (0.9, 1), we update ⌘ t = µ q from q = 0 and find the smallest integer q such that .


From the perspective of causality, the idea of a similarity measure is akin to the method of matching in counterfactual reasoning [13,14].

evaluating approximate counterfactuals by comparing individuals with similar values of covariates excluding the protected attribute.


Surprisingly, we show how TCL can be related to a nonlinear ICA model, when ICA is redefined to include temporal nonstationarities.

we show that TCL combined with linear ICA estimates the nonlinear ICA model up to point-wise transformations of the sources, and this solution is unique -thus providing the first identifiability result for nonlinear ICA which is rigorous, constructive, as well as very general.


Write T", for the transition probability matrix of the above Markov process.

the entry of T", in row (s, a) and column (s', a') will be equal to the probability of taking a step to (s', a') given that we start in (s, a).


A result of Lovász and Szegedy [16] is that any consistent, local random graph model is equivalent to the distribution on graphs defined by P W for some graphon W; the converse is true as well.

any such random graph model is equivalent to a graphon.


At the end of step I, there are m y component detectors, each of which can identify the component of a particular critical point of the object shape class C y .

when applied to a surface mesh, each component detector will determines which vertices it thinks belong to its learned component (positive surface points), and which vertices do not.


We first explore the relationship between minimum discrimination error, Jensen-Shannon Information and Fisher Information and show that the discrimination framework is more informative about the coding accuracy than Fisher Information as it defines an error for any pair of possible stimuli.

it includes Fisher Information as a special case.


The machines communicate via a publicly shown blackboard.

when a machine writes a message on the blackboard, all other machines can see the content of the message.


We often think of h as a distribution over topics.

the density of h ∈ ∆ k−1 (where the probability simplex ∆ k−1 denotes the set of possible distributions over k outcomes) is specified by: and α 0 := α 1 + α 2 + • • • + α k . Intuitively, α 0 (the sum of the "pseudocounts") characterizes the concentration of the distribution.


The best performing method is always either BAE-cr or BAE-tr, with BAE-cr having the best performance overall.

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


Learning is motivated from principles of discriminative learning rather than Bayes' rule, and it is optimizing a combination of an hand-crafted regularization term and the empirical loss.

our algorithm maintains an axis-aligned box, which only requires double number of parameters than maintaing a single weight-vector, a dominating model for many tasks.


TWF addresses this challenge by discarding terms having too high of a leverage on the search direction; this is achieved by regularizing the weights ν i via appropriate truncation.

where ∇ tr (•) denotes the truncated gradient given by for some appropriate truncation criteria specified by E i 1 (•) and E i 2 (•).


Interestingly, this sheds new light on connections between sparse methods and the literature of network flow optimization.

the proximal operator for the formulation we consider can be cast as a quadratic min-cost flow problem, for which we propose an efficient and simple algorithm.


Recently, many algorithms have been proposed for approximating the MAP problem [15,5,11,9,6].

linear programming (LP) relaxation of the MAP problem has emerged as a popular technique to solve large-scale problems such as protein design and prediction problems [17,10,11].


Table 1 shows that HIM improves the results obtained by the classifier by 6.9% for average accuracy and 5.3% for global accuracy.

in rows 6 and 7 in figure 4, one can observe that boosting gives many incorrect labels.


This question has been extensively studied in statistics.

savage studied the problem of designing reward functions that encourage probability forecasters to make accurate predictions [6].


Before defining the Lovász extension, we need the concept of a chain of subsets of [n]: A maximal chain is one where p = n. For a maximal chain, we have and there is a unique associated permutation π : A nice way to construct this combination is the following random process: choose a threshold τ ∈ [0, 1] uniformly at random, and consider the level set S τ = {i : x i > τ }.

the sets in the required chain are exactly the level sets which are obtained with positive probability, and for any such set A i , we have x = E τ [χ Sτ ].


It is important to explore the natural setting when the aforementioned assumption holds only in an approximate sense.

we study the following broad question: Question 1 (Robust Learning of Graphical Models).


Our algorithm starts with a particular MIS P i , denoted by x 0 . x t+1 , which is a neighbor of x t , is obtained by replacing some lower-weight vertices in x t with higher-weight vertices under the constraint of always being an independent set.

we first reduce x t by removing a proportion q of lower-weight vertices.


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

we give a precise definition of the notion of ✏-strategic buyer (Section 3.2).


We provide an upper bound on the resulting error of our convex relaxation, when a multi-set of items S i presented to user i is drawn uniformly at random with replacement.


Suppose that all elements of J are initialized to be unity, and the groups are presented sequentially as binary vectors e, ... ,~m.

the ath group is learned through the update if neurons i and j both belong to group a, then the connection between them is removed.


The Fenchel-Young inequality states that for any w and θ we have that f (w) + f (θ) ≥ w, θ . Sub-gradients play an important role in the definition of the Fenchel conjugate.

the following lemma, whose proof can be found in Borwein and Lewis [2006], states that if λ ∈ ∂f (w) then the Fenchel-Young inequality holds with equality.


Our results show that our 'knowledge transfer' approach is indeed successful.

our discriminator-trained G outperforms the MLE-trained G by 1.7% on recall@5 on the VisDial dataset, essentially improving over state-of-the-art [7] by 2.43% recall@5 and 2.67% recall@10.


A set function F mapping sets of recommended articles A to real values (e.g., the total information covered by A) is monotone and submodular if and only if respectively, for all articles a and sets A ✓ B.

since A is smaller than B, the benefit of adding a to A is larger than the benefit of adding a to B. Submodularity provides a natural framework for characterizing diminishing returns in information coverage, since the gain of adding a second (redundant) article on a topic will be smaller than the gain of adding the first.


For the exponential family the log-likelihood ' @( A0 2 ¦ 9 % © is directly related to a Bregman normal Poisson  It can be shown under fairly general conditions that u ¦ 9 © ( # ¤ ¦ 9 © .

application of these identities implies that the negative log-likelihood of a point can be expressed through a Bregman distance [1,3]: negative log-likelihood can always be written as a Bregman distance plus a term that is constant with respect to and which therefore can be ignored.


Although we state our results only for fully connected feed-forward ReLU nets, the proof techniques carry over essentially verbatim to any feed-forward network in which only weights in the same hidden layer are tied.

our results apply to convolutional networks in which the kernel sizes are uniformly bounded.


Sub-sampling is widely used in the first order methods, but is not as well studied for approximating the scaling matrix.

theoretical guarantees are still missing.


The graph-based GP has a small lead over other GPs.

it is better than the evidence 1/16 for kernels that treat the four labeled points essentially independently.


To compile an SDD for the hierarchical, simple routes of G, we first compile an SDD representing the simple routes over each region.

for each region N i , we take the graph induced by the edges A i and B i , and compile an SDD representing all its simple routes (as described above).


Therefore the partition should stop when the points inside a subrectangle are approximatly uniformly scattered.

we stop the partition when further Figure 1: Left: a sequence of binary partition and the corresponding tree representation; if we encode partitioning information (e.g., the location where the split occurs) in the nodes, there is a one to one mapping between the tree representations and the partitions.


One of the key contributions of [16] is the definition of a kernel specifically suited to linear system identification leading to an estimator with favorable bias and variance properties.

it is easy to see that if the autocovariance of f is proportional to W p , the variance of f (t) is zero at t = 0 and tends to ∞ as t increases.


The tangent cone is the conic hull of the descent set.

the smallest closed cone We note that the capability of the regularizer R in capturing the properties of the unknown weight vector w * depends on the size of the descent cone C R (w * ).


If we interpret Equation (1) in terms of error, we see that no assumption is made on the source of the error yielding the approximately submodular function.

there is no stochastic assumption: the error is deterministic and worst-case.


Second, we compared visual similarity of object instances in order to quantify the diversity of the training data.

we extracted GIST features [31] from each object instance and computed pairwise GIST distances (L2 norm) across all instances within each object category.


. . , G K } are trained using the CGAN approach at each level of the pyramid.

we construct a Laplacian pyramid from each training image I.


Now suppose the coin is considered lucky if it lands Tails and unlucky if it lands Heads.

the expected reward for selling the coin when it lands Heads is now −$0.50 and when it lands Tails is now $0.50.


In order to achieve sparsity, the most natural method is to round small coefficients (whose magnitudes are below a threshold θ > 0) to zero after every K online steps.

if i/K is not an integer, we use the standard SGD rule (3); if i/K is an integer, we modify the rule as: where: In other words, we first perform a standard stochastic gradient descent, and then round the coefficients to zero.


We note that we could have avoided this loss by bounding the 1 norm of the vector at the cost of a more technically involved proof.

one should bound the 1 norm of the embedding of the vector into a space where the 1 and 2 norms behave similarly, up to a multiplicative distortion of 1±ε.


for p = n + 1, the bound can be controlled a priori: approximate second-order critical points are approximately optimal, for any C. 4 Corollary 5.


Suppose that we define the first order transition probabilities of a PARW by Then, we see that state i is an absorbing state (either partially or fully) when λ i > 0, and is a transient state when λ i = 0.

the matrix Λ acts like a regularizer that controls the absorption rate of each state, i.e., the larger λ i , the larger p ii .


At the first iteration all messages are initialised to constant functions.

at each following iteration, each variable x i aggregates all incoming messages and computes the belief b i (x i ), which is then used to obtain the maxsum assignment x M S . for every variable The convergence of the max-sum is usually characterized considering fixed points for the message update rules, i.e.


This observation naturally begs the question of whether and when this trade-off really exists or if it is simply a result of the looseness in the bounds.

one could ask how tight the bound (3) is.


A GMRF is an undirected graphical probabilistic model that expresses a multi-dimensional joint Gaussian distribution in a reduced parameter space by making use of conditional independences.

we employ a standard representation of a GMRF derived from the inverse covariance matrix, or precision matrix Q = Σ −1 of the underlying Gaussian distribution: For X = (X 1 , .


Since S has an addition operation, we may parameterize h ∈ H explicitly as h a (x) = x + a for x ∈ u and parameter a ∈ v such that (u + a) ⊂ v. The restriction behavior of the translations in H prevents us from simply generating a group out of the elements of H. To get around this difficulty, we will decompose the h ∈ H into a composition of two functions: a translation group action and an inclusion.

let S generate a group of translations T by defining the injective map to every element of a ∈ S we associate a member of the group T whose action corresponds to translation in S by a: A ta (x) = x + a for x, a ∈ S. (Although we assume the specific case of translations throughout, the sets of intrinsic operations H i may more generally contain other kinds of transformations.


Prequential codes depend on the performance of the underlying training algorithm, and take advantage of the model's generalization ability from the previous data to the next.

the model training should yield good generalization performance from data [1; In practice, optimization procedures for neural networks may be stochastic (initial values, dropout, data augmentation...), and Alice and Bob need to make all the same random actions in order to get the same final model.


Note that given a distribution over an initial X 0 , we can apply an environment simulator multiple times to a distribution over the initial state, yielding a probability distribution over trajectories and cumulants.

temporally abstract environment simulators only need to represent a relaxed version of the above conditional probability distribution: where τ is some arbitrary time skip interval up to the end of the trajectory, which can be chosen by the model and R τ t denotes the sum τ k=t R k . a temporally abstract environment simulator must only be able to predict some future state of the system and additionally provide the sum of the cumulants since the last step.


On line 4 we construct the collection of sets P that are the maximal sets that any vertex can take as parent set during the upper bound computation.

the sets in P take immoralities relaxedly into consideration: For any v i , v j ∈ V , we have {v i , v j } ⊆ P for some P ∈ P if and only if when choosing parent sets during the upper bound computation, we allow immoralities to appear, as long as they are not between vertices of the fixed partial solution.


However, from a cognitive and neuroscientific perspective, there is one approach to solving MDPs that it seems particularly appealing to consider.

several researchers have suggested methods for solving MDPs through probabilistic inference [8][9][10][11][12].


The VCG mechanism, which we describe below, is the canonical strategy-proof mechanism, which means that every bidder's dominant strategy is to bid truthfully.

for every Bidder i, no matter the bids made by the other bidders, Bidder i maximizes her expected utility (her value for her allocation minus the price she pays) by bidding her true value.


We demonstrate that the decision boundary obtained by our loss has nice properties compared to standard classification loss functions.

we show improved empirical results on the MNIST, CIFAR-10 and ImageNet datasets on multiple tasks: generalization from small training sets, corrupted labels, and robustness against adversarial perturbations.


Construct a random walk on this graph where at each time, the random walk is likely to go from vertex i to vertex j if items i and j were ever compared; and if so, the likelihood of going from i to j depends on how often i lost to j.

the random walk is more likely to move to a neighbor who has more "wins".


In this work we show that for many graphical models it is possible to devise a partitioning strategy followed by a message passing algorithm such that efficiency can be improved significantly.

our approach adds additional terms to the energy function (i.e., regions to the Hasse diagram) such that the high-order factors can be pre-computed and remain constant during local message passing within each machine.


This equation is easily expressed in matrix form as Y = XH, where time is now indexed by matrix row in Y and X. H contains the concatenation of the terms and row t of X is similarly The standard solution for this regression problem is H = (X X) −1 X Y .

the parameters of the kernels are derived using the regression technique by correlating the input and the output, and are compensated by the covariance in the input, i.e.


We call the parameter α(k) ∈ (0, 1] the multitasking capacity of G for matchings of size k. Definition 1.1 generalizes to networks of depth r > 2, where instead of matchings, we consider first layer to last layer node disjoint paths, and instead of induced matchings we consider induced paths, i.e., a set of disjoint paths such that no two nodes belonging to different paths are adjacent.

the main question we shall consider here is what kind of tradeoffs one should expect between α, d and k. which network architectures give rise to good multitasking behavior?


To illustrate the complexities that can arise in this inferential setting, we adopt a latent variable network model with a standard flavor: a logistic regression model that simultaneously incorporates aspects of blockmodels, additive effects, and explanatory variables (see [10] for a more general formulation).

we incorporate a K-class stochastic blockmodel component parameterized in terms of a symmetric matrix Θ ∈ R K×K and a membership vector z ∈ {1, . . . , K} N whose values denote the class of each node, with P ij depending on Θ zizj .


Then we approximate the MAP classifier by using training data as a proxy for the latent sources.

we take ratio (6), replace the inner sum by a minimum in the exponent, replace V + and V by R + and R , and replace D + by D to obtain the ratio: Plugging ⇤ (T ) in place of MAP in classification rule (5) yields the weighted majority voting rule (2).


This pruning is done for efficiency; the question is whether it is hurting accuracy.


We study the problem of estimating a manifold from random samples.

we consider piecewise constant and piecewise linear estimators induced by k-means and k-flats, and analyze their performance.


In this paper, we depart from existing approaches, and present a new approach to lifted inference from the other, logical side.

we propose a set of rewriting rules that exploit the structure of the logical formulas for inference.


In the model defined in the previous section, each branch (k → l) ∈ T has a collection of contextdependent rule probabilities θ k→l .

θ k→l specifies a collection of multinomial distributions, one for each C = (c l , x, c r ), where c l is left phoneme, x is the old phoneme, c r is the right phoneme.


Stated in this way, multinomial estimation involves predicting the next observation based on the data.


In this section, we study the problem under the assumption that the predictors have a linear form and the loss functions are quadratic.

f ⇢ Lin(X , W) where W = {w 2 R d | kwk ⇤  w lim } and X = {x 2 R d | kxk  x lim } for some given constants w lim , x lim > 0, while `t(y) = (y y t ) 2 , where |y t |  x lim w lim .


To simplify notations in our description, we will replace the optimization problem in (1) with a more general formulation.

instead of working with n input data vectors x i ∈ R d , we work with d feature vectors f j ∈ R n (j = 1, . . . , d), and y ∈ R n . Each f j corresponds to the j-th feature component of x i for i = 1, . . . , n. f j,i = x i,j .


A linear model only uses linear relationships between variables, so our association measure only captures linear relationships.

we use the Pearson correlation coefficient, and we square it so that a higher association measure always represents a stronger proxy.


Just like the classic perceptron algorithm, our generalized perceptron algorithm (Algorithm 1) is mistake driven.

it only updates on round when a mistake, i.e., a non-zero loss, is incurred.


However, the ℓ 1 regularization approach of compressed sensing has been successfully used in this setting as well.

if x * is sparse, then the corresponding lifted matrix x * x * T is also sparse.


If the rates (w {i,j} ) are normalized such that {i,j}:i,j∈N w {i,j} = 1, then (w {i,j} ) is a distribution over all possible vertex pairs.


If i) e f λ is as in Corollary 2, i.e., e f λ (||x|| 2 ) = g(min{||x|| 2 , λ}), ii) X n has a (ρ 1 , ρ 2 )-balanced subset of samples I with k balls, and iii) the centers of the balls are at least v > 4r + 2g −1 ( ρ1+ρ2 ρ1 g(r)) apart, then for λ ∈ the set of outliers X n \I has no effect on the grouping of inliers I.


Our findings have been verified in large-scale machine learning applications.

we have consistently observed that SGHMC relies on a small stepsize h and large friction A, which significantly reduces its usefulness in practice as discussed.


Finally, on all datasets, the treeRMNs with CVI can achieve similar prediction quality as the existing methods (i.e., MSL, IRM and MRC), but is about two orders of magnitude more efficient in training.

it achieves significant improvements on the Animal and Nation data, but moderately worse results on the UML and Kinship data.


Further research will involve the acquisition of more pairwise similarity judgements in conflicting situations as well as the refinement of our existing experiments.

we would like to know whether it is possible to create larger, scalable conflicts, i.e.


Section 2) on the performance behavior of DualSGD.

we conduct an initial analysis to quantitatively evaluate the sensitivity of these hyperparameters and their impact on the predictive accuracy and wall-clock time.


These dynamics only require each player to know her own action and the reward she received for that action.

the dynamics in [24] guarantee that the optimal sum of utilities strategy profile will be played a sufficiently large portion of the time, even if it is not a Nash equilibrium.


Then, the spatial map M 1 : Ω 0 → R p1 introduced above can be obtained by (i) computing the quantities Z x for all patches x of the image I (spatial convolution after mirroring the filters z j ); (ii) contrast-normalization involving the norm x ; (iii) applying the pointwise non-linear function κ 1 ; (iv) applying the linear transform κ 1 (Z Z) −1/2 at every pixel location (which may be seen as 1×1 spatial convolution); (v) multiplying by the norm x making ψ 1 homogeneous.

we obtain a particular convolutional neural network, with non-standard parametrization.


In this light, the current study examines various network structures [15,19,21,20,22,6,7,9].

networks are being made deeper and wider because doing so improves accuracy.


However, traditional methods for dimensionality reduction and clustering are ill-suited to recovering the structure underlying the organization of neural circuits.

they do not take advantage of the rich temporal dependencies in multi-neuron recordings and fail to account for the noise in neural spike trains.


No matter the model satisfies the assumption or not, an easy way to fulfill it is to add an additional term to l(p), where µ is a small positive number.

for each s, we make an I i = {1, . . . , k} with I + i = {s}, r i = µ, and r ′ i = 0.


This is an example of OCO with stochastic constraints, where we aim to minimize the electricity cost subject to the constraint that incoming jobs must be served in time.

at each round t, we receive loss function f t (x(t)) and constraint function g t (x(t)) = !


The specific and well-studied prediction market mechanism we consider is the potential-based market maker [1].

here, traders interact with the market maker sequentially, and the cost for each trade is determined by a convex potential function C : R → R applied to the market maker's state s ∈ R. the cost for a trade dr when the market maker has state s is given by cost(dr; s) = C(s−dr)−C(s), i.e., the change in potential value of the market maker's position due to the market maker accepting the trade.


Despite each application domain has its own specificity, 4 in this paper we abstract such details away, and focus on the broad problem of building matches between the two parties in the reciprocal recommendation problem based on behavioral information only.

we do not consider explicit user preferences (e.g., those evinced by user profiles), but only the implicit ones, i.e., those derived from past user behavior.


It is obtained by adding 1 if the new breakpoint is before J t−1 and 0 otherwise.

if there is no minimum of P t (µ) in piece p t,jt , we must move the pointer from j t to its final position J t ∈ {1, ..., t + 1}, where J t is the index of the rightmost function piece that contains a minimum: See Figure 2 for an example.


One approach to deal with this issue has been to investigate special cases where these problems would be tractable.

the basic idea is to select models from a restricted class of Bayesian networks that have structural properties enabling fast learning or inference; this way, the computational complexity will not be an issue, though possibly at the cost of accuracy if the true distribution is far from the model family.


The purpose of the blocks is twofold: to collect local contextual information, and to reduce the area of the activation arrays.

we want to reduce the vertical dimension, since the CTC output layer requires a 1D sequence as input.


Contrast this with twice continuously differentiable concave functions where the Hessian matrix must be negative semidefinite.

this means that log-supermodular functions can be multimodel.


Our active learning theory and methods show promise for a number of problems.

in imaging techniques such as laser scanning it is possible to adaptively vary the scanning process.


In other words, the timevarying coverage function controls the propensity of occurring events over time.

for a fixed set S i , as time t increases, the cumulative number of events observed grows accordingly for that f (S i , t) is a continuous monotonic function over time; for a given time t, as the set S i changes to another set S j , the amount of coverage over domain U may change and hence can result in a different cumulative intensity.


For example, if Y := {−1, 1} and L is a convex, margin-based loss represented by ϕ : R → [0, ∞), that is L(y, t) = ϕ(yt) for all y ∈ Y and t ∈ R, then L can be clipped, if and only if ϕ has a global minimum, see [13,Lemma 2.23].

the hinge loss, the least squares loss for classification, and the squared hinge loss can be clipped, but the logistic loss for classification and the AdaBoost loss cannot be clipped.


In contrast to most existing trackers which only learn the appearance of the tracked object online, we take a different approach, inspired by recent advances in deep learning architectures, by putting more emphasis on the (unsupervised) feature learning problem.

by using auxiliary natural images, we train a stacked denoising autoencoder offline to learn generic image features that are more robust against variations.


We train our network in a spatio-temporally progressive manner.

we start with generating low-resolution videos with few frames, and all the way up to generating full resolution videos with 30 (or more) frames.


• Context Models: We include results from recent context models for deep networks.

we compare to state-of-the-art results from PSPNet [13], RefineNet [19] and Enc-Net [14].


CNN-based methods [2][3][4] show strong cross-scene prediction capability, due to the learning capacity of CNNs.

[3] uses a multi-column CNN with different receptive field sizes in order to encourage different columns to capture features at different scales (without input scaling or explicit supervision), while [4] uses a pyramid of input patches, each sent to separate sub-network, to consider multiple scales.


From the above Q dev p values we can compute player p's value for deviating from an equilibrium which recommends action a in state s: it is Q dev p (s, a ) for the best possible deviation a , since p will get the one-step payoff for a but be punished by the rest of the players starting on the following time step.

v dev p (s, a) is the value we must achieve for player p in state s if we are planning to recommend action a and punish deviations with π pun p : if we do not achieve this value, player p would rather deviate and be punished.


The modeling in terms of function mapping assumes a one/many to one mapping between input and output.

ideally the input should contain sufficient information to uniquely determine the output apart from some sensory noise.


The answer is simple in logit space: Proposition 3.

(i) If probabilities P are generated by Elo ratings r then the divergence of its logit is r. (ii) There is an Elo rating that generates probabilities P iff curl(logit P) = 0.


Note that simulating an outcome does not require evaluating the expensive f and g i .

f k+1 and g i k+1 are not f (x k+1 ) and g i (x k+1 ).


. . , x n ) be a feasible point in the domain of function f (x).

for each component x i , we define a sub-function we use the n-ary function f (x) to generate n sub-functions f x (x i ).


Specifically, for the ith experiment, select all vertices whose colour is 1 in the ith bit.

select , where bin i extracts the ith bit of a number.


In such a setting, we cannot use GREEDI as presented above, since we cannot evaluate f on the individual machines without access to the full set V . Fortunately, many such functions have a simple structure which we call decomposable.

more precisely, we call a monotone submodular function f decomposable if it can be written as a sum of (non-negative) monotone submodular functions as follows: there is separate monotone submodular function associated with every data point i ∈ V . We require that each f i can be evaluated without access to the full set V . Note that the exemplar based clustering application we discussed in Section 3.1 is an instance of this framework, among many others.


Let F i (x) denote the survival function of the distribution on arm i.


This gives O( p T ) regret with worse O(T The work [17] develops a (batch) offline algorithm that produces a solution with high probability performance guarantees only after sampling the problems for sufficiently many times.

during the process of sampling, there is no performance guarantee.


Spamming AF was simple because it only looks one link behind.

attributes for a document are either explicit terms in that document or explicit terms in documents linking to the current document.


However, the apparent practical efficacy of these approaches came without theoretical guarantees.

showing that this regularization yields an algorithm to compute or approximate general OT distances in time nearly linear in the input size n 2 was an open question before this work.


For the deterministic rule, i k is an arbitrary sequence that is assumed to be essentially cyclic.

there is an N ∈ N, N ≥ N , such that each block i ∈ {1, 2, . . . , N } is updated at least once in a window of N , that is, This encompasses different kinds of cyclic rules such as fixed ordering, random permutation, and greedy selection.


In the dual-stage, the decoded unlabeled pairs are again fed into the same autoencoder and parsed through the encoding-swap-decoding process for the second time.

the code parts that are swapped during the primary-stage are swapped back in the second stage.


In contrast, experimental and theoretical studies of neural systems suggest memory retrieval is a dynamic and iterative process: memories are retrieved through a potentially varying period of time, rather than a single step, during which information can be continuously integrated [3,7,20].

attractor dynamics are hypothesised to support the robust performance of various forms of memory via their self-stabilising property [8,12,16,28,33].


An ✏-Nash equilibrium is a strategy profile such that V i (r) V ˆ i (r) ✏ for all players i and ˆ = ( i , ˆ i ).

each player can gain at most ✏ by deviating to any other strategy ˆ i .


HIM's balance the trade-off between model and inference complexity by introducing a hierarchy of hidden states.

we introduce recursive segmentation and recognition templates which represent complex image knowledge and serve as elementary constituents analogous to those used in speech.


This is based on the assumption that a good model of p(x) contains information about the category distribution p(y|x).

if a representation is learned, from which a given sample can be reconstructed perfectly, then the representation is expected to also encode information about the category of the sample (ability to discriminate).


(2) If the Gram matrix is entry-wise non-negative and if the set of predictors indexed by {1, . . . , p} can be partitioned into subsets B 1 , .

. . , B B such that this applies to design matrices whose entries X ij = φ j (u i ) contain the function evaluations of non-negative functions {φ j } p j=1 traditionally used for data smoothing such as splines, Gaussians and related 'localized' functions at points {u i } n i=1 in some fixed interval, see Figure 1.


Example 1 (Plackett-Luce as an RUM [2]) In the RUM, let µ j 's be Gumbel distributions.

for alternative j ∈ {1, . . . , m} we have µ j (x j |θ j ) = e −(xj −θj ) e −e −(x j −θ j ) .


We then apply softmax normalization to the computed weights so that each element of the context is computed as a weighted average over center elements, rather than just a weighted sum.

r(Φ, φ) (j) = e (W φ+b) (j) / |Φ| k=1 e (W φ+b) (jk) Φ with weights W ∈ R |φ|×|Φ|×|c| , and biases b ∈ R |Φ|×|c| .


We call this algorithm OOMM (Oblivious Online Match Maker), The main idea is to develop a strategy that is able to draw uniformly at random as many pairs of reciprocal edges as possible from E r (recall that E r is the set of all reciprocal edges between B and G).

within the T rounds, OOMM will draw uniformly at random Θ(T )-many such pairs.


The tree T 0 is obtained as the intersection of X with dyadic partition of [0, 1] D (e.g.

by cycling though coordinates) of depth D 0 = O(D log n) and partition size we emphasize that the following conditions on subtrees then hold.


In this paper, we address this problem with a new analytic framework based on diffusion processes.

we focus on the concrete example of SGD applied on the tensor decomposition formula-tion of independent component analysis (ICA).


We use a simplicial complex K to model such a space.

given input sampled points P and the distance matrix of P , we first construct a proximity graph based on either r-neighborhood or k-nearest neighbors(NN) information; that is, a point p ∈ P is connected either to all its neighbors within r distance to p, or to its k-NNs.


invert the graphics engine efficiently using convolutional nets.

we use deep learning to train recognition models on the objects in our world for object detection, structure and viewpoint estimation, and physical property estimation.


., where each k i ∈ {1, 2, . . . , K} is an event type and 0 < t 1 < t 2 < • • • are times of occurrence.

1 there are K types of events, tokens of which are observed to occur in continuous time.


However, in a high-dimensional setting, where the number of covariates p could scale with the number of samples n, this performance of the LDA classifier breaks down.

bickel and Levina [3] show that when p/n → ∞, then the LDA classifier could converge to an error rate of 0.5, that of random chance.


P5: Any pair of interacting agents must belong to the same team plan.

if an agent i interacts with another agent j , i.e., i provides or deletes some conditions of j , then i and j should be in the same team, and activities of agents in the same team compose a team plan.


Let f ′′ t denote the resulting hypothesis, that is, Setting σ i,t+1 = φ t σ i,t for all i ∈ I ′ t , we can write, The third and last step of the update is the removal step discussed above.

if the budget constraint is violated and |I ′ t | > B then I t+1 is set to be I ′ t \ {r t } where r t = min I ′ t . Otherwise, I t+1 simply equals I ′ t . The recursive definition of the weight σ i,t can be unraveled to give the following explicit form, σ i,t = j∈It−1 ∧ j≥i φ j .


We use the notation nn for 'neural network' to indicate that this is a nAD.

m q is the identifier of a neural network model that specifies a probability distribution over its output values u, given input t. from the perspective of the probabilistic logic program, an nAD realizes a regular AD p 1 :: q( t, u 1 ); ...; p n :: q( t, u n ) :− b 1 , ..., b m , and DeepProbLog thus directly inherits its semantics, and to a large extent also its inference, from ProbLog.


. . , X p ) 2 X p ✓ R P . Each coordinate of the random vector X is associated with a vertex in V and the graph structure encodes the conditional independence assumptions underlying the distribution of X.

x a and X b are conditionally independent given all the other variables if and only if (a, b) 6 2 E, that is, the nodes a and b are not adjacent in G. One of the fundamental problems in statistics is that of learning the structure of G from i.i.d.


For small N , the data association problem now has an obvious Bayes filter solution.

let A be the space of all permutation matrices.


(3) We implement PCN with some architectural features common to modern CNNs.

feedforward and feedback connections are implemented as regular convolutions and transposed convolutions [10], respectively, with a kernel size of 3.


Finally, we show our proof technique can be employed to generalize some of the known online learning algorithms.

consider the Lazy update variant of the online Mirror Descent (LMD) algorithm (see for instance [16]).


In this section, we investigate the class of models that arise from specifying the node-conditional distributions as exponential families.

suppose we are given a univariate exponential family distribution, with sufficient statistics B(Z), base measure C(Z), and D(θ) as the log-normalization constant.


For a general hypothesis testing problem, namely, H 0 : θ ∈ G 0 versus H 1 : θ ∈ G 1 , the minimax testing risk with respect to an algorithm A and a statistical oracle r ∈ R[ξ, n, T n , η(Q A )] is defined as  • For any sequence {γ n } n≥1 satisfying γ n = Ω(γ * n ), there exist a constant η > 0 and an algorithm Throughout this paper, we assume that the covariance matrix Σ in (2.1) is known.

for some positive definite Σ ∈ R d×d , the parameter spaces of the null and alternative hypotheses are defined as Accordingly, the testing problem of detecting whether µ 0 � = µ 1 is to distinguish In §3.1, we present the minimax rate of the detection problem from an information-theoretic perspective.


These are algorithms that can only evaluate the query on the sample points they are given.

an algorithm M is natural if, when given a sample X = (X 1 , .


We consider learning a weight matrix consisting of the weight vectors for m linear predictive models: In this paper, we propose a non-convex multi-task feature learning formulation to learn these m models simultaneously, based on the capped-ℓ 1 ,ℓ 1 regularization.

we first impose the ℓ 1 penalty on each row of W , obtaining a column vector.


This follows from the approach of composite likelihood (or pseudolikelihood) [20] which replaces a difficult probability density function by a set of marginal or conditional events that are easier to evaluate.

( 9) corresponds to the so-called pairwise conditional likelihood that has been used in longitudinal studies and bioinformatics [21].


We exhibit a strong link between frequentist PAC-Bayesian risk bounds and the Bayesian marginal likelihood.

for the negative log-likelihood loss function, we show that the minimization of PAC-Bayesian generalization risk bounds maximizes the Bayesian marginal likelihood.


While our main contribution is the theoretical part, we also turn out to the practical suggestions of our results.

they suggest that, for binary classification, learning cost-sensitive classifiers may be more effective than thresholding probabilities.


In addition to providing fast general feature extraction for 360°imagery, our approach provides a bridge from 360°content to existing heavily supervised datasets dedicated to perspective images.

training requires no new annotations-only the target CNN model (e.g., VGG [33] pre-trained on millions of labeled images) and an arbitrary collection of unlabeled 360°images.


Our goal is to benchmark Optimistic Gittins Indices (OGI) against state-of-the-art algorithms in the Bayesian setting.

we compare ourselves against Thomson sampling, Bayes UCB, and IDS.


Structural risk minimization schemes over LR via various forms of regularizations have been widely studied and understood in the literature.

recent asymptotic analysis of the 1 norm and 1 / 2 mixed norm regularized LR proved that under certain conditions the estimated sparse coefficient vector β enjoys a property called sparsistency [34], suggesting their applicability for meaningful variable selection in high-dimensional feature space.


Given M k , UCFH computes a policy π k by performing optimistic planning.

we use a finite horizon variant of extended value iteration (EVI) [5,14].


With such utilities, Triple-GAN addresses two main problems of existing methods [26,25].

triple-GAN ensures that both the classifier and the generator can achieve their own optima respectively in the perspective of game theory and enable the generator to sample data in a specific class.


We expect that our results and constructions will naturally extend to a stochastic setting.

we expect that with random initialization, general stochastic gradient descent will need exponential time to escape saddle points in the worst case.


Model test (fr-en) test (de-en) Bilingual Enc-Dec [Bahdanau et al., 2015] 35.2 27.3 Multi-lingual Enc-Dec [Johnson et al., 2016] 35 As shown in the third row of Figure 2, on German and Adult, we achieve higher accuracy on the biased categories, even though our overall accuracy is similar to or lower than the baseline which does not employ fairness constraints.

on Adult, our performance on the biased categories is 0.788 while the baseline's accuracy is 0.748.


For the CoffeeScript-JavaScript task, we create several datasets named as XY-ZW: X and Y (C or J) indicate the source and target languages respectively; Z (A or B) indicates the vocabulary; and W (S or L) indicates the program length.

vocabulary A uses {x,y} as variable names and {0,1} as literals; vocabulary B uses all alphabetical characters as variable names, and all single digits as literals.


However, the method does not attempt to understand the scene semantics.

their method is unable to break the scene into separate objects (e.g., a row of cars will be parsed as a single region) and cannot capture combinations of classes not present in the training set.


Then, as training set size |S| → ∞, Inverse MCMC with proposal size k converges to block-Gibbs sampling where blocks are the last k nodes in each H i .

it converges to Gibbs sampling for proposal size k = 1 and to exact posterior sampling for k = |G|.


In order to make our approach practical, we introduce a number of practical techniques for running FOMs on EFGs.

we derive efficient and numerically friendly expressions for the smoothed-best response (SBR) and prox mapping, two optimization subproblems that EGT solves at every iteration.


For our prediction task, we took as observation sequence directions of the S&P500 price changes.

the direction d t , at time t, is d t sign(p t+1 − p t ), where p t are close prices.


We perform transfer learning by exploiting features from a pre-trained neural network that effectively convert raw images into relatively highlevel information [30].

we use a Deep Residual Network [31] pre-trained on the ImageNet classification task [32] to obtain the visual features used as inputs for the policy network.


Indeed, the Gaussian log-partition function serves as a variational upper bound for the QPGM.

under the restriction that θ ss < 0, we arrive at the following upper bound: by relating to the log-partition function of a node-conditional Gaussian distribution.


For example, in WNNM [15], j∈Ci Φ(X) j i G(X) j corresponds to the projection of X i onto the group-specific subspace as a function of the selected patches.

the subspace for calculating Z i is spanned by the eigenvectors , where diag{σ} is obtained by applying the shrinkage function associated with the weighted nuclear norm [15] to the eigenvalues of X T Ci X Ci .


The noise precision θ 2 does not change with N . Identical to [9], the transform A is modeled as a large, right-orthogonally invariant random matrix.

we assume that it has an SVD of the form (9) where U and V are N × N orthogonal matrices such that U is deterministic and V is Haar distributed (i.e.


This behaviour is slightly surprising as one could expect that it is harder to learn the protocol when the space of messages is larger.

using longer sequences helps to learn a communication protocol faster.


In a contracting system, all the trajectories converge to a single trajectory exponentially fast independent of the initial conditions.

if the system has a steady state solution then, by definition, the state will contract and converge to that solution exponentially fast.


The essential idea of linear response is to perturb the first-order condition M (m * ) = m * around its optimum.

define the distribution p t (θ|x) as a log-linear perturbation of the posterior: where C (t) is a constant in θ.


In the present study, we used Bayesian adaptive design optimization (ADO) [4,5,6,7] on groups of people to achieve the same goal.

a retention experiment was repeated four times on groups of people, and the set of retention intervals at which memory was probed was optimized for each repetition using data collected in prior repetitions.


Following [12] we chose to evaluate the performance of IDC with respect to a labeled data set.

we count the number of classification errors made by IDC as obtained from labeled data.


LSI uses singular value decomposition to discover the important associative relationships of word features [10], and create a reduced-dimension feature space.

we first perform singular value decomposition over M * , M * = U SV ⊤ , and then obtain a low dimensional representation matrix Z via a projection Z = M * V k , where V k contains the top k right singular vectors of M * .


If dj > 0, then we want P (d j ≤ 0) to be small, and vice versa.

for dj > 0, we want P (d j ≤ 0) < ǫ, where where Φ(•) denotes the cdf for the standard Normal.


In order to do that robustly, we need to know the joint distribution of their values.

we are interested in the joint distribution of the children f I,1: I of a node I (e.g.


State-of-the-art models [1,2,3,4] mostly adopt the encoder-decoder paradigm [3], where the content of the given image is first encoded via a convolutional network into a feature vector, which is then decoded into a caption via a recurrent network.

the words in the caption are produced in a sequential manner -the choice of each word depends on both the preceding word and the image feature.


While [22,25] consider the dynamics during stochastic gradient descent (SGD) optimization, we address the dynamics as more training data is gradually made available.

the model regression network from [21] empirically shows a generic nonlinear transformation from small-sample to large-sample models for different types of feature spaces and classifier models.


For concreteness, we show here some examples of the equations above for well-known probability distributions.

we choose the gamma, log-normal, and beta distributions.


This paper aims to address the problem of data and computation efficiency of program induction by leveraging information from related tasks.

we propose two approaches for cross-task knowledge transfer to improve program induction in limited-data scenarios.


This is the main difference to [4], where they enforce the global Lipschitz constant to be smaller than one.

in kernel methods one uses typically the regularization functional induced by the kernel which is given as the squared norm of the function, for translation invariant kernels one can make directly a connection to penalization of derivatives of the function f via the Fourier transform, see [20].


Real NVP [4] is a member of the normalising flows family of models, where some density in the input space X is transformed into a desired probability distribution in space Z through a sequence of invertible mappings [14].

real NVP proposes a design for a bijective function f : X → Z with X = R D and Z = R D such that (a) the inverse is easy to evaluate, i.e.


Dirichlet processes and their variations [7,[9][10][11] have gained recent attention for their ability to provide representations consisting of arbitrarily large mixture models.

they have been the subject of recent work in modeling intensity functions for Poisson processes defined over time [4] and space-time [5].


Provided Q(h) = 0 whenever P (h, v) = 0, we obtain: Importance sampling relies on the sampling distribution Q(h) being similar to the target distribution P (h|v).

the variance of the estimator is an α-divergence between the distributions [3].