Finally, we note that the quantity E c∼U (0,1) er 0-1,c D Thresh D, η,c • η that appears in Theorem 10 is also the area under the cost curve [20,22]; since this quantity is upper bounded in terms of regret rank D [f ] by virtue of Theorem 4, we also get a weak regret transfer bound from bipartite ranking to problems where the area under the cost curve is a performance measure of interest.

this implies that algorithms that are statistically consistent with respect to AUC can also be used to construct algorithms that are statistically consistent w.r.t.


In order to tackle this challenge, we present an approach to learn from noisy data.

we model noise as a latent variable and use two networks: one which predicts the likely noise and other that predicts the action to execute.


Table 1, left panel, shows that the td architecture outperforms all the other architectures for all the different models.

td in tanh RNN achieves a test BPC of 1.49 on PennTreebank, which is comparable to the BPC of 1.48 reported in [27] using stabilization techniques.


As described above, we ran our algorithm on patches harvested from YouTube thumbnails downloaded from the web.

we downloaded the thumbnails for over 1.4 million YouTube videos 4 , some of which are shown in Figure 2b.


Fortunately, WordNet contains relatively direct metadata related to the physicality of a word sense.

one of the main functions of WordNet is to put words in semantic relation to each other using the concepts of hyponym and hypernym.


The expected number of edges originating in x equals the expected number of points which lie in the intersection of this ball with the other side of the hyperplane.

setting we have E(N 1 |X 1 = x) = (n − 1)g(x, r n ), since the number of points in the intersection of B(x, r n ) with the other side of the hyperplane is binomially distributed with parameters n − 1 and g(x, r n ).


However, identifying representative eigenvectors is not very trivial because in real life depending on the separation between high density clusters the representative eigenvectors can have no sign change up to some small precision > 0.

we say that a vector e = (e 1 , e 2 , ..., e n ) ∈ R n has no sign change up to precision if either ∀i e i > − or ∀i e i < .


We are continuing to work actively to extend our approach.

we wish to demonstrate the generality of our approach by providing algorithms that calculate best response to different sets of opponents (conditional strategies, finite automata, etc.)


Various other metrics are important for providing insight into the operation of the network.

we may expect there to be a relationship between the actual error in the phase of firing of the neurons recalled by the memory, and the firing rates and concentrations (in the form of burst strengths) of the associated neurons themselves.


Against such a pricing strategy, it is in the buyer's best interest to be truthful, accepting if and only if v t ≥ p * , and the seller would receive a revenue of Informally, a no-regret algorithm is able to learn D from previous interactions with the buyer, and converge to selecting a price close to p * .

we therefore define regret as: Finally, we will be interested in algorithms that attain o(T ) regret (meaning the averaged regret goes to zero as T → ∞) for the worst-case D. we say A is no-regret if sup D Regret(A, D, T ) = o(T ).


Unlike previous linear models which behave differently under l ∞ and l 2 attacks, nonlinear DNN models show a consistent trend of adversarial robustness with respect to the sparsity.

we observe increased r ∞ and r 2 values under different attacks when continually pruning the models, until the sparsity reaches some thresholds and leads to inevitable capacity degradations.


We use multiple datasets with different types of annotations for training our network.

we first train our M 2d component on COCO [32] which contains a large variety of images with multiple people in natural scenes.


Let k denote iteration count, T k denote time when iteration k starts for k 2 N. Initially, k = 0, T 0 = 0, and for t 2 [T k , T k+1 ), the policy is in iteration k. The iteration is updated from k to k + 1 when starting with t = T k , all ball-action (B i , a) pairs have been visited at least once.

in the policy description, the counter N k (c i , a) records how many times the ball-action pair (B i , a) has been visited from the beginning of iteration k till the current time t; that is, N k (c i , a) = P t s=T k 1{Y s 2 B i , a s = a}.


We exploit the impact of the prior distribution in mitigating the influence of individual data points.

we focus on sampling from an exponential family and specific generalized linear models, such as logistic regression.


The rank of L 0 is unknown, the support set Ω (i.e., the locations of the nonzero entries of S 0 ) and its cardinality (i.e., the amount of the nonzero entries of S 0 ) are unknown either.

the magnitudes of the nonzero entries in S 0 may be arbitrarily large.


In particular, when this probability is proportional to exp{η s M e (s−1)}, for a certain choice of η s , this algorithm is known to minimize regret [1,2].

by letting j s (s = 1, 2, . . .) denote the observed actions of the opponent up to stage s, and letting σ X denote the strategy induced by the experts algorithm, we have The main deficiency of the regret minimization approach is that it fails to consider the influence of chosen actions of a player on the future choices of the opponent -the inequality (1) holds for any fixed sequence (j s ) of the opponent's moves, but does not account for the fact that different choices of actions by the agent may induce different sequences of the opponent.


At each iteration the meta-algorithm processes only one dataset.

it firstly estimates the stochastic LS objective function, by splitting this dataset into two subsets used to train and test the inner algorithm, respectively.


Rather than learning a single 'best' MRF model that can be sampled from to estimate quantities of interest, herding combines learning and inference into a single process.

herding produces a trajectory of weights and states that reproduce the moments of the training data.


00 00 n=O n=O a necessary and sufficient condition is an ~ 0 for all n E N if no assumption about the dimensionality of the input space is made (for finite dimensional spaces of dimension d, the condition is that bn ~ 0).

the polynomial series expansion in dot product kernels plays the role of the Fourier transform in translation invariant kernels.


Therefore, we iterate the above semantics-guided attention process using multiple attention layers, each extracting more fine-grained visual attention information for class semantic descriptions.

for the k-th attention layer, we compute: where U 0 I and u 0 G are initialized to be V I and v G , respectively.


As illustrated in Figure 3(Right), the relative performance between NormSpecSync and the other three algorithms is similar to CMU Hotel and CMU House.

normSpecSync shows an advantage over SpecSync on G sparse .


. . , (t s , y s )} having likelihood N (Y ; x T , Λ) give rise to a posterior GP s (x; µ s , k s ) with GPs are closed under linear maps.

the joint distribution over x and its derivative is A recursive algorithm analogous to RK methods can be constructed [5,6] by setting the prior mean to the constant µ(t) = x 0 , then recursively estimating xi in some form from the current posterior over x.


2 Unless otherwise stated, the embedding we refer to is the aforementioned w2vNEWS embedding, a d = 300-dimensional word2vec [19,20] embedding, which has proven to be immensely useful since it is high quality, publicly available, and easy to incorporate into any application.

we downloaded the pre-trained embedding on the Google News corpus, 3 and normalized each word to unit length as is common.


Specifically, transition matrix p(a) = [p Finally, p(a) i ] be a stationary distribution of the Markov chain defined by p(a) .

computationally, we suggest obtaining estimation of π by using power-iteration for T iterations.


We derived two equations and presented two accelerated algorithms for geodesically strongly-convex and general convex optimization problems, respectively.

our theoretical results show that our accelerated method attains the same convergence rates as the standard Nesterov's accelerated method in Euclidean space for both strongly G-convex and G-convex cases.


SplineNets employ a unified loss function with a desired level of smoothness over both the network and decision parameters, while allowing for sparse activation of a subset of nodes for individual samples.

we embed infinitely many function weights (e.g.


Below, we develop the intuition for this disadvantage by applying Kalman filter analysis [20] to examine uncertainties in the simplest possible MDP that exhibits the issue.

consider a state with two actions, each associated with a pair of terminal states.


Rather than attempting to identify direct interactions between neurons (where the number of interactions grows with the number of neurons squared), we propose to extract a smaller number of latent variables from each population and study how these latent variables interact.

we propose extensions to probabilistic canonical correlation analysis (pCCA) to capture the temporal structure of the latent variables, as well as to distinguish within-population dynamics from across-population interactions (termed Group Latent Auto-Regressive Analysis, gLARA).


This equation indicates that a state value is a weighted sum of dynamic effects, with rewards serving as the weights of summation.

let B = (I − γP π ) −1 , then the equation above becomes ).


Generally speaking, any estimator that can be expressed as a regularized empirical loss minimization is consistent under "reasonable" conditions.

one can consider regularized loss minimization to be a (generally) sound principle for formulating regression estimators, at least from the perspective of consistency.


persistence lanscapes [Bubenik, 2015], tangent vectors from the mean of the square-root framework with principal geodesic analysis [Anirudh et al., 2016], or persistence images [Adams et al., 2017]), using points in PDs as roots of a complex polynomial for concatenated-coefficient vector representations [Di Fabio and Ferri, 2015], or using distance matrices of points in PDs for sorted-entry vector representations [Carriere et al., 2015], (ii) implicit representation via kernels such as the Persistence Scale Space (PSS) kernel, motivated by a heat diffusion problem with a Dirichlet boundary condition [Reininghaus et al., 2015], the Persistence Weighted Gaussian (PWG) kernel via kernel mean embedding [Kusano et al., 2016], or the Sliced Wasserstein (SW) kernel under Wasserstein geometry [Carriere et al., 2017].

geometry on PDs plays an important role.


We find that the network with STD can generate both static and traveling bumps, and STD enhances the performance of the network in tracking external inputs.

we find that STD endows the network with slow-decaying plateau behaviors, namely, the network being initially stimulated to an active state will decay to silence very slowly in the time scale of STD rather than that of neural signaling.


In this case, x can also be regarded as a linear transformation of a vector s containing independent unit-variance Gaussian components, as: x = Σ −1/2 s. In fact, the Gaussian is the only density that is both elliptically symmetric and linearly decomposable into independent components [14].

the Gaussian densities correspond to the intersection of the class of ESDs and the class assumed by the ICA methods.


Let Y be the N × N binary matrix that contains these links.

let y ij ≡ Y (i, j) = 1 if we observe a link from entity i to entity j in that relation and y ij = 0 if we observe that there is not a link.


However, the conditional probability of ending up at x 1 = 1 given that the algorithm did leave x 0 is , which does not depend on α.

provided α is small, SR, on average, makes the same decisions/transitions with learning rate α as it does with learning rate α/10; it just takes 10 times longer to make those decisions when α/10 is used.


We show that the additive error of the MLE is constant with respect to the sample size, which means that the convergence rate is O P (1).

it converges in probability to the true change-point k ⇤ in constant time.


Specifically, the Copeland score is defined as j =i 1(pij > 1/2), and the normalized Copeland score is defined as ζi = A dueling bandit algorithm Γ decides which pair of arms to compare depending on the historic observations.

define a filtration H t−1 as the history before t, i.e., Ht−1 = {a (1) τ , a τ , wτ , τ = 1, 2, . . . , t − 1}.


This procedure is a generalization of the spectral learning algorithm developed for PSRs [7], which is a consistent estimator.

let the set of all observed tuples of sequences of length 3 be denoted by H and T simultaneously.


Underlining the difficulty of this challenge, first exact algorithms for CMSL have only recently been proposed [6,12,13,14], and generally do no scale up to 20 variables.

the constraint optimization approach introduced in [6] does not scale up to 10 variables within hours.


Since L(Θ) is a separable sum over the N points, then the theorem follows, with L i (θ i ) summing those training points in S i , L j (θ j ) summing those in S j , and the remaining points being summed in the "constant" term.

the respective terms are: Note that L i depends on the parameters θ k of other nodes k besides i but it does not depend on θ j .


These issues can be addressed by adopting a batch MCMC approach.

particle Markov Chain Monte Carlo (PMCMC) procedures [24] established a framework for learning the states and the parameters in general state space models.


However stateof-the-art neural networks reached the hardware limits both in terms the computational power and the memory.

modern networks reached the memory limit with 89% [21] or even 100% [25] memory occupied by the weights of the fully-connected layers so it is not surprising that numerous attempts have been made to make the fully-connected layers more compact.


WGAN training and validation losses on a random 1000-digit subset of MNIST show overfitting when using either our method (left) or weight clipping (right).

with our method, the critic overfits faster than the generator, causing the training loss to increase gradually over time even as the loss drops.


Finally, notice that the sampler is easy to parallelize.

by iterating over events on a per-process basis, we parallelize the algorithm by scheduling different processes to different CPU cores.


However, as mentioned in Section 1, such solutions do not fare well on the three key requirements mentioned above due to training data inefficiency (see Section 1).

while the actual class-signature is a small part of the entire data point, in absence of more fine-grained labels, existing methods typically process the entire sequential data point to predict the class label which leads to expensive computation and large model sizes.


First, we introduce a domain-invariant task, namely visual feature self reconstruction.

after projecting a feature vector representing the object visual appearance into a semantic embedding space, it should be able to be projected back in the reverse direction to reconstruct the original feature vector (see explanation in Sec.


Later on, in Section 7 and Section 8, we will see that the similarities just described go beyond the structure of the processes, and they extend to the acceleration mechanism itself.

the choice of splitting parameters that yields subdiffusive convergence rates, matching the asymptotic rates of shift register methods, is also shown to depend on global information about G. We apply Min-Sum Splitting to solve network averaging.


To make a model unbiased, importance sampling can be used.

we can let which is similar to an approach used by Hinton [18].


For a sequence of learning rates α ∈ [0, 1] N and a constant γ ∈ [0, 1], Q-learning [26], a very important algorithm in the multi-agent systems literature, updates its Q-values for an experience e t ∈ E by 3 Interruptibility Orseau and Armstrong [16] recently introduced the notion of interruptions in a centralized context.

an interruption scheme is defined by the triplet < I, θ, π For Bob, I Bob = 0 and for Adam, I Adam = 1 if his car goes fast and Bob is not too close and I Adam = 0 otherwise.


The values of α's were specified in such a way for us to explore how the structure of feature sharing influences the multitask learning models when various regularizers are used.

we illustrate the cases where the two newly proposed formulations outperformed other methods.


The large margin recognizers in the first group were "low-cost" discriminative CD-HMMs whose GMMs were merely trained for frame-based classification.

these GMMs were estimated by solving the optimization in eq.


One of the most robust findings in the literature on perceptual multistability is that switching times in binocular rivalry between different stable percepts tend to follow a Gamma-like distribution.

the "dominance" durations of stability in one mode tend to be neither overwhelmingly short nor long.


In other words, we must spend at least this many time steps in order to acquire a sample from a distribution close to P L . Our next result states that the chain in Algorithm 1 mixes rapidly:  One advantage of having a rapidly-mixing Markov chain as means of sampling from a DPP is that it is robust to addition/deletion of elements.

when a new element is introduced to or removed from S, we may simply continue the current chain until it is mixed again to obtain a sample from the new distribution.


A routine calculation shows that the expected reward of the optimal policy is equal to the fraction of coin flip sequences that cause to accept when communicating with an optimal .

with the construction above, we can now describe our result: Theorem 1.


We have evaluated seven nowcasting algorithms, including the simplest model which always predicts the last frame, two optical flow based methods (ROVER and its nonlinear variant), and four deep learning methods (TrajGRU, ConvGRU, 2D CNN, and 3D CNN).

we have evaluated the performance of deep learning models in the online setting by fine-tuning the algorithms using AdaGrad [4] with learning rate equal to 10 −4 .


1 (b) to be a good fit for the data generated from our hidden variable chain graph family, where we omit the values of U .

we would expect the observed deviances of our models fitted to data generated from our family to closely follow a χ 2 distribution with 14 degrees of freedom.


The generalization power of compression was recognized by [17] and [22].

it was shown in [21,Theorem 8] that if the mapping S n → S n is a compression scheme, then with probability at least 1 − δ, for any S n which is an (α, m)-compression of S n ∼ μn , we have (omitting the constants, explicitly provided therein, which do not affect our analysis) Defining Q(n, α, m, δ) as the RHS of Eq.


In this paper, we carefully analyze the AllReduce based setup, propose timing models which include network latency, bandwidth, cluster size and compute time, and demonstrate that a pipelined training with a width of two combines the best of both synchronous and asynchronous training.

for a setup consisting of a four-node GPU cluster we show wall-clock time training improvements of up to 5.4× compared to conventional approaches.


In order to fit the "orthogonal" rank-k X * , we need a weighted trace-norm of X * tr(p,q) = tc pq (X) = √ k. How large a sample S ∩ A can we now shatter using such a weighted trace-norm?

we can shatter a sample if Y S∩A tr ≤ √ k. We can calculate: we can shatter a sample of size up to |S| = 8kn A < 8kn.


The only difference is the set K, specialized in various ways, over which the minimum, min K∈K ω(K), is computed.

it also is important to note, that with the generalization of the theta function comes an implicit generalization of the geometric representation of G. for any feasible K in (11), there is an embedding U = [u 1 , .


The space of possible hyperparameters to explore in GC-LDA is vast, so we restrict our comparison to the aspects of the model which are novel relative to the original Correspondence-LDA model.

for all three model variants, we compared the log-likelihood of the test data across different values of γ, where γ ∈ 0, 0.001, 0.01, 0.1, 1 .


In this case the dissimilarities can be transformed into a set of values more suitable for embedding through the use of an appropriate transformation: Metric MDS can be formulated as a continuous optimisation problem through the definition of an appropriate error function.

least squares scaling algorithms directly seek to minimise the sum-of-squares error between the disparities and the inter-point distances.


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

a novel Generative Adversarial Network is designed to model the latent distribution of each novel class given its related base counterparts.


The nature of the neural spike code remains a central problem in neuroscience [1][2][3].

no consensus exists on whether information is encoded in firing rates [4,5] or individual spike timing [6,7].


Analyzing the approximate SDE suggests that our SGD algorithm iterations can get rid of the unstable equilibria (including local maxima and stationary points with negative curvatures) whereas the traditional gradient descent (GD) method gets stuck.

under weak distributional assumptions the stochastic gradient plays a vital role that helps the escape.


Our CPU and GPU implementations yield similar speedups to the theoretical one and can thus be used in practical applications, which could be explored in further work.

neural language models seem good candidates.


Meanwhile, artificial neural networks have been used in computer music [4,12].

the work of (Todd [11]) is the basis for phase 1 of CHIME, a novice machine improvisor that learns to trade fours.


In this paper we show that there is a family of locality-sensitive hash functions that achieves both objectives.

the hash functions match the theoretical guarantee of Spherical LSH from [2] and, when combined with additional techniques, give better experimental results than the hyperplane LSH.


Hence, the component likelihoods are The parameters of component likelihoods partition the network parameters.

the parameters of two component likelihoods are always non-overlapping.


Following the standard multi-view framework, in which all views are observed [3,13], we assume that we are given V deterministic classifier sets (H v ) V v=1 , each working on one specific view 1 .

for each view v, H v is a set of functions h v : X v → {0, 1}.


We consider the problem of classification using similarity/distance functions over data.

we propose a framework for defining the goodness of a (dis)similarity function with respect to a given learning task and propose algorithms that have guaranteed generalization properties when working with such good functions.


Word representations can then easily be extracted from the encoder and used in the context of a supervised NLP task.

we demonstrate the quality of these representations for the task of cross-language document classification, where a labeled data set can be available in one language, but not in another one.


Consider F, the set of all functions f : R d → R where f can be realized with a neural network described in (1).

in a fully connected neural network structure, W = R d×k .


Since exact inference in SLDS is intractable, we present three approximate inference algorithms and compare their performance.

a new variational inference algorithm is obtained by casting the SLDS model as a Dynamic Bayesian Network.


In the remainder of this section, we show theoretically that choosing d > 0 does not hurt in the sense that it does not reduce the space of policies available to the policy gradient method.

we show that when using an expressive enough reward parameterization, PGRD's space of policies is not restricted relative to OLPOMDP's space of policies.


An immediate consequence of this result is that increasing minibatch size can improve convergence.

the above result assumes a minibatch size of 1.


For Algorithm 1 running on (1) where f is L-smooth and g i is µ-strongly convex with µ > 0 for all i ∈ [n], it holds that where σ := A [P] 2 op and η P := min t θ E P [ρ t,P | α (t) ].

expectations are over the choice of P. for strongly convex g i , Algorithm 1 has a linear convergence rate.


For example, in the case of the urban sound detection problem [5], the training data contains the relevant sound somewhere in the given 1-2 secs clip, while the actual vehicle noise itself might last only for few hundreds of milliseconds.

the sliding window length should be greater than 1 sec while ideally we should restrict ourselves to 100ms window lengths.


For b ∈ {1, . . . , k}, (1) (applied under the conditional distribution given V b−1 , combined with the law of total probability) implies that ∀m > 0, letting By a union bound, this holds for all m ∈ N, with probability at least 1 − δ/(2k).

this means it holds for m = i bM − i (b−1)M . But note that for this value of m, any h, g m (since for every (x, y) ∈ Z b,m \ Q b , either both h and g make a mistake, or neither do).


For instance, it can be used for image sequence prediction either in an encoder-decoder framework [17] or by combining with optical flows [14].


Over the past years, advances in adopting methods from algebraic topology to study the "shape" of data (e.g., point clouds, images, shapes) have given birth to the field of topological data analysis (TDA) [5].

persistent homology has been widely established as a tool for capturing "relevant" topological features at multiple scales.


We describe an application of probabilistic modeling and inference technology to the problem of analyzing sensor data in the setting of an intensive care unit (ICU).

we consider the arterial-line blood pressure sensor, which is subject to frequent data artifacts that cause false alarms in the ICU and make the raw data almost useless for automated decision making.


Formally, for any x i , x j ∈ X , it assumes that where f X denotes ((L i f )(x i )) M i=1 and ⊥ denotes probabilistic independence between two random variables.

the original empirical covariance matrix K X is replaced by a rank-M approximation , where K X is the covariance of f X and K X, X ∈ R N ×M is the cross-covariance between f X and f X .


We start from the combined hypothesis that 1) bottom-up saliency is based on centersurround processing, and 2) this processing is optimal in a decision theoretic sense.

it is hypothesized that, in the absence of high-level goals, the most salient locations of the visual field are those that enable the discrimination between center and surround with smallest expected probability of error.


As shown in [13], every stochastic policy can be represented by a convex combination of deterministic policies and every convex combination of deterministic policies corresponds to a stochastic policy.

for any stochastic policy π s ∈ Π s , we can represent π s = i p i π d i using some set of {π d 1 , .


We now derive efficient updates that avoids an explicit computation of V. Our derivation involves two key steps.

the first step is to show that V k+1 can be parameterized by γ k . if we initialize V 0 = Σ, then we can show that: , where with γ 0 = γ 0 .


We will demonstrate that this task can be accomplished in a principled manner by local probabilistic models and in-network information sharing, implemented as recursive distributed probabilistic learning.

we focus on probabilistic PCA (PPCA) as a prototypical example and derive its distributed version, the D-PPCA.


In particular, we will choose the confidence function g(x) so that is a potential function, which serves as a repository for guarding our loss (we will chose g(x) to be an odd function, and hence will always have Φ t ≥ 0).

we will choose g(x) so that the change of Φ t lower bounds the payoff of the algorithm.


We can decompose the approximation ratio as follows: 1 ))] As k increases from 1, the tightening ratio T (k) increases towards 1 and the rounding ratio R(k) decreases from 1.

in this section, we lower bound T and R each in turn, thus lower-bounding the approximation ratio as a function of k. we show that T (k) reaches 1 at small k and that R(k) falls as 2 ⇡ + ⇥( 1 k ).


Our factor regression model is fundamentally nonparametric.

we treat the gene-tofactor relationship nonparametrically by proposing a sparse variant of the Indian Buffet Process (IBP) [5], designed to account for the sparsity of relevant genes (features).


As is common in machine learning applications, we relax the rank constraint to a nuclear norm constraint.

let our constraint set be Up to constants, a bound on hM t , Ki is a bound on x T i Kx i .


Approximate Learning: Exact maximum likelihood learning in this model is intractable, but efficient approximate learning of DBMs can be carried out by using a mean-field inference to estimate data-dependent expectations, and an MCMC based stochastic approximation procedure to approximate the model's expected sufficient statistics [14].

consider approximating the true posterior P (h|v; ψ) with a fully factorized approximating distribution over the three sets of hidden units: where µ = {µ 1 , µ 2 , µ 3 } are the mean-field parameters with q(h l i = 1) = µ l i for l = 1, 2, 3.


Update w t+1 by maximizing the expectation of objective (1).

w t+1 = argmax w i Pr(h i |x i , y i ; w t ) log Pr(x i , y i , h i ; w).


3 These two networks are structurally different: on Delicious, payoffs depend on users more strongly than on Last.fm.

there are more popular artists, whom everybody listens to, than popular websites, which everybody bookmarkssee Figure 3.


While there are many ways in which prediction tasks may be related [20], most of the existing approaches to transfer or lifelong learning are exploiting possible similarities between the optimal predictors for the considered tasks.

one widely used relatedness assumption is that these predictors can be described as linear or sparse combinations of some common metafeatures and the corresponding methods aim at learning this representations [10,2,15,3].


Embeddings of probability measures into reproducing kernel Hilbert spaces have been proposed as a straightforward and practical means of representing and comparing probabilities.

the distance between embeddings (the maximum mean discrepancy, or MMD) has several key advantages over many classical metrics on distributions, namely easy computability, fast convergence and low bias of finite sample estimates.


The binary labeling of the samples in S on this interval is fixed.

for any sample v j ∈ S, rev v j (c) is either at least z j or strictly less than z j for all c ∈ (t 1 , t 2 ).


The mechanisms of statistical cooperation, kinetic sampling and waiting illustrate the importance of dynamical considerations in describing the system behavior, and the capability of multiagent systems to self-organize in their collective dynamics.

it is interesting to note that given enough waiting time, agents with limited abilities can cooperate to achieve dynamics unachievable by individuals.


An important property of ( 6) is that if concentration parameter α is large relative to t Nt , then counts Nt and t Nt are effectively ignored.

as α → ∞ the hierarchical, asymmetric Dirichlet prior approaches a symmetric Dirichlet prior with concentration parameter α.


The key idea of this paper is to introduce an object bounding box B as an abstracted interface to manipulate the semantic label map.

we define a controllable bounding box B = {b, c} as a combination of box corners b ∈ R 4 and a class label c = {0, . . . , C}, which represents the location, size and category of an object.


We approach this problem using a spectral clustering and embedding algorithm.

we build a similarity graph whose nodes represent the data points and whose edges represent the similarity between data points.


Figure 5: Test set accuracy on full and limited training sets To test the ability of our pretrained features to generalize across rotations and lighting conditions given only a weak supervised signal, we limited the labeled training set to comprise only examples with a particular set of viewing angles and lighting conditions.

nORB contains images spanning 9 elevations, 18 azimuths and 6 lighting conditions, and we trained our linear classifier only on data with elevations {2, 4, 6}, azimuths {10, 18, 24} and These results demonstrate that Tiled CNNs perform well even with limited labeled data.


In the restricted-information scheme, we make a much milder assumption that the learner is informed about the losses of the available actions.

we define the set of available components as and assume that the learner can observe the i-th component of the loss vector t if and only if i ∈ D t . This is a sensible assumption in a number of practical applications, e.g., in sequential routing problems where components are associated with links in a network.


Recently, for the reasons explained above, several authors have investigated CVaR MDPs [20].

in [4], the authors propose a dynamic programming algorithm for finite-horizon risk-constrained MDPs where risk is measured according to CVaR.


In fact, we note that Diag(w) * = w 1 and p −1/2 1 Diag(w) * = w * = w 2 .

we can express the 1 and 2 -norms of w using the trace norm of a given matrix times the matrix Diag(w).


We evaluated the learned causal DAGs based on their accuracy in predicting the true effects of each of the interventions (shown in Figure 5(a)) when leaving out the data for that intervention.

if the predicted DAG indicates an arrow from gene A to gene B, we count this as a true positive if knocking out gene A caused a significant change 2 in the distribution of gene B, and a false positive otherwise.


In this paper we provide formal evidence that intrinsic motivation and count-based exploration are but two sides of the same coin.

we consider a frequently used measure of learning progress, information gain (Cover and Thomas, 1991).


The result strongly suggests that there are many fewer than D relevant dimensions.

there seem to be two outstanding modes; the STA itself lies largely in the subspace of these modes, as shown in Fig.


This result implies that our recipe is complete.

we cover all possible continuous Markov process samplers in our framework.


Towards this grand goal, we have witnessed an increased interest in tasks at the intersection of computer vision and natural language processing.

image captioning [16], visual question answering (VQA) [1,23] and visually grounded dialogue systems [5,6] constitute a popular set of example tasks for which large-scale datasets are now available.


As recent work has highlighted the possibility that neurons encode fractional derivatives, it is noteworthy that the non-local nature of fractional calculus offers a natural framework for predictive coding.

as we will show, when we assume that the predictive information about the future signal is fully contained in the current set of spikes, a signal approximated as a sum of powerlaw kernels corresponds to a fractional derivative in the form of a sum of Dirac-δ functions, which the neuron can obviously communicate through timed spikes.


The (i + 1)st neuron distinguishes subsequently left from right in the subintervals of the ith neuron.

the response of the second neuron is always 1, if the stimulus is in the right part of the intervals [ 0 5 0] and [0 0 5].


We instead opt for an approach borrowed from the work on neural network language models [19,20].

we use a probabilistic tree decomposition of p( x = x i |φ(x)).


In what follows, we will assume that the m th fidelity mean of an arm is within ζ (m) , a known quantity, of its highest fidelity mean, where ζ (m) , decreasing with m, characterise the successive approximations.

|µ for all k ∈ K and m = 1, . . . , M , where = 0 and the ζ (m) 's are known.


To eliminate such preprocessing step from the equation, one has to develop a class of new statistical estimators that admit strong performance guarantees, such as exponentially tight concentration around the unknown parameter of interest, under weak assumptions on the underlying distribution, such as existence of moments of only low order.

such heavytailed distributions serve as a viable model for data corrupted with outliers -an almost inevitable scenario for applications.


As with the usual definition of differential privacy, we guarantee that the output of our algorithm is similarly distributed on neighboring databases, only our notion of neighboring databases depends on the hypothesized distributions.

the a single entry in X drawn from either P 0 or P 1 may be replaced without detection by another entry drawn from either P 0 or P 1 , even if the rest of the database is arbitrary.


Since TrackIPTree cannot distinguish between these two situations, it simply splits any node that makes sufficient mistakes.

trackIPTree starts with only the root node, and tracks the number of mistakes made at every node.


[17] explored a similar technique, however their construction deviated from the above description.

it was a white-box construction with weak accuracy guarantees; their guarantees also involved making strong assumptions about the learning model and the loss function used in training.


Consider the normalized likelihood, where clearly (θ) may be replaced by (θ)/N , Finally, while we have chosen to present our methodology as applied to topic models, we expect the same techniques to be useful in a notably broader context.

our methodology is directly applicable to problems solved through Nonnegative Matrix Factorization (NMF), a close relative of PLSA where matrix columns or rows are often similarly constrained in their L 1 norm.


Based on their approach, [12,29] have suggested to include such deviation as a loss into the training process for deep feedforward generative neural networks.

the feed-forward networks in [29] are trained to convert noise vectors into textures.


Suppose we run Algorithm 1 in the realizable case with inputs example oracle U , labelling oracle O, hypothesis class H, confidence-rated predictor P , target excess error � and target confidence δ.

then with probability 1 − δ, for all k = 1, 2, . . . , k 0 + 1, and for all h ∈ V k , err D (h) ≤ � k . the ĥ returned at the end of the algorithm satisfies err D ( ĥ) ≤ �.


2 The advantage of GIANT mainly manifests in big-data regimes where there are many data points available.

when the number of data points is much larger than the number of features, the theoretical convergence of GIANT enjoys significant improvement over other similar methods.


To minimize (3), we propose to leverage the fact that, as discussed below, C can be thought of as the parameters of an additional network layer, which lets us solve for Θ and C jointly using backpropagation.

1 consider the self-expressiveness term in (3), Z Θe − Z Θe C 2 F . Since each data point z i (in the latent space) is approximated by a weighted linear combination of other points {z j } j=1,••• ,N (optionally, j = i) with weights c ij , this linear operation corresponds exactly to a set of linear neurons without non-linear activations.


While rewards (or returns) are not comparable across sources, they are comparable within a source.

we know that if R;l > R ;2 that source 8 prefers policy 'if1 to policy 'if2 .


2 Category Structure Aware Image Categorization ImageNet organizes the different classes of images in a densely populated semantic hierarchy.

image categories in ImageNet are interlinked by several types of relations, with the "IS-A" relation being the most comprehensive and useful [11], resulting in a tree hierarchy over image categories.


We were able to fill 16, 750 out of 111, 628 entries in A.

we observed 15% of the total number of entries.


For instance, consider the scenario where one of the transformations is identity and the other one is linear in the unknowns.

xt = x t and h 0 (x s , λ 0 ) = φ(x s ) T λ 0 where φ(•) is some known transformation.


Recent work on AL has adopted a different approach by learning a policy without directly estimating the corresponding reward function.

generative Adversarial Imitation Learning (GAIL, [12]) is a recent AL method inspired by Generative Adversarial Networks (GAN, [13]).


To this end, we use the analysis of CoSaMP [41] and leverage a recent result by [42], to show per step decrease in the signal estimation error using the generic chaining technique of [43,44].

we show that any "phase errors" made in the initialization, can be suitably controlled across different estimates.


A fresh interpretation of Bayesian inference was given by Zellner [15], which leads to our novel interpretation of MedLDA.

zellner showed that the posterior distribution by Bayes' rule is the solution of an optimization problem.


The same conditions on the synaptic weight matrix also lead to conditional multistability, meaning that there exists an input for which there is more than one stable steady state.

forbidden sets and conditional multistability are inseparable concepts.


Secondly, this notion helps clarify how our assumptions are much less restrictive than those considered previously.

independence given the label: Independence given the label implies that for any S 1 ⊆ X + 1 and S 2 ⊆ X + 2 we have Pr(S 2 |S 1 ) = Pr(S 2 ).


As an extreme example, if all columns of Z ⊤ B ⊤ are discretized to take values from a set of n vectors, PCSA degenerates to Mixture of PPCA [7,20] with n components, whose subspace loadings are the same.

learning such a PCSA model actually implements the group PPCA [24] throughout different components.


Problem (1) can be solved by alternately updating W k and T k through the stochastic gradient descent (SGD) method, which will be introduced in the following paragraphs.

since binary matrix T k can be determined with the constraints in (1), we only need to investigate the update scheme of W k . Inspired by the method of Lagrange Multipliers and gradient descent, we give the following scheme for updating W k . in which β indicates a positive learning rate.


(See also Lemma 8 in the supplementary material.)

let now p(s) denote the product of the probabilities of the transitions on the path from s 0 to s. for any policy tree Π containing s, a trajectory for Π goes through s with probability p(s).


Strategic interactions in several real world systems such as decision/voting often exhibit local structure in terms of how players are guided by or respond to each other.

different agents make rational moves in response to their neighboring agents leading to locally stable configurations such as Nash equilibria.


We evaluate SphereFace+ with two different architectures (SphereFace-20 and SphereFace-64) proposed in [28].

sphereFace-20 and SphereFace-64 are 20-layer and 64-layer modified residual networks, respectively.


Such methods may achieve quadratic convergence rates with O(np 2 + p 3 ) per-iteration cost [Bis95,Nes04].

for t large enough, Newton's method yields k ✓t+1 ✓ ⇤ k 2  ⇠ 2,NM k ✓t ✓ ⇤ k 2 2 , and it is insensitive to the condition number of the Hessian.


The possibility that speakers' use of syntactic reduction optimizes information density leads to questions as to how speakers estimate the probability of an upcoming syntactic event.

one can ask what types of cues language users employ when estimating these probabilites.


In the prediction phase, all we have to do is to keep the trained β fixed, and turn the optimization problem ( 5) into an analogous one that optimizes over the response y.

given a new sample x t of unknown response, our sample matrix X grows by one column X → [X, x t ], which means all our feature vectors gets one more dimension.


SVP is a simple projected gradient descent method where the projection is onto the set of low-rank matrices.

the t-th step update for SVP is given by: where M t is the t-th step iterate, η > 0 is the step-size, and P L (M ) is the projection of M onto the set of rank-L positive semi-definite definite (PSD) matrices.


Hence, once assuring the algorithm finds a local minimum in R2C , then some shifted truncation of the ground truth kernel a 0 can be recovered.

if we can find an initialization point with small objective value then a descent algorithm minimizing the objective function guarantees that q always stays in R2C in proceeding iterations.


Although this is a weak prior, one can ask: is this enough to predict transparency?

is the most probable interpretation of figure 1a one with two layers and the most probable decomposition of figure 1b one with a single layer?


We proposed that the form of the sensory likelihood is a critical feature that drives non-linear behavior, especially at large stimulus disparities.

a heavy-tailed likelihood function more accurately fits subjects' bias and variance in a cue combination task.


At any given time, workers at their will adopt an arbitrary combination of effort level and reporting strategy.

we define eft t i ∈ [0, 1] and rpt t i ∈ [0, 1] as worker i's probability of exerting high efforts and reporting truthfully for task j, respectively.


In order to bound the computational complexity, we limit the maximum number of images to be considered each run of Algorithm 1 by constant number N . N should be small enough not to suffer from computational burden.

simultaneously, it should be large enough to successfully detect the meaningful statistics from an extremely variable c . the highly ranked (i.e.


For the image classification branch, we choose φ α enc as the rest of the original VGG-M network for image classification.

the decoder function ψ cls dec for the image-level labels is initialized to be the same as the fully-connected layers of the original VGG-M, such that φ VGG-M enc = ψ cls dec • φ img enc .


The parameter γ is referred to as the path threshold for local separation.

the γ-local separator S γ (i, j) separates nodes i and j with respect to paths in G of length at most γ.


2, that iteratively expands a buffer q old → q new around a given subchain y S . Growbuf terminates when all belief residuals satisfy The GrowBuf sub-routine can be computed efficiently due to (1) monotonicity of the forward and backward messages so that only residuals at endpoints, q(x S 1 ) and q(x S L ), need be considered, and (2) the reuse of computations.

the forward-backward pass can be rooted at the midpoint of y S so that messages to the endpoints can be efficiently propagated, and vice versa [22].


there exists B > 0 such that x 2 ≤ B for all x ∈ X(u, θ).


Thus, the time-complexity becomes O(M n A mv + M nd) = O(M n A mv ).

when M n d and A mv = o(d 2 ), the cost can be significantly cheaper than O(d 3 ) of exact computation.


Setup To show this quantitatively, we the ✏ value for a traditional perturbation-based attack (a 100-step PGD) until the attack success rates on the certified defenses are similar to those for our technique.

we used an ✏ of 0.31 and 0.2 to attack [16] and [17] respectively, resulting in success rates of 86.0% and 83.5%.


We consider the task of autoassociative recall of binary patterns from a palimpsest memory.

the neural circuit consists of N binary neurons that enjoy all-to-all connectivity.


The requirements on N i=1 ri and N i=1 ci guarantee that no additional securities or cash have been created.

there exists some set of trades among traders that would lead to the market-clearing allocation, although the definition says nothing about how the equilibrium is reached.


It is therefore possible to select particles before the sampling step.

one chooses the fittest particles at time q r ¥ using the information at time q .


However, we argue that it's actually rather unrestrictive.

in fact the individual valuations v k,t can be generated arbitrarily so long as v k,t  w ⇤> t x t and equality holds for some k. we can imagine that nature first computes the market valuation v + t , then arbitrarily (even adversarialy) selects which buyer gets this valuation, and the other buyer valuations.


Though it is hard to draw samples directly due to nonconjugacy, we can leverage recent advances in data augmentation to solve this inference task efficiently, with analytical local conditionals for Gibbs sampling, as detailed below.

we have the likelihood of "observing" the topic assignments z d for document d 1 as .


in the case of c → ∞, the objective in (1) is a monotonically decreasing function of a.


Their approach breaks down the concept of similarity into one-to-one mappings, one-to-many mappings and many-to-many mappings, and probes each kind of mappings by ad-hoc techniques.

they applied linear correlation and mutual information analysis to study one-to-one mappings, and found that some core representations are shared by differently-initialized networks, but some rare ones are not; they applied a sparse weighted LASSO model to study one-to-many mappings and found that the whole correspondence can be decoupled to a series of correspondences between smaller neuron clusters; and finally they applied a spectral clustering algorithm to find many-to-many mappings.


Maxima hunting (MH) is a method for feature selection in functional classification based on measuring dependencies between values selected from {X(t), t ∈ [0, 1]} and the response variable (Berrendero et al., 2016b).


To address this more challenging situation, we study informationbased learning strategies of agents in unbounded state spaces using non-parametric Bayesian models.

we demonstrate that the Chinese Restaurant Process (CRP) model is able to solve this problem and that an Empirical Bayes version is able to efficiently explore bounded and unbounded worlds by relying on little prior information.


Despite the apparent simplicity of the linear model, inference over the latent variables is computationally hard except for a few special cases such as when all sources are Gaussian distributed.

the posterior distribution over sources p(s | x) is constrained to a linear subspace and can have multiple modes with heavy tails (Figure 1A).


Since it has been shown [13] that the empirical estimate of the mean, µ X = 1 /m i k x i , is a good proxy for µ P , the injectivity of µ can be used to define distances between distributions P and Q, observed via samples X = {x i } m i=1 and Y = {y i } n i=1 .

this can be done via the maximum mean discrepancy where F denotes a suitable class of functions X → R, and E x∼P [ f (x)] denotes the expectation of f (x) w.r.t.


We show that the player can benefit from such a hint if the set of feasible actions is sufficiently round.

if the set is strongly convex, the hint can be used to guarantee a regret of O(log(T )), and if the set is q-uniformly convex for q ∈ (2, 3), the hint can be used to guarantee a regret of o( √ T ).


(1993) assume integer weights, but this hypthosis can be easily removed from their Theorem 3.6.

theorem 3.6 assumes nothing about the lower weights, and as we will see, the integrality assumption on the top level weights can be easily replaced with a margin condition.


The estimation function g 1 (•) is called the denoiser and can be designed identically to the denoiser g(•) in the AMP iterations (2).

the denoiser is used to incorporate the structural or prior information on x.


Moreover, the error does not follow the standard significance ordering of the bit positions.

the information for the secret image is spread across the color channels; hence the reason it was not detected earlier.


Classically, cue combination models assume a generative model in which two observations arise from the same hidden source.

the hidden source for observation 1 is equal to the hidden source for observation 2 (Fig 5A).


In this paper, we describe how to design a single classification utility function that integrates the various debugging heuristics.

determinism of some features is a significant issue in this domain, and an additional penalty term for false positives is included to deal with this aspect.


By selecting different values for the total number of arcs, we can obtain models representing the brain connectivity at different levels of strength.

given a small value for the total number of arcs, only strong arcs will show up in the resulting connectivity model, so the model is a model of strong brain connectivity; when increasing the total number of arcs, mild arcs will also show up in the resulting connectivity model, so the model is a model of mild and strong brain connectivity.


Attending to memory is formalized as the problem of computing w. A content addressable memory, proposed in [7,21,2,17], is an external memory with an addressing scheme which selects w based upon the similarity of memory words to a given query q.

for the ith read weight w(i) we define, where d is a similarity measure, typically Euclidean distance or cosine similarity, and f is a differentiable monotonic transformation, typically a softmax.


Complementing our theoretical analysis, the experiments clearly demonstrate that regardless of the actual stability measures per fixed sample size, they seem to eventually follow roughly constant and differing convergence rates, with no substantial degradation in performance.

when stability works well for small sample sizes, it should also work at least as well for larger sample sizes.


Therefore, during training we are masking the calculation of the unification success of a known ground atom that we want to prove.

we set the unification score to 0 to temporarily hide that training fact and assume it can be proven from other facts and rules in the KB.


We limit ourselves here to point processes on X ⊂ R d such that one can extend the notion of likelihood.

we define here a DPP on X as in [1, Example 5.4(c)], by defining its Janossy density.


This is motivated by the fact that there exist unseen/seen classes that fall into the same superclass, i.e., the unseen class samples become 'seen' at the superclass level and thus easier to recognize.

our DIPL model is employed for ZSL with superclasses as follows: 1) Group all unseen and seen class prototypes  Datasets.


The validation data is used to select the best parameters by running the considered algorithms and selecting the best parameters according to the final F-measure.

for FOFO, OFO, and LR, we tune the initial step parameter for learning the posterior probability in the range 2 [−4:1:4] .


This algorithm also requires a suitable choice of T to guarantee that OFFLINEPCPD is called for a window of data that actually contains k ⇤ .

t should be large enough that the algorithm is unlikely to call OFFLINEPCPD when j < k ⇤ but small enough so that it is likely to call OFFLINEPCPD by time j = k ⇤ + n/2.


Typically, in vision systems, this information is not used.

the so-called bag of visual words model is employed.


We now provide lower bounds on the number of learners and sample complexity for arbitrary online boosting algorithms to evaluate the optimality of OnlineMBBM under 0-1 loss.

we construct weak learners that satisfy the online weak learning condition (1) and have almost matching asymptotic error rate and excess loss compared to those of OnlineMBBM as in (7).


Since the losses are non-differentiable, we solve the problems using stochastic subgradient method.

we implement the proximal gradient algorithm in [17], handling the -2 norm constraints with proximal operators.


For now, we would like to note that our reason for focusing on the parallel rounding of [5,10] is that they provide the best known polynomial-time theoretical guarantees for metric labeling.

we are interested in their approximation factor, which is defined next.


Under Condition 2, our proof actually shows that the optimal number of queries is dominated by the number of queries used by CheckSignificant function.

a simplified variant of Algorithm 1 which excludes use of abstention feedback is near optimal.


Multiplicative Integration can be viewed as a general way of combining information flows from two different sources.

[26] proposed the ladder network that achieves promising results on semi-supervised learning.


1 is square and invertible, we can marginalize out the latent variables and write: p(y) = i S(y i ), where y i = C i T x and S is a Student's t distribution.

there is an underlying assumption that filter outputs are independent.


The only exceptions are object root particles for which we predict the global dynamics.

the state prediction module (g, p i , e i ) predicts the local future delta position t+1 i,`= t+1 i t+1 par(i) using the particle state p i , the total effect e i on p i , and the gravity g as input.


Theorem 5 suggests an asymptotic test, which is computationally preferable to a permutation test.

for a desired Type I error rate α ∈ (0, 1) our test rejects the null hypothesis p = q if and only if When s = 0, this approach is closely related to several two-sample tests in the literature based on comparing empirical characteristic functions (CFs).


An attractive feature when using KME estimators is the ability to reduce the number of expansion points (i.e., the size of the weighted sample) in a principled way.

if μX k with n < N. Often the resulting x i are mutually dependent and the w i certainly depend on them.


In other words, 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.

we used the approach described in [8] to build a unified representation for all objects in the sub-class level, which is the representation computed for the parent object whose classifier had accepted (positively recognized) the object.


To compress M, we consider each D ∈ D independently and learn a new domain D where |D | ≤ D and g : D → D is a surjective mapping, i.e., ∀ µ ∈ D , ∃ C ∈ D such that g(C) = µ.

each cluster of objects is replaced by its cluster center in the reduced domain.


For both neurons i = 1, 2 we maximize information transmission under the constraint that their outputs stay as statistically independent from each other as possible.

we maximize Since the same terms (up to the sign) are optimized in (7) and ( 15) we can derive a gradient ascent rule for the weights of neuron i, w ij , analogously to section 3: Figure 4 shows the results of an experiment where two neurons receive the same Poisson input with a rate of 20Hz at their 100 synapses.


In the outcome prediction experiment, our goal is to measure and compare how well human and machines can predict the moving distance of an object if only part of the video can be observed.

for behavioral experiments on Amazon Mechanical Turk, we first provide users four full videos of objects made of a certain material, which contain complete collisions.


We modify conjugate gradients to (1) perform linear solves with multiple right hand sides simultaneously, and (2) return tridiagonal matrices corresponding to partial Lanczos tridiagonalizations of K XX with respect to each right hand side.

2 mBCG takes as input a matrix [ y z 1 • • • z t ], and outputs: where T1 , .


Tournament solutions have long been used in social choice and voting theory to define winners in general tournaments when no Condorcet winner exists [12,13].

a tournament solution is any mapping that maps each tournament on K nodes to a subset of 'winning' nodes in [K]; for our purposes, we will define a tournament solution to be any mapping S : P K →2 [K] that maps each preference matrix P (via the induced tournament T P ) to a subset of winning arms S(P) ⊆ [K].


Therefore, we also experimented with feature extraction using only a subset of the training set.

we first sample the dataset, and then use k-Space to compute the mapping S • R −1 • W . We apply this mapping to the entire dataset before doing regression.


3 Answerer in Questioner's Mind (AQM) Preliminary In our experimental setting, two machine players, a questioner and an answerer, communicate via natural dialog.

there exists a target class c, which is an answerer's intention or a goal-action the questioner should perform.


We call this method the normalized hybrid algorithm.

for the sake of comparison, we will also consider an algorithm in which the exponents in Equation ( 7) are not normalized by n r . we replace θ r /n r there by just θ r . We refer to this latter method as the unnormalized hybrid algorithm.


For instance, the non-recalling √ n-run policy consists in exploiting the first arm giving a run larger than √ n. For a uniform mean-reward distribution over [0, 1], the average number of explored arms is √ n and the selected arm is exploited for the equivalent of n time steps with an expected failure rate of 1/ √ n, yielding the regret of 2 √ n. We introduce a second target to improve the expected failure rate of the selected arm, at the expense of a slightly more expensive exploration phase.

we show that it is optimal to explore n/2 arms on average, resulting in the expected failure rate 1/ √ 2n of the exploited arm, for the equivalent of n time steps, hence the regret of √ 2n.


Instead, we take a complementary approach and focus on exploratory analysis.

our goal is to discover and visualize topic-specific subnetworks.


It is conventional to plot the graphon as one typically plots an adjacency matrix: with the origin in the upper-left corner.

darker shades correspond to higher values of W. Figure 1b depicts a graphon W φ which is weakly isomorphic to W. W φ is the relabeling of W by the measure preserving transformation φ(x) = 2x mod 1.


Obviously, by the max-flow min-cut theorem, the resulting cut set C mf has the smallest cut.

c mf,n is the cut set restricted to the graph G n . Lemma 1 Given labeling L mf,n ∈ L mf , S n forms a single connected area within graph G n . ∀i ∈ S n , there is a path with nodes {i, j, k, .


Recently, Valiant and Valiant [1,2] showed that a class of distributional properties, which includes such practically relevant properties as entropy, the number of distinct elements, and distance metrics between pairs of distributions, can be estimated given a sublinear sized sample.

given a sample consisting of independent draws from any distribution over at most n distinct elements, these properties can be estimated accurately using a sample of size O(n/ log n).


In this paper we describe a technique that yields strong guarantees for maximization of monotone submodular functions from approximate surrogates under cardinality and intersection of matroid constraints.

we show tight guarantees for maximization under a cardinality constraint and 1/(1 + P ) approximation under intersection of P matroids.


Moreover, to achieve the same error, HYBRID needs 100⇥ less samples than MC.

to achieve the error of 0.01, (a) shows HYBRID needs 10 3 and MC needs 10 5 samples; (b) shows HYBRID needs 10 4 and MC needs 10 6 samples.


During our experiments we have observed that the ADMM-based methods do not guarantee the feasibility of the iterates.

the norms of the estimated atoms might be greater than 1 during the iterations.


All three paradigms seldom exploit a common trait of real-world optimization problems: instances of the same type of problem are solved again and again on a regular basis, maintaining the same combinatorial structure, but differing mainly in their data.

in many applications, values of the coefficients in the objective function or constraints can be thought of as being sampled from the same underlying distribution.


The UCI Higgs dataset [1,11] is a dataset with 11 million observations, where the problem is to distinguish between the signal process where Higgs bosons are found, versus the background process that do not produce Higgs bosons.

we will consider a two-sample test with the ME and SME test on the high level features derived by physicists, as well as a two-sample test on four extremely low level features (azimuthal angular momentum φ measured by four particle jets in the detector).


While the efficient verifiability of a condition is by no means necessary for a condition to be meaningful and useful, we believe also that verifiability has its value and is worthy of being investigated.

the verifiability property allows us to design new recovery routines with explicit confidence bounds for the recovery error and optimize these bounds with respect to the method parameters.


This makes |S a (w, l, x)| = 2 i , which further implies that or equivalently, Case (ii): If w(a, x) ≤ M 2 l+1 , we have |S a (w, l, x)| = 1.

hence, the following bound holds in both cases (i) and (ii): The lemma holds by summing up over X and maximizing over A on all sides of Inequality 9.


Many spectral unmixing methods rely on the non-negative decomposition of spectral data onto a dictionary of spectral templates.

state-of-the-art music transcription systems decompose the spectrogram of the input signal onto a dictionary of representative note spectra.


We often assume that we do not explicitly form matrices A and B i , but we can only compute Ax, B i y i and their adjoints A > and B > i for any given x, y i , and for i = 1, • • • , m. Problem (1) is sufficiently general to cope with many applications in different fields including machine learning, statistics, image/signal processing, and model predictive control.

(1) covers convex empirical risk minimization, support vector machine, LASSO-type, matrix completion, compressive sensing problems as representative examples.


The analysis shows more problematic mixing for BCR with respect of LBCR.

in LBCR the 95% of the chains have a potential reduction factor lower than 1.35, with a median equal to 1.11, while in BCR the 95th quantile is 1.44 and the median equals to 1.18.


The construction of the meta-elliptical distributions is based on the copula technique and it was initially introduced by [25].

when the latent elliptical distribution is the multivariate Gaussian, we have the meta-Gaussian or the nonparanormal distributions introduced by [16] and [19].


Our results show that untying weights is beneficial for classification performance.

we find that selecting a tile size of k = 2 achieves the best results for both the NORB and CIFAR-10 datasets, even with deep networks.


A decentralized Markov decision process (Dec-MDP) is a Dec-POMDP that is jointly fully observable.

there exists a functional mapping, J : In a Dec-MDP, then, the sum total of the individual agent observations provides a complete picture of the state of the environment.


The proof of Theorem 2 is provided in the extended version of this paper [8].

we show the teaching sequences for an adaptive teacher which matches the above bounds for the 2-REC and LATTICE classes.


Since this maximization problem belongs to the zero-one integer problem (i.e., NP-hard problem), an exhaustive search is prohibitive for a large L. Therefore, we solve this problem approximately with the help of the following greedy-search algorithm.

first, only one y l1 value is set to 1 so that P (y|x * ; Θ) is maximized.


Data of recent psychophysical experiments suggest that an observer's previous perceptual decisions provide additional form of context that can substantially influence subsequent perception [3,4].

the outcome of a categorical decision task can strongly bias a subsequent estimation task that is based on the same stimulus presentation.


BP was studied in a number of papers which have gradually increased our understanding of the convergence properties and accuracy of the algorithm.

recent developments show that the stable fixed points are local minima of the Bethe free energy [10,1], which paved the way for more accurate "generalized belief propagation" algorithms and convergent alternatives to BP [11,6].


The essential difference from the statistical dimension for learning is that we must additionally bound the average covariances of indicator functions (or, rather, continuous analogues of indicators) on the outputs of functions in C. The essential claim in our lower bounds is therefore in showing that a typical pair of (indicator functions on outputs of) s-wave functions has small covariance.

to prove Theorem 1.1, it suffices to upper-bound the quantity for most pairs f m,S , f m,T of s-wave functions, where χ is some smoothed version of an indicator function.


Retinal dynamics are known to exceed the duration of the filters that we used (400 ms).

changes in stimulus statistics such as luminance, contrast and spatio-temporal correlations can generate adaptation lasting seconds to tens of seconds [5,28,14].


∆ MV = Ω(1)) then Ω(K log K) samples suffice to learn π * .

sSL is approximately as difficult as CCP in very general settings.


The central computational problem in topic modeling is to compute the posterior distribution of the latent structure conditioned on an observed collection of documents.

our goal is to compute the posterior topics, topic transitions, per-document topic weights, per-word topic assign-ments, and top-level weights conditioned on a set of documents, each of which is a collection of parse trees.


3 The gain and bias can be expressed in terms of P * .

the gain g = P * R, and the bias or average-adjusted value function is given by: where the last equality holds for aperiodic Markov chains.


To define this concept, first consider repeatedly playing an extensive game.

let σ t i be the strategy used by player i on round t. The average overall regret of player i at time T is: Moreover, define σt i to be the average strategy for player i from time 1 to T . for each information set I ∈ I i , for each a ∈ A(I), define: There is a well-known connection between regret, average strategies, and Nash equilibria.


Finally, we consider binary classification in GLM with the convex loss function (w, (x, y)) =  In this section we derive a bound for an algorithm that optimizes a surrogate of the loss directly.

we consider the Bayes loss for linear LGM with conjugate likelihood p(y|f and where a, b, and σ 2 are functions of x.


All the proofs are given in the supplementary material.

our simple, unified proof for all the lower bounds is given in Appendix A.


This paper focuses on paired comparison, in which there are exactly two objects to choose from, and its solution using linear estimation.

it is concerned with the environmental structures that make it possible to mimic the decisions of the linear estimator using less information and less computation, asking two questions: How much of the linear estimator do we need to know to mimic its decisions, and under what conditions?


We demonstrate the relevance and consistency of these axioms by showing that several natural notions satisfy these requirements.

we introduce quality-measures that reflect the underlying intuition of center-based and linkage-based clustering.


The GAMP method reduces the complexity of loopy BP by exploiting the linear nature of the relations between the variables w and z.

it is shown that when each term z[t] is a linear combination of a large number of terms w j [ ], the belief messages across the factor node for the linear constraints can be approximated as Gaussians and the factor node updates can be computed with a central limit theorem approximation.


Set α t = a, and L t = aµt + L + a −1 (µ − L) + , where a ∈ (0, 1) is a constant.

then the regret of Algorithm 2 can be bounded as with a = 1 2 , the regret bound reduces to 3µ 2 + L D 2 + 2Q 2 µ log(N + 1).


If the magnitude of change is comparable across feature dimensions, does it matter whether the disks are rendered in size, color, or orientation?

does visual search vary according to whether the same array of disks are: 1) small and large, 2) black and white, or 3) horizontal and vertical disks?


The relaxed condition is that the regions {f −1 θ (R k )} 1≤k≤K are obtained by partitioning R n with L (n−1)-dimensional hyperplanes.


An ablation study is also conducted on components of the proposed compositional paradigm, as shown in the last three rows of Table 1.

we represented the input image with groundtruth noun-phrases collected from 5 associated captions, leading to a significant boost in terms of all metrics.


that the signs of the numbers inferred by the recognizers correspond to the bits encoded by the synthesizer.

we can measure the success of the recognition using a simple loss function based on element-wise sigmoid: where the loss is distributed between −1 (perfect recognition) and 0.


We write this error loc (x k+s ) and define it as loc (x k+s ) x k+s − x(t k+s ), where x k+s is computed using the real solution x(t k ), ..., x(t k+s−1 ).

the difference between x k and y k can be described as follows We now write a complete definition of stability, inspired by Definition 6.3.1 from Gautschi [2011].


The training of the R 2 SVM is then carried out in a purely feed-forward way.

we train a linear SVM for the l-th layer, and then compute the input of the next layer as the addition of the original feature space and the random projection of previous layers' outputs, which is then passed through a simple sigmoid function: ) where θ l are the linear SVM parameters trained with x l , and W l+1 is the concatenation of l random projection matrices [W l+1,1 , W l+1,2 , • • • , W l+1,l ], one for each previous layer, each being a random matrix sampled from N (0, 1).


In the hidden variable case-when the same variables are missing in each observation-there is a complete symmetry between the missing values.

for any optimal solution (y, w) there must be other, equivalent solutions (y , w ) corresponding to a permutation of the hidden variable values.


We also seek to further understand whether our model extends to segmenting and imitating policies that perform different tasks.

we evaluate whether our framework is able to learn a multi-modal policy on the Walker-2D task.


The affinity matrix G l is then combined with the current features to compute the next-layer features at each position t, where v is a compositional function such as a GRU cell [8] or a linear layer with residual connections.

in other words, the feature at each position is computed as a weighted sum of other features, where the weights are determined by the graph G l , followed by transformation function v. Objective Function At the top layer, we obtain the features F L . At each position t, we use the feature f L t to initialize the hidden states of an RNN decoder, and employ the decoder to predict the units following x t . the RNN decoder maximizes the conditional log probability log P (x t+1 , • • • , x t+D |x t , f l t ) using an auto-regressive factorization as in standard language modeling [47] (also see Figure 2).


The setting is the one described in the previous section.

it is assumed that the oracle has a center-based clustering in his mind which satisfies the γ-margin property.


In this paper, we propose new convex formulations for the estimation of sparse low-rank matrices.

we assume that the matrix of interest should be factorized as the sum of rank one factors that are the product of column and row vectors with respectively k and q non zero-entries, where k and q are known.


We provide a comprehensive analysis and results that apply to various special cases.

our results contain as special cases the known optimal rate results for the expectation minimization problem, i.e., O(1/ p K) for general objectives and O(1/K) for strongly convex objectives.


Note that our motivating example in (9) is an example of a consistently ordered 2-cyclic matrix, for which Theorem 4.7 is applicable.

for the example in (9), we can apply Theorem 4.7 with µ = 1 1/n leading to ⇢(C) = 1/n 2 , which exactly coincides with our previous computations of ⇢(C) in Section 3.2.


The representation of the belief is necessarily approximate due to our use of samples, but the samples are drawn from the true current belief-no other approximations have been made.

we are not filtering: each run of the beam sampler produces samples from the current belief.


We demonstrate the error bounds for perturbed messages with a set of Monte Carlo trials.

for each trial we construct a binary-valued 5 × 5 grid with uniform potential strengths, which are either (1) all positively correlated, or (2) randomly chosen to be positively or negatively correlated (equally likely); we also assign random single-node potentials to each x s . We then run a quantized version of BP, rounding each log-message to discrete values separated by 2 log δ (ensuring that the newly introduced error satisifies d (e) ≤ δ).


Accordingly, we denote the last n − k columns of U by U S c . We let the diagonal elements of Σ S , ΣS , Σ S c , ΣS c be identified by their column indices.

the diagonal entries σ S,c of Σ S and σS,c of ΣS are indexed by c ∈ {1, . . . , k}; the diagonal entries σ S c ,c of Σ S c and σS c ,c of ΣS c are indexed by c ∈ {1, . . . , n}.


As shown in [21,22] (and in many other works) there is an intimate connection between the smallest eigenvalues of H b and mean exit times out of these metastable states.

in the asymptotic limit of small noise D 1, exit times are exponentially distributed and the first non-trivial eigenvalue (after µ 0 = 0) is given by µ 1 = 1/τ where τ is the mean exit time to overcome the highest potential barrier on the way to the deepest potential well.


We note that there are alternative names for these metrics in the literature.

the tp-rate is also called sensitivity, while one minus the fp-rate is usually called specificity.


Despite its simplicity and the effectiveness shown on various benchmarks [5,6], the sequential model has a fundamental problem.

it could not reflect the inherent hierarchical structures of natural languages [7,8] in image captioning and other generation tasks, although it could implicitly capture such structures in tasks taking the complete sentences as input, e.g.


(Our results easily generalize to random initial states and random costs.)

let the space of admissible histories up to time t be H Let Π H,t be the set of all history-dependent policies with the property that at each time t the randomized control action is a function of h t . Π H,t := µ 0 : H 0 → P(A), µ 1 : H 1 → P(A), .


The sparsity of the feature space provides us a possibility of designing a nearly lossless approach to reduce the number of features.

in a sparse feature space, many features are mutually exclusive, i.e., they never take nonzero values simultaneously.


(7-8), consider the example of external-regret matching.

since Y is the unit simplex in R d , Ȳ is the positive orthant in R d . So, with W 2 (ȳ) = ȳ 2 2 /2, the optimization problem (8) will be equivalent to ȳ = arg min ȳ is the projection of s onto R d + by minimum Euclidean distance.


In other words, despite being non-convex, CCA admits a tractable algorithm.

numerical techniques based on power iteration method and its variants can be applied to these problems to find globally optimal solutions.


If γ 2 > γ 2 c , the optimal Z is a certain point between 0 and M on the real axis.

for M = 2 the optimal configuration of the unit-length connected bars is unique (up to flipping about x-axis), meaning that the encoding/decoding vectors are symmetric about the principal axis; for M ≥ 3, there are infinitely many configurations of the bars starting from the origin and ending at the optimal Z, and nothing can be added about their regularity.


It follows that the switching parameter γ is immaterial to the selection of an optimal strategy.

the combined error of an optimal strategy is γρ We assume throughout this paper a finite support of size N ; that is, Ω = {1, . . . , N } and are probability mass functions.


Intuitively, this assumption allows the loss to be parameterized in terms of the propensity matrix Θ Z and the unnormalized output kernel Θ Θ (hence the superscript of L u ).

the (i, j)-th component of Θ Z stands for the linear response value of example j with respect to the label of the example i.


We assume that for each object O i ∈ {M, S, P }, the stock price O i .Stock, centered at the mean, is given by where each i is a Gaussian random variable.

the fact that there are several hidden common causes between M and S can be modeled by the covariance of m and s , σ ms . unlike in standard directed Gaussian models, σ ms is allowed to be non-zero.


Since the number of parameters in the sampling space is a unknown, some proposals must change the model dimension.

these jump moves (following the terminology of Tu and Zhu [27]) arise from changes in topology.


We instead propose adaptive parameterization, a method for learning to adapt the parameters of the affine transformation to a given input.

we present a generic adaptive feed-forward layer that retains the basic structure of the standard feed-forward layer while significantly increasing the capacity to model non-linear patterns.


The elements u j of u have the effect of directly modifying the transition probabilities of an uncontrolled Markov chain.

given an uncontrolled transition probability matrix P with elements p ij , we de ne the controlled transition probabilities as Note that P (0) = P . In some sense this is the most general notion of "control" one can imaginewe are allowing the controller to rescale the underlying transition probabilities in any way it wishes.


In this paper, we focus on Bayesian learning.

for DPMM, the predictive distribution of component parameters, conditioned on a set of observed samples x 1:n , is given by Here, E D|x1:n takes the expectation w.r.t.


. . , ψ m } each associated with the elements of W . The factor graph implies that p(Y ) factorizes as p(y 1 , .

. . , where Z is a normalizing partition function (the dependence on parameters is suppressed here) and Y c is a subset of the random variables that are associated with the neighbors of node c. Y c = {y i |i ∈ Ne(c)} where Ne(c) is the set of vertices that are neighbors of c. Inference in graphical models requires the evaluation and the optimization of Z.


This finding agrees with the results reported in the literature [12,13].

we find that with STD, the network can have slowdecaying plateau states, that is, the network being stimulated to an active state by a transient input will decay to silence very slowly in the time order of STD rather than that of neural signaling.


In this case the time series consists mainly of transitions within a class, whereas switching between the two classes is relatively rare.

therefore the covariance of time derivatives is mostly determined by the within-class scatter of the two point sets, and both matrices become approximately proportional: ẋ ẋT t ≈ 2/N • S W . Moreover, if we assume that S W (and therefore ẋ ẋT t ) is positive definite, we can rewrite the SFA objective (2) as the weight vector that optimizes the SFA objective (2) also optimizes the FLD objective (4).


Our next experiment is to test which adaptive strategy works better in practice given the same initial selection of columns.

in Figure 2, ADP-AE uses an adaptive sampling based on the residual A − CC + A and then adaptively samples according to the adaptive strategy in [8]; the initial columns are chosen with the additive error algorithm.


We define the clipping fraction as the percentage of examples where the clipping is active.

it is the percentage of examples with a non-empty memory buffer, for which ⇡ B † ↵.


1 The PSDD is a complete and canonical representation of probability distributions.

pSDDs can represent any distribution, and there is a unique PSDD for that distribution (under some conditions).


To address these issues, we propose a novel parametrization of the 3D bounding box as well as a set of cooperative losses.

we parametrize the 3D boxes by the predicted camera pose and object attributes from individual modules.


We see that the skip-based setting consistently outperforms the conventional setting, and the gains obtained are moderate to high depending on the underlying distribution of the workers' errors.

the gains are quite striking under the hammer-spammer model: this result is not surprising since the mechanism (ideally) screens the spammers out and leaves only the hammers who answer perfectly.


Each step in this descent is a convex optimization that can be solved with a standard SVM solver.

consider The above optimization is convex in W y but does not directly translate into the trace-based SVM formulation from (6).


Furthermore, it is easy to see [2] that two characterizers We call two characterizers similar if this holds, and write for some G satisfying GV = 0 and 1G = 0.

the similarity equivalence class of some characterizer C is the set {C + G|GV = 0, 1G = 0}.


In the undiscounted setting, then ||h π || p(•|s,a) � span(h π ), and thus C π M � span(h π ).

we define the class of C-"hard" MDPs by the class of MDPs with optimal policy having a low environmental-value norm, or for short, MDPs with low environmental norm.


An interesting observation is that algorithm 1 (User Average) and algorithm 2 (Item Average) have similar pattern of sorting order in Figure 3 (right column).

these two algorithms are similar in nature, and are relatively strong or weaker in similar regions of Ω. Algorithm 8 (NLPMF) on the other hand, has a very different relative strength pattern.


if K and L only had rank-1, the problem could be solved by sorting X and Y in matching fashion.


The modeling need motivates us to consider a generalization of SR measures that allows for easy tuning of the relative importance given to quality and diversity considerations.

we introduce the class of Exponentiated Strongly Rayleigh (ESR) measures, which are distributions of the form ν(S) ∝ µ(S) p , where S is a set, p > 0 is a parameter and µ is an SR measure.


. . , τ (λ n ))Φ x, where applying a function to a matrix is understood in the operator sense and boils down to applying the function to the matrix eigenvalues.

the authors used parametric filters of the form where β 1 (λ), .


The construction is identical to that of the proof of Lemma 5.

a set of vertices in G assigned the same color necessarily form an independent set, and so their corresponding negative points in S can be separated from all positive points by some halfspace, and vice-versa.


Note that unlike the methods described in [4,23] we will not be able to obtain the optimal move at each iteration.

if in the m th iteration we move from label f m to f m+1 then it is possible that there exists another labelling .


1 (lower) showing a maximum deviation of 3.2%.

the relative deviation is extremely small around the phase transition.


A and q W r# sE q $# # Yh © $# # t $# for all $# u $# # Y£ and P£ ¥ $# # with $# Y£ § !© © v# # u .

the heuristics q D# approximate the best-case plan-execution cost from to ¢# .


This ensures that, on average, every element of the RDP contains many sample points; therefore we obtain a low variance estimate, although the estimator bias is going to be large.

we obtain a very "stable" coarse estimate of f , where stable means that the estimator does not change much for different realizations of the data.


Finally, the scoring function for a given class is computed as the dot product between the embedding function and the class code vector Now, we are able to describe a kernel-based method for the effective solution of the PLM problem.

we present the problem formulation and the associated optimization method for the task of learning the embedding function given fixed codes for the classes (embedding problem).


for x 2 {0, 1} n one has F (x) = f ({i : x i = 1}), and (3) it can be computed efficiently and deterministically given access to the sets P u , u 2 U .

we can compute the value of F (x) using at most O(|U | ⇥ |V |) operations.


Furthermore, we noticed that the quality of attention significantly improves (1.5 points, Table 4) if we provide it with additional linguistic information.

at each time step t our phrase RNN also predicts a phrase label l t , following the standard definition from the Penn Tree Bank.


In this paper, we study the impact of replacing uniform with leverage score sampling.

we prove that the derived method still achieves optimal learning bounds but the time and memory is now e O(nd eff ), and e O(d eff 2 ) respectively, where d eff is the effective dimension which and is never larger, and possibly much smaller, than p n. To the best of our knowledge this is the best currently known computational guarantees for a kernel ridge regression solver.


Finding independence in Algorithm 1 and invariance in Algorithm 2 can also be done from top to bottom, similar to the approach used in [SIS + 11].

in each round we can also find a variable with highest causal order as well.


We assume that instead of a sample (x i , y i ) a distribution over (x i , y i ) is specified.

we derive a robust formulation when the distribution is given by a normal distribution.


We observe that agents with policy ensembles are stronger than those with a single policy.

when pitting ensemble agents against single policy adversaries (second to left bar cluster), the ensemble agents outperform the adversaries by a large margin compared to when the roles are reversed (third to left bar cluster).


Regretfully, this technique suffers from a computational efficiency problem.

the suffix averaging technique only chooses the suffix length after the entire hypothesis sequence has been constructed.


( 8), we employ maximum likelihood estimation.

the log likelihood of the training data for the CPS model can be written as below, It is not difficult to prove that L(θ) is concave with respect to θ.


(3) It leverages the sub-sampling operation to explicitly control the model complexity.

each group maintains indicators of whether particular atoms are inherited, and as a consequence, the ones that are deemed irrelevant are put out of scope.


We considered a route prediction task where we predict the next road segment, given the route taken so far; see, e.g., [Letchner et al., 2006, Simmons et al., 2006, Krumm, 2008.

for each route of the testing set, we consider one edge at a time and try to predict the next edge, given the edges observed so far.


To help design a unified framework, we reduce all instances of verification problems to a canonical representation.

the whole satisfiability problem will be transformed into a global optimization problem where the decision will be obtained by checking the sign of the minimum.


This fact suggests it may be possible to get a good idea of the correct behavior for an information set by only sampling a fraction of the associated game states.

for each iteration, we sample deterministic actions for the chance player.


We again use a special case of Algorithm 3 (Appendix B.2).

we replace line 10 with the step Recall that the group (2, r)-norm is the `r norm of the `2 norm of the columns of W . We set r = log(p)/(log(p) 1).


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

. . , s k }, is the predictive probability of seeing a stop trial is just the mean of the predictive distribution p(r k |s k−1 ).


This allows us to represent conditional distributions in a compact, yet expressive way and efficiently capture their many nuanced aspects thus enabling more accurate causal inference.

by way of the kernel trick, we can efficiently compute the variability of infinite-dimensional objects using finite-dimensional quantities that can be easily estimated from data.


The gating function (see Section 2) can be easily adopted into the gradient by discounting the contribution from convolution units that have been turned off by the gating function.

we use stochastic gradient descent for the optimization of models.


Finally, our algorithm learns only L parameters and therefore is quite practical.

note that if an item is chosen in one context, it helps in refining the estimate of the gain g i (y) in all other contexts.


Constrained optimization problems are often challenging to solve, due to complex interactions between the goals of minimizing (or maximizing) the objective function while satisfying the constraints.

non-linear constraints can result in complicated feasible spaces, sometimes partitioned in disconnected regions.


This has been a major area of machine learning research in the past decade [19], with several exciting developments on understanding its underlying statistical principles [27,18,4,3,29,21,15,7,31,10,34,6].

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


We furthermore extend this surjective property to some restricted distribution families, which allows additional prior information to be incorporated and hence less conservative solutions to be obtained.

we prove that surjectivity of linear projections remains to hold for distribution families that are additionally symmetric, log-concave, or symmetric linear unimodal.


In this work, we made a first step towards understanding variable importances as computed with a forest of randomized trees.

we derived a theoretical characterization of the Mean Decrease Impurity importances as computed by totally randomized trees in asymptotic conditions.


Thus, we attempt to put a distance margin between them.

we seek to push known samples into what we call the Objectosphere where they have large feature magnitude and low entropy -we are training the network to have a large response to known classes.


(2) Let w k denote the prior weights of different sampling sources which may also change during the sampling.

we set w k = q k c k for k > 0, w −1 = α ν , and w 0 = α 0 .


A more general model, proposed in [6,16], employs a hierarchical prior for P (u) with adapted parameters tuned to the global patterns in higher-order dependencies.

the logarithm of the variances of P (u) is assumed to be a linear function of the higher-order random variables v, Conditional on the higher-order variables, the joint distribution of coefficients is factorisable, as in GSM.


This complexity can be reduced by restricting the size of the initial Y .

we first randomly initialize Y with a small size, say o(n 1/3 ), and compute the inverse L −1 Y .


For clarity of presentation, we will use a binary 1-of-K representation for the latent state assignments.

we will write the event of the latent state at time step t being k as z tk = 1 and z tl = 0 ∀l = 1...K, l = k. Then the transition probabilities can be written as T ij = Pr(z tj = 1|z t−1,i = 1).


The second is the recent work in econometrics and computational economics that aims to estimate critical concepts directly from a limited data set, and reason about the sample complexity of the computational problems.

in all of the above papers, the algorithm must be able to query or compute C(S) for an arbitrary set S ✓ N . In our work, we are instead given a collection of samples from some distribution; importantly the algorithm does not know C(S) for sets S that were not sampled.


When we evaluate the computational complexity, we assume the shape of G is roughly symmetric.

we assume there exist I, R 2 N such that I k = O(I) for k = 1, . . . , K and R k = O(R) for k = 1, . . . , K 1.


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

upon applying the action a t and observing the new state s t+1 , the posterior distribution at t + 1 can be updated according to Bayes' rule as Let N t (s, a) be the number of visits to any state-action pair (s, a) before time t. With these notations, TSDE is described as follows.


For example, we might want to learn that elastic deformations or swirls should only rarely be applied to images in CIFAR-10, but that small rotations can be applied frequently.

a mean field model also provides a simple way of effectively learning stochastic, discretized parameterizations of the TFs.


Using our framework we also show how the asymptotic theory of Liu and Ihler applies more generally to distributed composite likelihood estimators.

the Strong LAP Condition provides a sufficient condition to guarantee the validity of a core assumption made in the theory of Liu and Ihler, namely that each local estimate for the parameter of a clique is a consistent estimator of the corresponding clique parameter in the joint distribution.


We study the online influence maximization problem in social networks under the independent cascade model.

we aim to learn the set of "best influencers" in a social network online while repeatedly interacting with it.


In Figure 2, we show four first-layer filters of the CNN trained from Seaquest for UCTtoClassification-agent.

each filter covers four frames of 8*8 pixels, which can be viewed as a spatio-temporal template that captures specific patterns and their temporal changes.


This suggests that the pool of manuscripts that can be made accessible in this way is large.

we have used our method, trained on 22 instances of letters from one document, to search another document.


The message for entry d from node ρ i on the tree to its parent is a vector The local likelihood term is then: The logarithm of the proposal density is then: This is not of standard form, and we use an approximation log qlr (t lr ) instead.

we use a piecewise linear log qlr (t lr ), which can be easily sampled from, and for which the normalization term is easy to compute.


Like its discrete counterpart, Theorem 3.1 provides necessary and sufficient conditions for the continuous relaxation to be tight.

for the relaxation to be tight, the optimal solution on any Mcover, appropriately scaled, cannot exceed the value of the optimal solution of the MAP problem over G. Theorem 3.1 provides necessary and sufficient conditions for the tightness of the continuous relaxation.


The kinds of latent structure that have been considered for use in predicting links in such networks have been relatively limited.

the machine learning community has focused on latent class models, adapting Bayesian nonparametric methods to jointly infer how many latent classes there are while learning which entities belong to each class.


However, it is not clear how to store data or how to distribute the tensor factorization computation to multiple machines (see Appendix D).

there is a lack of distributable algorithms in existing studies.


In the following section, we will investigate how to find the optimal tradeoff between sparsity and variance for the sparsification technique.

we consider how to find out the optimal sparsification strategy, given a budget of maximal variance.