(2016), the authors propose the use of batch normalization (Ioffe and Szegedy, 2015) to alleviate the problems encountered when training deep models.

in our experiments, we let each NN() have three convolutional layers, where the two hidden layers have ReLU activation functions and 512 channels.


Since Hodgkin and Huxley [1] described the ionic flux across the neuronal membrane with four nonlinear differential equations more than half a century ago, continuous efforts have been made either to extract an essence of the nonlinear dynamical aspect by simplifying the model, or construct ever more realistic models by including more ionic channels in the model.

the leaky integrate-and-fire model [4], originally proposed far in advance of the Hodgkin-Huxley model, consists of only one variable that corresponds to the membrane potential, with a voltage resetting mechanism.


Conceptually, this can be done by designing another ASF centered in that area of motor cortex representing the specific limb.

the second CSP (bottom row) on the other hand does not extract the ERD related to motor imagery, but focuses on a strong artifactual component above 15 Hz.


aT (cp(X) -cp(y)) = 1, (20) where, as in ( 12), the optimal value of b will be given by b* = a; cp(x) -"'*Jar~cp(x)a* = a; cp(y) + "'*Jar~cp(y)a*, where a* and "'* are the optimal values of a and '" respectively.

we can also write (23) as -- which is a second order cone program (SOCP) [5] that has the same form as the SOCP in ( 16) and can thus be solved in a similar way.


Applying -IOV to Vlun and -OV to Vinj activates adaptation.

we only need to indicate when the circuit should adapt, not how it does adapt.


Let X k be the n-by-k matrix consisting of the k largest eigenvectors of AT A.

---v-----" Then it is easy to see that Using the partition in (1), the right-hand side of the above can be written as a weighted sum of the squared Euclidean norms of the mean vector of each clusters.


The only two free parameters are κ prod and κ r . Since only κ r has an direct effect on all sets of belief species, we fixed κ prod = 50 and varied κ r . Small values of κ r results in better approximation as less of the probability mass in each belief species set is in an unassigned state.

together, reactions for recycling probability mass, implementing sum-product messages, and implementing product messages define a reaction network whose equilibrium computes the messages and marginal probabilities via the sum-product algorithm.


As conditional independence tests require at least three variables, they are not applicable in the two variable case.

one would first apply the PC algorithm to the data.


Next, sparse weight vectors w * are randomly generated with D * nonzero entries.

these results are restrictive in the sense that the dictionary dependent constants ν i significantly confine the class of signals t that we may represent.


In Section 2, we briefly introduce the necessary background.

these are realistic approximations for our problems with the following reasons.


As we can see, ZO-SVRG-Ave requires more queries than ZO-SGD to achieve the first significant drop in attack loss.

we next elaborate on assumptions of problem (1), and provide a background on ZO gradient estimators.


The (p, q)-norm of a matrix, denoted as A p,q , is obtained by first taking the p norm of each row, and then taking q norm of these row norms.

these two methods hinge on the spiked covariance assumption, and require the data to be exactly Gaussian (sub-Gaussian not included).


For example, consider the scenario in Figure 1.

neural LP also obtains state-of-the-art results on the KB version of the WIKIMOVIES dataset [16] for question-answering against a knowledge base.


As to experimental results, only a few has reported strong empirical performance using these loss functions alone [19,26], but many have combined with softmax loss to train deep networks [22,31,18,14,32].

for evaluation, we extract a feature vector and compute the cosine similarity for verification.


We have shown that, for finite-length LDPC sparse graphs, the accuracy of the marginal estimation with the method proposed significantly outperforms the BP estimate for the same graph.

indeed, the distribution tends very quickly to n to a Gaussian [1,15].


Finally, it can be shown that the CCA problem given in Problem ( 1) is ill-posed if the population auto-covariance matrices This observation follows from the fact that if there exists a direction in the kernel of in which x and y exhibit non-zero covariance, then the objective of Problem (1) is unbounded.

the objective is no longer an expectation, but is instead a ratio of expectations.


For example, if a strong artifact is present in only one of the data sets, the CSP is trained on the artifact and not on the differences caused by motor imagery [7].

optimization of the center and extent of the ROI, either by a-priori knowledge gained by fMRI scans or by numerical optimization of the ERD in specific frequency bands, is expected to lead to higher SNRs and hence higher classification accuracy.


The figure shows that the approximate method overestimates many of the pairwise marginals.

we know of no previous work studying efficient representations of exact distributions over clusterings.


Theorem 2 states that the regret is upper bounded in this case by Θ(∆ −1 * log T ).

let (θ s ) s∈N be a decreasing sequence of R * + and (δ s ) s∈N ∈ R N + .


this conversion is done by noting that for n × n Hermitian matrices A, B: So if we define the vector A v as an n 2 vector such that its elements are for this subproblem, the memory usage scales linearly with N , the number of measurements, and quadratically with n, the dimension of the data.


The performance of MMD is sensitive to both the regularization parameter λ and the kernel bandwidth σ, so we need to tune both parameters.

definition 1 (Weak Convergence of Measure [48]).


The Leaky Integration Unit architecture [22] proposed residual connections for RNNs but were unable to learn the state transition matrix due to the problem of exploding and vanishing gradients.

fastRNN updates the hidden state h t as follows: where 0 ≤ α, β ≤ 1 are trainable weights that are parameterized by the sigmoid function.


The amount of regularization needed to achieve optimal performance typically depends on unknown properties of functions one wishes to approximate such as their smoothness, compositional pattern and/or the number of variables they depend on.

the posterior concentrates on networks with up to the optimal number s n of links.


The factor analysis model, for each sample i, thus becomes: We have Z ∼ IBP(α, β).

our model discovers the factor hierarchies as part of the inference procedure itself.


Moreover, this hard family of functions is realizable with a small (sublinear in dimension) number of activation units in the single hidden layer.

lower bounds for regression problems in the SQ framework have so far not appeared in the literature, and the existing notions of statistical dimension are too weak for this setting.


A recent empirical study [6] of a large number of 3 × 3 images, represented as points in R 9 revealed that they approximately lie on a two dimensional manifold known as the Klein bottle.

. . , Rx u } is at least 2 u−1 using the Johnson-Lindenstrauss Lemma [11] and the fact that {x 1 , .


Because the representation uses overlapping features of the observation the elements of the descriptor are not independent.

2), and not log-linear models [9] (these would require intractable normalization).


For simplicity, we use the terms "norm", "inner product", and "distance" for the remainder of the paper.

they require quite different theoretical analysis; unlike prior work, our estimator is constructed and analyzed entirely in the frequency domain, and then related to the data domain via Parseval's identity.


The most drastic simplification our model makes is the assumption of Gaussian noise.

the M step is unchanged from the classical factor analysis and is given by equation 9.


In Figure 1 line 3, the agent plans to compute the policy, rather than storing the policy directly.

we compare the objective return achieved by PGRD to the objective return achieved by PGRD with the reward adaptation turned off.


In particular as the values of this covariate increases, we expect an improved survival time.

the model perfectly detects the cross in the survival functions.


In both cases, the gaussian model gave a smooth spectrum of response magnitudes, while the sparse model was more 'all-or-nothing'.

finally, we demonstrate how kernelized versions of the algorithm can be used to address a broad range of problems with non-linear relation between X and Y .


A second assumption is required to compute the supremum on H a .

we reiterate the interpretation of human Rademacher complexity for psychology.


Similarly, CONV layer indices can be represented with only 8 bits.

comparing the yellow and green lines shows that L2 outperforms L1 after retraining, since there is no benefit to further pushing values towards zero.


When performing PCA in practice with massive d and a large/growing dataset, an incremental method like that of Krasulina or Oja remains practically viable, even as quadratic-time and -memory algorithms become increasingly impractical.

let Ω denote the sample space of all realizations (v no , x no+1 , x no+2 , .


We will also compare the results to GCPRL and the PR algorithm PhaseLift [13].

dong is supported by the NSF Graduate Research Fellowship under grant DGE 1106400, and by the Team for Research in Ubiquitous Secure Technology (TRUST), which receives support from NSF (award number CCF-0424422).


The weighted size w 1,2 with respect to C 1 , C 2 , n 1 and n 2 is defined as Theorem 1.

given a column centered data matrix A, set B = D(A) and Then, X is the optimal solution to Problem (1) iff we can determine whether X is the membership matrix of A by solving Problem (5).


by predicting the future information in the sequence.

instead, we work in a sequential setting, in which we have a latent variable for each timestep in the sequence.


Given a continuous model ¤ §¦ ¡ ©¨, we consider the following prediction rule: predict # ¥ if ¤ §¦ ¡ ¨ , and predict # $ ¥ otherwise.

such an analysis would have led to a result of the following form for our problems: It is also interesting to compare Theorem 3.1 with the leave-one-out analysis in [7].


Instead of working with whole images, which contain much irrelevant information, we worked with face images that were normalized as shown in figure 2.

inspired by [11], we tried to enforce local features by restricting the weights to be non-negative.


Intuitively, U-Net-1 to U-Net-k all have the same input size, while U-Net-1 views the smallest region with the highest resolution and U-Net-k views the largest region with the lowest resolution.

we manually labeled the first 16 slices in one stack as the training data and used the other four stacks, each containing 81 sections, for evaluation.


First, we formulate our objective in terms of how to minimize an expected risk function with respect to the labeled training data L = L s ∪ L t and the translator φ by extending the risk minimization framework in [5].

for data preprocessing, the SIFT descriptor [6] was used to find and describe the interesting points in the images, and then clustered the extracted interest points into 800 clusters to obtain the codebook.


For the second stage, w mi is a linear pooling weight from the m'th subunit at position i, and g is the neuron's output nonlinearity.

the stimulus consisted of oriented binary white noise ("flickering bar") aligned with the cell's preferred orientation.


In all our tests we centered and normalized the data, included a bias term (a linear intercept), and choose the regularization parameter as = 1/m, where m is the number of data points.

the above is a sketch-and-project update for a linear system in R n 2 , which allows to obtain an alternative proof of Theorem 5, without using our results from Euclidean spaces.


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.

in the following experiments, we set the number inducing functions to 512.


Let x t ∈ R nx be the n x dimensional state at time t. The system is initialized to x 0 = 0.

we believe that the lack of safety guarantees represents a significant barrier to the wider adoption of many powerful learning algorithms for online adaptation and control.


TAGS is the number of distinct tags that were used to describe the items.

in 4Cliques we assigned the same unit norm random vector u i to every node in the same clique i of the original graph (before adding graph noise).


EWC is a monumental recent work that uses sequential Bayesian for continual learning of neural networks.

the weight-transfer technique is motivated by the geometrical property of neural networks discovered in the previous work [23].


When polynomial decay is applied to decay the learning rate (LR), the power of 0.5 is used to decay LR from the base LR to zero.

even using 2 bits to encode a ternary gradient, the reduction factor is still 16×.


The primary reason for this task choice was practical: ShapeNet is a readily available and high-variability source of 3D objects.

motivated by these successes, in this work we illustrate initial steps toward using DNNs to model rodent somatosensory systems.


we then incorporate the labels to train a descriptive classifier given a corresponded localization.


We assume that the distributions of the mixture components h r differ only in a small number of dimensions, 1, . . . , d race and are identical on the other d other := d − d race dimensions.

efficient coding is necessary given that the brain accounts for   [12], with the middle face being a 50% blend of the Asian and Caucasian faces on either side.


After t steps, the probability of going from a point x i to a point x j should be high if the points are in the same cluster.

for example, the classical k-means algorithm is O(rkmd), where m is the number of data points, d is their dimensionality, and r is the number of iterations required.


We regard each component as representing a single cluster.

it can be obtained from the UCI repository [10].


the positive semidefinite block partitioned matrix with blocks k(x i , x j ).

let g = GP(µ, k) be a Gaussian process in F ×1 .


In a typical setting, we are given as input a protein interaction data set, specifying a set of proteins P and a set of observed interacting pairs T.O.

we then use the EM algorithm [15], to fill in the details of the model, learning both the motif affinities and activities from the observed data of protein-protein interactions and protein motif occurrences.


This is coherent with our theoretical analysis, since GFM needs to estimate more parameters.

additionally, one can easily construct families of probability distributions that obtain a relatively fast convergence rate as a function of m. Solving (2) becomes straightforward in the case of a specific distribution in which the probability mass is distributed over vectors y containing only a single positive label, i.e., m i=1 y i = 1, corresponding to the multinomial distribution.


Different with NAO that tries to reduce the huge computational cost brought by the search algorithm, weight sharing aims to ease the huge complexity brought by massive child models via the one-shot model setup [5].

for the ease of introduction, we use the same notation x = {x 1 , • • • , x T } to denote such string sequence of an architecture x, where x t is the token at t-th position and all architectures x ∈ X share the same sequence length denoted as T . T is determined via the number of nodes B in each cell in our experiments.


The latter motivation can be "lifted" to the matrix domain by adding n virtual outcomes at I/n: The worst-case regret of classical Laplace after T iterations equals log T +n−1 n−1 ≤ (n−1) log(T +1) (see e.g.

the worst-case regrets of classical and matrix LSM coincide.


The bounds above are illustrated in Table 1.

since λ (m) > λ ( ) it might be the case that λ ( ) /∆ (m) .


We first augment the state of the AR sampler to include the derivation auxiliary variable described in Sec.

because alignments between the sequences are unknown in practice, it is difficult to exploit this structure in a principled way.


Unfortunately because of extinct species, we don't have a perfect input and must account for noise.

in general there is no reason to believe that PCA+ would perform well in clustering truly hierarchical data: there are regimes of the HSBM for which applying only phase 1 of the algorithm might lead to a high missclassification error and high cost and for which we can prove that LINKAGE++ is an p1`εq-approximation.


Some guidance is offered in [6] regarding how c might be chosen.

if we remove the slack function by setting s 2 to zero and let s 1 = −(1 − α)c T Φr, our LP (1) becomes maximize c T Φr (2) subject to min u (g u + αP u Φr) − Φr ≥ 0, which is precisely the LP considered in [6] for approximating the optimal cost-to-go function in a discounted MDP with discount factor α.


An interesting observation about our proof technique is that the only concentration inequality we invoked was McDiarmid's Inequality (in [6,Theorem 5] to obtain (20)-a bound on the deviations in terms of the Rademacher complexity).

consider f (w; θ) as in (2), where (z; θ) is convex and L-Lipschitz in z, the norm of φ(θ) is bounded by B, and r is λ-strongly convex.


Assuming that the g n are small we perform a power series expansion of ln Here we have repeatedly used the fact that each factor z n in expectations z l n z s m have to be paired (by Wick's theorem) with a factor z m where m = n (diagonal terms vanish by ( 17)).

we compute explicit expressions for the remainder terms of the approximation.


We resized the images to 150 × 150 pixels and made them grayscale to match our face dataset.

we train this representation using SGVB, but we make some key adjustments to the outputs of the encoder and the gradients which train it.


From optimization perspective, enforcing the Lipschitz constraint is challenging.

comparing SWGAN methods with and without latent representation, we find that the ones with latent representation perform better.


The stimuli are 16×16 images of handwritten digits from the MNIST data set, presented sequentially, one per "time slice".

we learn these parameters w ν jointly with the other model parameters.


In this section we describe our results for strongly convex costs.

to release a private approximation to wt+1 , it suffices to approximate v t+1 = t τ =1 f t ( ŵτ ) while ensuring differential privacy.


The learning algorithm learns the parameters of the individual labelers, and uses them to decide which labeler to query for each example.

algorithm 5 generates a Ŝk such that the set V k defined as: has the property that: This is achieved by labeling, through inference or query, a large enough sample of unlabeled data drawn from U. Labels are obtained from three sources -direct inference (if x lies outside the disagreement region as identified by Algorithm 4), querying O (if the difference classifier predicts a difference), and querying W . How large should the sample be to reach the target excess error?


Since the feedback the learner receives is limited, this task of finding the optimal cell may be challenging.

the goal of the learner is to minimize her cumulative loss.


This is the natural notion of risk for the learning task, since we wish to infer the likelihood of future data, and our goal can now be more concretely stated as using the data to produce an estimator Q n with a 'small' value of D(P Q n ).

this will not eliminate the zero problem, since a whole column may be zero.


We conduct experiments on a large-scale dataset [17] for conversation question answering, which consists of 200K dialogs with 1.6M turns over 12.8M entities from Wikidata.

since previous questions and answers/responses in conversation are useful contexts, we concatenate them with the current question as an input x = (x 1 , ..., x T ).


The mechanism for this construction is an optimistic interpretation of the learned model.

this gives us the first apprenticeship learning framework where a teacher only shows demonstrations when they are needed for efficient learning, and gracefully blends autonomous exploration and apprenticeship learning.


As we shall see later, this fact will be crucial for the greedy algorithm to be tractable in this case.

using a single theorem, they are able to rederive a wide range of known results on high-dimensional consisteney and error bounds for the various regularized and constrained estimators.


Each particle in our SMC algorithm is a sequence of states and waiting times for the current sequence k. By using a Particle MCMC (PMCMC) method [1], we then compute an acceptance ratio that makes this proposal a valid MCMC move.

the application of non-parametric Bayesian techniques to time series has been an active field in the recent years, and has led to many successful continuous time models.


Similarly to Theorem 2 in (Abbasi-Yadkori, Pal, and Szepesvari, 2011) 2 , for any state history and with probability of at least 1 − δ, it holds for all t > 0 that θT t,a x(s t ) − θ * a T x(s t ) ≤ we define δ = δ/k and bound this probability for all the actions, i.e., ∀a, t > 0 Recall that any valid action a at state s satisfies E[e t (s, a)] = θ * a T x(s t ) ≤ .

a practical challenge here is that the features must be fixed over time when used by the contextual bandit, while the activations change during optimization.


The second component is the addressing variable a 2 {1, ..., |M|} which selects a memory entry m a from the memory buffer M. The varitional posterior distribution q(a|x) is parameterized as a softmax over a similarity measure between x and each of the memory entries m a : where S q (x, y) is a learned similarity function described in more detail below.

since we have a discrete latent variable a in the model we can not simply backpropagate gradients through it.


In practice, this problem can be shown to be acute even for values of γ = 0.9 or γ = 0.99, which are quite common in experiments.

the other results can be derived through similar analysis.


We show that (i) the problem (4) can be solved within O( P 0 (k + log( P 0 )) + (n + m)k 2 ) time, where k is the rank of X, and (ii) the algorithm converges to the critical points of f (X, d).

we also vary r in the range {10, 20,  Accuracy Figure 1(a) and 1(b) clearly show that the proposed algorithm can perfectly recover the underlying inter-purchase durations with varied numbers of users, items, and categories.


the necessary entropies were cached in advance.


One iteration involves drawing a sample from the window and updating the hyperparameters by gradient descent as illustrated in Algorithm 1 in the left side of Figure 3.

in DGPs, sampling from the posterior is inexpensive, since it does not require the recomputation of the inverse covariance matrix, which only depends on the hyperparameters.


These combine proof and disproof numbers [19] and the number of threads examining a node.

(Other conditions in these tests are discussed later.)


In a detailed study on AMS-based broad-band SNR estimation [11) it was shown that harmonicity which is well represented in AMS patterns is the most important cue for the neural network to distinguish between speech and noise.

the input matrix consists of 5 times the auditory model feature vector with 30 elements, glued together in order to allow the network to memorize a time sequence of input matrices.


p n is necessarily orthogonal, we would ideally like to solve minimize with µ large enough to guarantee that the global solution is indeed a permutation.

we focus on optimization problems written over the set of permutations.


The comparative results in Table 3(a) show that, as expected, under this stricter ZSL setting, all ZSL models suffer from performance degradation.

the results in Figure 1(b) show that: (1) Our DIPL algorithm converges very quickly (≤5 iterations).


Using straightforward algebra and the Sherman-Morrison inverse formula, we can show that the resulting solution to the minimization of (2.1) is: where The detailed derivation will appear in a longer version.

the results show that the accuracy achieved by our LEGO+LSH algorithm is comparable to the LEGO+linear scan (and similarly, L 2 +LSH is comparable to L 2 +linear scan), thus validating the effectiveness of our online hashing scheme.


Assume Consider two cases: Firstly, assume u 1 , • • • , u S−1 are orthogonal, i.e., u i u j = 0 for i = j.

proposition 3 Assume a reversible ergodic Markov chain with transition matrix T and let J = QT .


We formalize this problem as that of decomposing X into two constituent graphs E 1 and E 2 , the true and the noise graphs respectively, such that e We use a training set to fit our model parameters and then measure task performance on a test set.

we test our model on the task of discerning which of the edges in X are also in Y gold .


• For the s-th segment, {Y s , t s , l s }, 1. l s is selected as either class 1 or 2.

when evaluating the models, we merge the labels of 48 phonemes into the commonly used 39 phonemes [11].


In this case, the Kullback-Leibler divergence of projection (1) of P on (T, C) from P is bounded [13]: This bound means that if we have an ε-junction tree for P (V ), then instead of P we can use its tractable principled approximation P (T,C) for inference.

we can get a probabilistic estimate of I (A, B | C), that has accuracy ±∆ with probability 1 − γ, using number of samples and computation time polynomial in 1 ∆ and log 1 γ : Theorem 11.


Working with a distribution over trees, although costly, could improve performance when there is not sufficient data to strongly constrain the best tree, or when the domain is not strongly tree-structured.

figure 3a shows the performance of the algorithms under random sampling for four representative datasets.


Hence a natural question to ask is: given a point cloud in N -dimensional Euclidean space, what is the dimension of the manifold that best captures the structure of this data set?

if we choose a sufficiently small value for δ and ρ, we are guaranteed estimation accuracy levels as close as desired to those obtained with ID estimation in the original signal space.


Examples having non-zero coefficients are called support vectors that form the final solution.

proposed an efficient depth-first search algorithm to enumerate all subgraphs from a given graph [12].


We hypothesize that the apparent uninformativeness of the questions asked by subjects on these trials is due to imperfections in the current version of Tenenbaum's model, and are working to improve the model's descriptive accuracy, to test this hypothesis.

we found that in some situations, a simple confirmatory strategy maximizes information gain.


To match the fact that our image contrast distribution is zero mean Gaussian, and therefore symmetric about the origin, we pair the types into two pairs of equal-size populations and keep the number of cells the same across each pair during this optimization, expecting that ON and OFF homologous types will emerge.

the total density of cells varies across eccentricity by 3 orders of magnitude in the primate retina.


First we bound the difference between the target risk ǫ T (h) and weighted risk ǫ α (h).

the proofs of these lemmas, as well as the proof of Theorem 2, are in Appendix B. Lemma 1 Let h be a hypothesis in class H. Then The lemma shows that as α approaches 1, we rely increasingly on the target data, and the distance between domains matters less and less.


Since the initial work of Szegedy et al.

applying the triangle inequality, we get that v 2 (X) and v 2 (X ) are close.


As a common means to encouraging sparsity in machine learning, the 1 norm has been incorporated into the NMF objective function [6] as a sparsity regularizer.

in this work, we focus on the generalized Kulback-Leibler divergence (a special case of the Bregmann divergence), and use its decomposing property to simplify the mfNMF objective and remove the undesirable multitude of equivalent solutions in the general formulation.


Baldi & Lu (2012) recently provided a proof for Conjecture 2.2 (i), leaving the proof of Conjecture 2.2 (ii) for future work.

a5u) that corresponds only to the model assumption as A1p-m (resp.


Our contribution is based on a generalized view of state estimation that subsumes the naïve, piecewisetrained models discussed in the previous section and allows them to be trained end-to-end using simple and scalable stochastic gradient descent methods.

because the dynamics model is non-linear, we equipped our model-based state estimators with extended Kalman filters, which is a straightforward addition to the BKF framework.


Surprisingly, for approximate representation, the conditional gradient algorithm can approximate any homogeneous mixture within accuracy by combining O(1/ 2 ) shallow models, where the hidden constant may decrease exponentially wrt the depth.

the nonnegative rank characterizes the smallest size of shallow SPNs (LCMs) that represent the density mixture W. Similarly, we can prove the following result when the leaf nodes are from F instead of the convex hull G. Theorem 4.2.


If A i commute, the product of exponentials is equal to an exponential of sums, which in the limit evaluates to the solution in (7).

the remaining complementary slackness and dual feasibility conditions effectively require that X is spanned by the top eigenvector(s) of A.


As in the training set results before, PEERsum performs slightly better than PEERone.

our proposed methods continue to reduce the average mistake rate by requesting labels from peers.


The idea is to attach numerical quantities to persistence barcodes, which can then be used as input to any machine learning algorithm in the form of feature vectors.

[13] restrict F to functions on a unit ball in H , i.e., F = { f ∈ H : f ∞ ≤ 1}, and show that Eq.


As shown in (3), this allows for a modular representation of Q π in which the MDP's dynamics are decoupled from its rewards, which are captured by the weights w. One potential benefit of having such a decoupled representation is that only the relevant module must be relearned when either the dynamics or the reward changes, which may serve as an argument in favor of adopting SFs as a general approximation scheme for RL.

as such, it provides stronger guarantees: instead of comparing the performance of π with that of the previously-computed policies π j , Theorem 2 quantifies the loss incurred by following π as opposed to one of M i 's optimal policies.


However, when aspects of the computation are likely to reflect internal mental states, which may vary substantially even when external covariates remain constant, the relevant variables must be uncovered from neural data alone, most typically using a latent variable model [1][2][3][4][5][6].

first, we extend Gaussian Process Factor Analysis (GPFA) [2], an algorithm that has been successfully applied in the context of extracting time-varying low-dimensional latent structure from binned neural population activity on single trials, to directly model the point-process structure of spiking activity.


Heading is then represented by the preferred heading direction of the most active template(s) .

these models assume heading is encoded by a set of units that each respond best to a specific pattern of flow that matches their preferred heading.


We refer to this model as the controller.

doing so would completely throw away the information about the position of the fixations.


We then define the connecting module as a classifier, which takes the left and right phrases P (l) and P (r) as input and outputs a normalized score S(P (m) j | P (l) , P (r) , I) for each j ∈ {1, . . . , L}.

conventional captioning methods usually encode the content of the given image into feature vectors, which are often difficult to interpret.


Given the strong lower bounds in the general setting, we initiate the study of the distributed parameter estimation problems with structured parameters.

we provided a generic tool called direct-sum for relating the information cost of d-dimensional problem to one-dimensional problem, which might be of potential use for other statistical problem than gaussian mean estimation as well.


Since LFW is a dataset with a different set of persons from those in the training set (from VF), we observe a decrease of accuracy.

many neurons denote abstract features/attributes that are difficult for humans to perceive.


We use mIoU for semantic segmentation, error of per-pixel regression (normalized to image size) for instance segmentation, and disparity error for depth estimation.

we also consider task-specific loss functions Although many hypothesis classes and loss functions have been proposed in the MTL literature, they generally yield the following empirical risk minimization formulation: for some static or dynamically computed weights c t per task, where Lt (✓ sh , ✓ t ) is the empirical loss of the task t, defined as Lt (✓ sh , ✓ t ) , 1 Although the weighted summation formulation (1) is intuitively appealing, it typically either requires an expensive grid search over various scalings or the use of a heuristic (Kendall et al., 2018;Chen et al., 2018).


The mean AUC values over 20 trials as well as the computation time are summarized in Table 2, showing that uLSIF works fairly well.

proposed uLSIF is overall shown to work well and computationally efficient also in outlier detection.


This differs from our approach where we base our causal inference method on a novel interpretation of the asymmetry between cause and effect, and based on this derive three decision rules with one of these decision rules relying on classifying feature representations.

one example of this is linear Gaussian dependence which is non-identifiable for most other causal discovery methods too.


Decoding involves the inference of the hand motion from the firing rate of the cells.

note that the negative logarithm of the prior term can be approximated by the robust statistical error function Figure 5 shows the various estimates of the receptive fields.


We index # $ by the response R because it is not sensible to assign a time cost to a "no go" response, where no response is produced.

for example, the input to the perceptual pathway in the discrimination task is one of "!


In this subsection, we applied the LPP to images of faces.

as can be seen, LPP performs much better than PCA.


However, it is known to provide a false sense of security [30,6,2].

we believe that this work will serve as an essential step towards both certifiable and robust deep learning models.


Our definition for equalized odds can be applied also to score functions: a score R satisfies equalized odds if R is independent of A given Y .

this data is used to construct a (possibly randomized) predictor Ŷ (X) or Ŷ (X, A), and we also use such labeled data to test for non-discriminatory.


The parameter settings of a model encode what the model has learned from the data during training, and determine test set performance.

we explain the source of this phenomenon in our discussion section.


The most straightforward application of GPs is the standard regression model with Gaussian likelihood, for which the posterior can be computed in closed form.

on the plots, we use the shorter notations, FULL, MIX, and MIX2 due to the limited space.


We compare the proposed method with the following baselines: (i) bag-of-words-based methods like TF-IDF [17] and LDA [8]; (ii) word/document embedding methods like Word2Vec [30], Glove [33], and Doc2Vec [27]; and (iii) the Wasserstein-distance-based method in [26].

besides transfer learning, the idea of model distillation has been extended to control the learning process of neural networks [34,35,42].


More closely related to our work is the Riemannian SVGD algorithm [18], which generalizes a gradient flow interpretation of SVGD [15] to Riemannian manifolds, and thus also exploits geometric information within the inference task.

the SVGD algorithm then seeks a transport map T l+1 = I + Q that further decreases the KL divergence between (T l+1 ) * p l and π, for an appropriate choice of Q ∈ H d . the SVGD algorithm seeks a map Q ∈ H d such that where 0(x) = 0 denotes the zero map.


The fit model had positive spike prediction accuracy for 79.6% of neurons (469 out of 589) whose firing rates were greater than 0.5 Hz in both the training and validation periods (Figure 5c).

the size of these datasets makes inference computationally expensive.


We compare our algorithm with other approaches including LPBoost, Brown-Boost, and SmoothBoost.

for each of the splits we use 5-fold cross-validation to select the optimal regularization parameter for each of the algorithms.


Let I(a) = 1 when predicate a is true and I(a) = 0 otherwise.

within this approach, we consider a prior distribution P over a space of classifiers that characterizes our prior belief about good classifiers (before the observation of the data) and a posterior distribution Q (over the same space of classifiers) that takes into account the additional information provided by the training data.


HOG-LDA is a computationally effective foundation for estimating similarities s ij between large numbers of samples, Here φ(d i ) is the initial HOG-LDA representation of the exemplar and S is the resulting kernel.

separate exemplar classifiers are trained by learning the similarities of individual exemplars against a large set of negatives.


Since this reformulation depends only on conditional probability estimates, we can perform fringe expansion in CTW and add nodes dynamically without biasing the mixture.

as L is decreased, the performance of D2-CTW may naturally degrade.


. . , θ K , there is a gap g > 0 between Φ 1 and Φ 2 and both Φ 1 and Φ 2 are bounded away from zero by b > 0.

if the mixing coefficients are very similar, a larger sample is required.


With n u = 3n l , the model considerably improves upon the one discarding unlabeled data.

the diagnosis models behave well, and the minimum entropy algorithm is not distracted by the two clusters; its performance is nearly identical to the one of training with labeled data only (cross-validation provides λ values close to zero), which can be regarded as the ultimate performance in this situation.


More specifically, our classifier is composed of several regression functions, each of which is trained to predict a word embedding of the target label.

we propose to use several word representations obtained from different corpora or architectures as target labels.


Several projections to lower dimensions have been tested and t = 5 turned out to be a good choice, eliminating the bulk of noise while retaining the essential cluster structure.

we performed usual k-means clustering, followed by a majority voting to match cluster labeling.


( 4) is a fixed (loose) upper bound λ max (A) for all k. But in branch-and-bound search, any intermediate subproblem A m , with k ≤ m ≤ n, yields a new and tighter bound λ max (A m ) for the objective v * (k).

finally, we note that even simple thresholding (ST), once enhanced with the variational renormalization, performs quite adequately despite its simplicity, as it captures at least 92% of the optimal variance, as seen in Figure 3(a).


For low-trace-norm learning, consider a sample S of size |S| ≤ Cn, for some constant C. Taking entries of Y to be of unit magnitude, we have Y S F = |S| ≤ √ Cn (recall that Y S is defined to be zero outside S).

shifting the solid red (bottom) curve by this amount yields the dashed red (bottom) curve.


For comparison with the model by Yu and Ballard [4], we chose the files me03 and di06, each of which consisted of approximately ten minutes of interaction between a mother and a preverbal infant playing with objects found in a box of toys.

the most parsimonious option according to the prior was not to learn any new words, but this did not account for the new evidence.


In terms of convex techniques, lifting-based methods transform the signal recovery problem into a rank-one matrix recovery problem by lifting the signal into the space of positive semidefinite matrices.

the authors in [20] analyze the same optimization problem in [4] but exhibit global guarantees regarding the non-convex objective function.


It maintains an exponential moving average of label predictions on each training example, and penalizes predictions that are inconsistent with this target.

an additional difference between the three algorithms is that the ⇧ model applies training to ✓ 0 whereas Temporal Ensembling and Mean Teacher treat it as a constant with regards to optimization.


Note that the training sets and testing sets for a classifier are disjoint.

by exploiting the availability of auxiliary unlabeled data, we are able to improve the performance of the state of the art supervised DRF approach.


In Section 2, we formally define coding cost, statistical typicality, and attentional focusing in face processing.

these experiments show that a classical phenomenon known as the beauty-in-averageness (BiA) effect (see Figure 1a), whereby blends of multiple faces are usually found to be more attractive than the originals [10], can be suppressed or even reversed (termed Ugliness-in-Averageness or UiA), when the facial blends are created from recognizable faces [11] (see Figure 1d;e), or when attractiveness judgment of a mixed-race/mixed-gender blend is preceded by a racial/gender categorization task [12,13] (see Figure 2a;b), respectively.


To gain more insights on this, we conducted some additional experiments, whose results are shown in Figure 2a and 2b.

we rank the attributes according to the number of local machines who select them, and choose the top-2k attributes from the ranked list.


for some loss function (see examples in Section 4).

this result is similar to Lemma 1 of [17] but holds under RSC/RSS conditions (rather than the RIP condition as in [17]), as well as for the general loss functions.


The size of joint representation C is the same with the rank K in lowrank bilinear pooling, C = K = 1, 024, but K 0 = K ⇥ 3 is used in the bilinear attention maps to increase a representational capacity for residual learning of attention.

we evaluate on the VQA 2.0 dataset [1,8], which is improved from the previous version to emphasize visual understanding by reducing the answer bias in the dataset.


Furthermore, Q-learning in particular achieves higher accuracy models at a fraction of the computational cost of using all features, and is more effective than imitation learning.

we have the following expression, where we use z(a) to indicate the a'th element of z: Note that in practice we can choose each f a to be a sparse vector such that f a • f a = 0 for all a = a; that is, each feature function f a "fills out" a complementary section of the feature vector f . A much more powerful approach is to create a feature vector as the composite of different extracted features for each vertex and edge in the model.


We show that this model can identify features that are location invariant by modeling a previous experiment on human feature learning.

there were nine test images presented in a random order: Seen Both (an image in both training sets), Seen Unit (an image that only the unitized group saw), Seen Sep (an image only the separate group saw), New Unit (an image valid under the unitized feature set), New Sep (a image valid under separate feature set), and four other images that acted as controls (the images are under the horizontal axes of Figure 4).


Figure 3a shows how the number of edges varies versus the total number of active vertices for the multigraph, with different colors representing different random seeds.

at a high level, this earlier model generates a weight measure W = i,j w ij δ (θi,θj ) (Caron and Fox [12] used, in particular, the outer product of a completely random measure), and the graph measure G is constructed by sampling g ij once given w ij for each pair i, j.


Many authors have studied settings where one moving object comes to a stop, and a second object starts to move [17].

every particle that exists at time t 1 must also exist at time t 2 .


We preprocess the data by applying PCA to reduce the dimensionality of the input space.

we cast the problem of learning spatio-temporal primitives as a tensor factorization prob-lem and introduce tensor group norms over the primitives that encourage sparsity in order to learn the number of elements in the dictionary.


Importantly, these results show that by addressing the evidence/grounding problems, we can process large, arbitrarily structured MLNs/evidence without running out of memory in a reasonable amount of time.

to make this weight-computation step feasible, we propose the following approach.


( 7) to a generalization of PA-II in Mahalanobis distances (see Eq.

u is distributed according to a Gaussian distribution, U ∼ N μ, Σ .


The rationale behind this scheme is that the initial model Â(0) is obtained essentially from an uninformed, ad hoc characterizer, for which one has to expect a large model variation and thus (on the average) a poor Â(0) .

all computations were done in Matlab on 2 GHz PCs except the HMM training on dataset (d) which was done on a 330 MHz machine (the reported CPU times were scaled by 330/2000 to make them comparable with the other studies).


This is a dramatic improvement over previous techniques.

expressing the relevant terms using Pold and k i we obtain where 'Y := (C + BT A -1 B)-1.


Our objective here is to show that on a WAGB, BAP with GLIE exploration will converge to the ("clustered") terminal state.

in RL, the agents usually do not know the environmental model (game) up front and receive noisy payoffs.


We then construct the most accurate filter under the least favorable distribution in this set.

the Wasserstein distributionally robust filter now significantly outperforms the classical Kalman filter and, to a lesser extent, the KL distributionally robust filter.


Existing source location and recovery algorithms used in magnetoencephalographic imaging generally assume that the source activity at different brain locations is independent or that the correlation structure is known.

with imaging methods, a grid of voxels is used to represent the entire brain volume.


If covariances in the posterior between f conv and f rbf are to be allowed, S must be a full-rank 2M × 2M matrix.

implementation 2 requires minimal changes to existing implementations of sparse variational GP inference, and can leverage GPU implementations of convolution operations (see appendix).


We will propose a method termed Mutual Boosting to incorporate contextual information for object detection.

by transforming each m-detection image to an m-detection cube, (having scale as the third dimension) multi-scale context detection could be achieved 10 .


These two desires are at odds, and the rate degrades to O(1/✏).


When the input of a capsule network is transformed, not only the deeper pose vectors change accordingly.

if we apply a transformation from G on the input of a sequence of those layers (e.g.


Note that by definition if C i is in the Markov blanket of C j , then C j is in the Markov blanket of C i .

the marginal probability for each variable can be estimated by averaging the conditional marginals: Note that in Markov networks, P (X i |x The sampling distribution of Gibbs sampling converges to the posterior distribution (the distribution associated with the evidence instantiated Markov network) as the number of samples increases because the resulting Markov chain is guaranteed to be aperiodic and ergodic (see [15] for details).


In the course of doing so, because we are invoking Taylor's remainder theorem, we need to bound the first few derivatives of U (S, c).

what is the minimax value of the option, as well as the optimal hedge, when we fix the variance budget c and the asset's current price S, but let the number of rounds tend to 1?


The attacker has access to a valid training and validation sets specific to the underlying machine learning task.

it cannot arbitrarily change the data of victim parties.


Figure 2 (right plot) supports our claim that standard IRL is ineffective at learning rewards from misguided user demonstrations.

8 Acknowledgements We would like to thank Oleg Klimov for open-sourcing his implementation of the Lunar Lander game, which was originally developed by Atari in 1979, and inspired by the lunar modules built in the 1960s and 70s for the Apollo space program.


The advantage of this "greedy" homotopy path is that it provides a set of action-values that are a greedy fixed point for all settings of the L 1 regularization parameter.

given a square matrix M and a vector q, a linear complementarity problem (LCP) seeks vectors w ≥ 0 and z ≥ 0 with w T z = 0 and w = q + Mz.


. . , z m ) of m examples, the task of a learning algorithm is to construct a classifier with the smallest possible risk without any information about D. To achieve this goal, the learner can compute the empirical risk R S (f ) of any given classifier f according to: We focus on learning algorithms that construct a conjunction of rays from a training set.


If r ≥ d, then there exists weights α ∈ R r which recover the unknown A * as where α i = 1/(rt i ) and Σ = r i=1 x i x i /r.

current methods for learning transformations have two limitations.


When the domain size exceeds 40000, a random set of n = 10000 rados is computed from the training fold.

in Table 2, Ω-R.ADABOOST unregularized ("∅") is virtually always beaten by its SLOPE regularized version.


This gives the Matrix Stochastic Gradient (MSG) algorithm, which, in detail, consists of the following steps: 1.

there exist cases in which it can get stuck at a suboptimal solution.


This global pooling approach ignores any hierarchical structure that might be present in the graph, and it prevents researchers from building effective GNN models for predictive tasks over entire graphs.

by separately pooling distinct parts of a sparse subgraph, DIFFPOOL can learn to capture the meaningful structures present in sparse graph regions (e.g., as in Figure 2).


. .} along the relevant dimensions: P (spike|s) = P (spike)g(s 1 , s 2 , ..., s K ), If the inputs are Gaussian, the last requirement is not important, because relevant dimensions can be found without knowing a correct functional form for the nonlinear function g in Eq.

in practice this involves finding a single relevant dimension first, and then iteratively increasing the number of relevant dimensions considered while adjusting the previously found relevant dimensions.


The face images were captured by 13 synchronized cameras and 21 flashes, under varying pose, illumination and expression.

tSA is much more computationally efficient in time and storage.


These can be naively computed with 6rb FFTs.

we consider the task of shrinking a large model for this task whose architecture is as follows [23]  Results with 11 different models are reported in Figure 4 (left) including the state of the art keyword spotting model developed in [23].


Second, predictive variances using moment-matching are generally conservative and increased the uncertainty even further.

in practice, time series often have an unknown dynamical structure, and they are high dimensional and noisy, violating many of the assumptions made in established approaches for state estimation.


We make the following assumptions on the error matrix W: 1.


Because, similarly to the chaser loss, Reptile (Nichol et al., 2018)  As shown in Fig.

(2017) proposed MAML that formulates meta-learning as gradient-based optimization.


Our method could be combined with other methods which are orthogonal to us, like only transmitting large coordinates and accumulating the gradient residual which might be transmitted in the next step [1,21].

it can be seen from the following simple derivation.


We next consider the case, where A is an irreducible positive definite M-matrix.

this raises the question whether the best known convergence rates of CCD in the literature are tight or whether there exist a class of problems for which CCD provably attains better convergence rates than the best known rates for RCD, a question which we will answer in Section 4.


This research is supported in part by NSF CISE Expeditions Award CCF-1139158, LBNL Award 7076018, and DARPA XData Award FA8750-12-2-0331, and gifts from Amazon Web Services, Google, SAP, The Thomas and Stacey Siebel Foundation, Apple, C3Energy, Cisco, Cloudera, EMC, Ericsson, Facebook, GameOnTalis, Guavus, HP, Huawei, Intel, Microsoft, NetApp, Pivotal, Splunk, Virdata, VMware, WANdisco, and Yahoo!.


Before conducting intersections, a critical task is to (quickly) estimate the sizes of the intermediate results to plan the optimal intersection order [20,8,25].

it is highly desirable to have a mechanism which can estimate join sizes very efficiently, especially for the lower-order (2-way and 3-way) intersections, which could potentially result in much larger intermediate results than higher-order intersections.


In subsequent sections, we show how we can learn a new modulation function which takes into account the three issues we highlighted in this preliminary discussion.

b is the constant bias which normalizes the classification margins as −1 and +1.


The live bonus heuristic encourages the agent to live longer so that it will potentially have a better chance of getting extrinsic rewards.

the second baseline augmented the agent with a count-based bonus generated by the pixel-SimHash algorithm [Tang et al., 2017] (henceforth, A2C-pixel-SimHash baseline agent in short.)


In the other extreme case q = ∞ the conditional probability η is bounded away from 1 2 .

let us now discuss a recent result (see [11]) on rates for the following modification of the original SVM: Note that unlike in (3) the norm of the regularization term is not squared in (9).


The inference model not only learns a nice latent manifold structure, but also acts as a discriminator to maximize the divergence of the approximate posterior with the prior for the generated data.

stackGAN-v2 [42] and HDGAN [43] adopt multi-scale discriminators in a treelike structure.


This is a Nyquist-type reconstruction formula.


For image classification, we train ResNet [19] and VGG [39] with different number of layers on CIFAR-10 [24].

a larger p leads to a smaller communication overhead, but a larger second term in (11).


With a softmax function, we normalize the parameters for all the devices to obtain a probability distribution of the placement.

for Inception-V3, Post is able to find optimal placements that outperform the Single GPU case.


Acknowledgments This work is supported by US Army Research Office under contract W911NF-16-1-0265 and by the US National Science Foundation under grants CCF-1319140 and CCF-1718698.

they show that the mean-squared error (MSE) of the estimation, together with a few other "order parameters", can be characterized as the solution of a deterministic system of coupled ordinary differential equations (ODEs) in the large system limit.


This, however, only applies whenever the empirical risk decomposes into individual loss terms (e.g.

the current paper provides a) significantly improved performance bounds which match better what can be observed in practice and which apply to a wide range of regularization terms, b) a variant of the algorithm which does not require quadratic programming, yet enjoys the same fast rates of convergence, and c) experimental data comparing the speed of our solver to Pegasos and SVMPerf.


The problem is illposed, in the sense that the set of parameters giving rise to a particular voltage trace cannot be uniquely determined.

to observe this, we adopted a conductance-based model proposed by Pospischil et al.


Similarly, for classic bootstrap, we sample l datasets with replacement, learn l different CPDAGs using RAI, and record the number of CI-tests.

for the number of CI tests, the ratio between B-RAI and RAI is k i=0 s i .


Work by GC was performed while at Google Brain Research.

our graph is not a complete graph and our goal is to design an architecture that will be invariant to any automorphism of the graph, such as permutations of the entity variables.


When there are multiple classes, this measures the closeness of the threshold for distinguishing the correct class out of the union of the rest of the classes (i.e., one-versus-rest).

in this simple example, we can also see that the gradient magnitude is proportional to the difficulty because − w log(p(y i |x i , w)) = (1 − p(y i |x i , w)) x i .


For any subset S µ  This work was supported in part by NSF grants CMMI-1335155 and CNS-1161964, and by Army Research O ce MURI Award W911NF-11-1-0036.

if ÷ AE 1/6, then any algorithm with success probability at least 2/3 requires at least min{¸/4, 1/48"} samples from the Unbiased Oracle.


Given N (t) denoting the number of events occurred in the time interval [0, t) and τ t indicating the arrival times of the temporal events before t, the intensity for a time point t conditioned on the arrival times of all the previous events is defined as: It is worth noting that we do not consider edge effect in this paper, hence no events exist before time 0.

unlike the SSMs, it lacks the capability of modelling events' latent states and their interactions.


That paper demonstrated that upper-confidence-bound (UCB) exploration schemes for concurrent reinforcement learning (concurrent UCRL), such as those discussed in [15,4,16], fail to satisfy the diversity property due to their deterministic nature.

in concurrent UCRL, Thompson resampling and seed sampling, at each time t k,m , the agent k generates a new MDP M k,m based on the data gathered by all agents up to that time, computes the optimal policy π k,m for M k,m and takes an action a k,m = π k,m (s k,m−1 ) according to the new policy.


Specifically, we calculate a sequence of {f  i } n i=1 , and use kS t U > f tB k 2 n to approximate the bias term, where , B is a positive integer.

in this section, we first derive the null limit distribution of (standardized) D n,t as a standard Gaussian under mild conditions, that is, we only require the total step sizes ⌘ t goes to infinity.


It includes methods for finding and using hidden state to make predictions more accurate.

large divergence in the curves corresponds to the creation of synthetic items and the discovery of schemas that predict synthetic item state.


Network Architectures: We use the implementation of ResNet-50 [33] and VGG-16 [34] in Tensor-Flow as the neural networks that compute the bias coefficients in the energy function of our CRF (Eq.

removing the x x x − y y y link generally improves the performance significantly.


The statistics were low in all cases but increased with increasing dimensionality.

all in all, our results suggest that our framework can yield substantial advantages in terms of goodness of fit and in terms of estimated entropy in particular for high-dimensional problems.


For example, this may be achieved by solving a linear system of equations [3,20] involving the Laplacian, and a solution may be computed in O(|E| log O(1) n) time [18], where E is the edge set.

we present experiments on two web-spam classification tasks, one of which includes a graph with 400,000 vertices and more than 10,000,000 edges.


In fact, if f is supermodular (α ≡ 1) and for = k, we recover the 1 − e −1 ≈ 0.63 guarantee from [18].


While restricted to discrete states, [2] provides an important insight that we exploit in this work: only a finite number of partitionings of the observation space are required to distinguish between the optimal conditional policy over a finite set of belief states.

the Γ h in this optimal h-stage-to-go value function can be computed via Monahan's dynamic programming approach to value iteration (VI) [4].


By definition of w * , the third quantity in Equation 1 is non-positive.

data-mining algorithms have been introduced that aim to respect other notions of privacy that may be less formally justified.


Similarly, Wi-Fi hotspots are carefully arranged to cover every corner of a floor.

the users are labeled as 1, 2, 3, . . . , n user , where n user = 40.


These algorithms involve hidden variables or structured labels in discriminative training.

han and Zhu [18] applied grammar rules, in a greedy manner, to detect rectangular structures in man-made scenes.


To relate this to current PoE models, if λ T e φ(•) were replaced with a log Student-t function then this FRAME model would take the same form as the Product-of-Student-t formulation of [12].

we model the joint probability of population spiking times and 2D hand position and show that the likelihood of test data under our model is significantly higher than under other models.


L(x, p, q) lower-bounds the marginal log-likelihood for any choice of q, and the bound is tight when q is the true posterior p(z|x).

a known pathology when training stochastic latent variable models with the ELBO is that stochastic states can go unused.


In normal operation, Bob shows news articles to users to maximize the click-through rate.


In principle, distances should then be defined as geodesic distances using this local metric on a Riemannian manifold.

unfortunately, the Fisher kernel is quite generic, and need not necessarily improve nearest neighbor performance.


These inhibitory patterns, which we call shadow patterns, are activated after the excitatory patterns fire, but have no special in-pattern connectivity or structured projections onto other patterns.

the maximal load of our system is determined in terms of the available synaptic resources, and is proportional to the size of the excitatory population, N E . For the parameters used here it turns out to be P=0.06N E . This limit was estimated by a combinatorial argument of synaptic availability, and shown to be realized by simulations.


While the ranking from recursive independent component elimination did not reveal any evidence of an overwhelming contribution from artefacts related to muscle activity, it is not possible to rule out completely the involvement of such artefacts-possibly the only way to be sure of this is to implement the interface with locked-in patients, preparations for which are underway.

there is considerable motivation to add to the palette of available BCI paradigms by exploring EEG signals that occur in response to auditory stimuli-a patient's sense of hearing is often uncompromised by their condition.


Obviously this itself would not be an improvement, but performance would be identical to the algorithm described in Section 3.

the number of CFR iterations during which a sequence can be skipped depends on how poorly the sequence has performed in previous CFR iterations.


To examine the robustness of our approach, we ran a series of experiments in which we varied the diameter of the acoustic events relative to the diameter of the sensors.

18 leads to the optimal affine solution of the SFS problem: this solution is not yet Euclidean, since Γ might not be of the form of Eq.


The RCV1-v2 and BioASQ datasets provide label relationships as a graph.

we can observe a consistent benefit from using the reverse label ordering on both approaches.


hw, xi over R d such that kwk 1  B with ✏-insensitive loss bounded by ✏ 0 + ✏ 1 .

most of the existing work focuses on classification tasks and provides specialized techniques for the same, albeit with little or no theoretical guarantees.


The details of the trajectory emerge from the interaction of this controller and the uncontrolled stochastic dynamics.

for each state we found the optimal transition probabilities (14).


#" and $ %$ , we use the NOISY-AND (assumes exception independence) model (Pearl, 1988) for combining conjunctive sources.

we suggest that any evidence which causes the probability of the best interpretation to drop below its next competitor will also cause increases in reading time.


Note that this is a special case of the class of methods studied in [6] (which considers more general projections) that leads to non progressive regret bounds, and this is the method of significant current interests [3,8].

proposition 1 Let f j ∈ R n be a set of fixed vectors (j = 1, . . . , M ), and assume that q j ≥ 0 with j q j = 1.


2 is called the upper bound on the variance of stochastic gradients [26].

there is still an open question: whether e O(n ^✏ 2 + ✏ 3 ^n1/2 ✏ 2 ) is the optimal gradient complexity for finite-sum and stochastic nonconvex optimization problem?


Their key insight is that DNNs perform better not because they have better representative power, but because they are better regularized and therefore easier to train [4].

when f ⇡ is nonlinear, we can verify stability (and compute U ) by finding a Lyapunov function V : S !


We generate 5000 (x, y) pairs for each mixture component.

there exist several key differences that make our work unique.


For each x i ∈ D compute the Jacobian of the last layer representation J (K) (x i ) = ∂h (K) ∂x (x i ) and its SVD 1 .

we will show record-breaking improvements by using TangentProp for fine tuning CAE-pre-trained deep neural networks.


The source code of MiME is publicly available at https://github.com/mp2893/mime.

there could be no (or many) treatment codes associated with O (t) i , and therefore we used |B| number of sigmoid functions for predicting each treatment code.


In fact, when we consider the "worst" approximation which outputs y with the smallest score, its approximation error equals to the exact inference since h(x, w) = h -(x, −w).

solving the "arg max" operation is essential for training and testing structured prediction models, and it is also one of the most time-consuming parts due to its combinatorial natural.


. . , s T , computed by some deterministic policy π, it is clear that the final cumulative reward R π (s 0 ) is the difference between the starting error rate and the rate of the last state satisfying the budget: where t is the index of the final state within the budget constraint.

we therefore learn parameters β for an approximate Q as follows.


The coordinate descent algorithm is guaranteed to converge, as it monotonically decreases the approximated structured prediction objective in Theorem 1, which is lower bounded by its dual program.

note that our approach is able to cope with large amounts of noise.


This achieves the same optimal rescaling as the Newton method, while preserving the sign of the gradient, thereby turning saddle points into repellers, not attractors, of the learning dynamics.

we are not aware of any proper justification of this algorithm or even a detailed exploration (empirical or otherwise) of this idea.


Further, the second layer in our model encodes correlations of the first layer responses in the data.

weights represent excitatory connections between model V1 and model V2 units, whereas negative elements represent inhibitory connections.


All optimization problems are implemented in MATLAB via the modeling language YALMIP [27] and solved with the state-of-the-art nonlinear programming solver IPOPT [28].


• Finally, one may criticise our method as being of minor relevance to practical applications, because our calculations require the knowledge of the unknown function 1* and the density of the inputs x.

an obvious interesting quantity is given by the sample fluctuations of the generalization error which gives confidence intervals on Cg.


generated, previous work provided the finite sample analysis of the GTD algorithms with constant step size by converting them into convex-concave saddle point problems.

in each experiment we sample the data Â, b three ways: sample from two Markov chains with different mixing time but share the same stationary distribution or sample from stationary distribution i.i.d.


[4] considered a dataset containing only six motion capture sequences and proposed a Markov chain Monte Carlo (MCMC) method that required careful initialization and tens of thousands of burn-in iterations.

like most MCMC samplers, their proposals only modified small subsets of variables at each step.


Let O = S 1 ∩ S 2 be the indices for which both sensors are available, and By using the samples in S 1 and S 2 as two independent training sets, we may obtain two separate classifiers (denoted w 1 and w 2 ).

by treating Υ( w) (the expectation of Γ(λ)) as deterministic, we obtain an evidence-type approximation [14]  , where p i is the (m − 1)-dimensional vector computed from (1), the c-th element of which indicates the probability that sample x i belongs to class c. Now let x * ∈ D U be an unlabelled sample and y * its label.


In this section, we empirically study the proposed dual GAN algorithms.

the main results illustrating stable training are provided in Fig.


The singular values of PT ,H P > f,H correspond to the cosine of their principal angles.

when modeling discrete-time, finite-observation dynamical systems from data, a central challenge is state representation discovery, that is, finding a compact function of the history that forms a sufficient statistic for the future.


an important question is whether one can design an algorithm that can perform well on large datasets?


1 Motivation and Approach Subspace methods have been applied successfully in numerous visual recognition tasks such as face localization, face recognition, 3D object recognition, and tracking.


If f and H are conjugate, we can analytically compute the marginal likelihood of the K + 1st state, but this can also be approximated by Monte Carlo sampling for non-conjugate likelihoods -see Neal [2000] for a more detailed discussion of this argument.

the key to constructing a generic, truncation-free sampler for the iHMM to resample the latent states, s 1:T , is to note that the finite number of particles in the sampler are "localized" in the latent space to a finite subset of the infinite set of possible states.


Under this assumption, we wish to modulate a clutter score (Feature Congestion) by a multiplicative factor, given the target and fixation location.

we use Feature Congestion clutter maps for our foveated clutter model.


Second, in Theorem 6.2 we show that, by assigning suitable complexity priors over the network architecture, Bayesian deep ReLU networks can be near-minimax tuning-free.

for comparison, we also build a shallow network with only 1 hidden layer but 2048 units.


Intuitively the evaluation function must combine distances between the query trajectories and trajectories generated by the latent target policy.

the disagreement measure is g = (ξi,ξj ) P (ξ i |θ i , s 0 , K)P (ξ j |θ j , s 0 , K)f (ξ i , ξ j ), which we estimate via sampling a set of K length trajectories from each policy.


In (Garrigues and Olshausen, 2010) the coefficients were given by a Laplacian scale mixture prior, leading to multiplicative modulation, as in this work.

boltzman machines (Ackley et al., 1985) have a similar term, but the z and the inference are stochastic, e.g.


We discuss the general change first before explaining the spikes.

while VFE's objective recognises a good configuration, it is often more susceptible to local optima and harder to optimise than FITC.


In general, TCL followed by linear ICA does not allow us to exactly recover the independent components because the function q(•) can hardly be invertible, typically being something like squaring or absolute values.

in spite of years of research [20], no generally applicable identifiability conditions have been found.


For any distribution P on X , we define er ], the probability of h making a mistake for X ∼ P and Y with conditional probability of being +1 equal η(X).

to be concrete, we have the following open problem.


We already saw in Figures 1 and 2 that these measures capture the difference in generalization behavior of models trained on true or random labels, including the increase in capacity as the sample size increases, and the difference in this increase between true and random labels.


This establishes the feasibility of estimating the mixing time in this setting.

this is the setting of the celebrated Markov Chain Monte Carlo (MCMC) paradigm [1], but the problem also arises in performance prediction involving time-correlated data, as is common in reinforcement learning [2].


Our proposed weighted ensemble method applies to other types of kernels as well but we specialize to uniform kernels as it makes the derivations clearer.

we draw 500 instances each of random samples of size 10 3 from the probability distribution f (a, b, p, d), described in Sec.


A binary feature-assignment matrix Z represents which observations possess which hidden features, where Z nk = 1 if observation n has feature k and Z nk = 0 otherwise.

this algorithm, the first parallel inference scheme for IBP-based models, scales to datasets orders of magnitude larger than have previously been possible.


Let ψ z m (i, σ) be the posterior probability density of the rescaled data-dependent posterior distribution Q over the classifier space with respect to the volume measure P. We can now replace δ for this bad event by the delta of the Occam's hammer defined as: where ln + denotes max(0, ln), the positive part of the logarithm.

occam's hammer work by bounding the probability of bad event defined as follows.


"Easy" negative are not shown here: they involve taking audio samples and visual clips from different videos.

as our primary goal is to use AVTS as a self-supervised proxy for audio-visual feature learning, we define g(.)


A crucial advantage of Algorithm 2 over GIES is that it is nonparametric and does not require Gaussianity.

in the following, we report results for studies conducted on two real datasets coming from genomics.


If there are two sources, they are assumed to be independent.

a useful quantity to gain more insight into the structure of multisensory data is the cross-modal bias.


by using LfD to find initial policy parameters.

in many problems, we do not have access to the exact Bellman operator T π , but only to samples In this case, one might want to use the empirical Bellman error It is known, however, that this is a biased estimate of the Bellman error, and does not lead to proper solutions [14].


Assuming that A 10×785 is encoded into F 20×785 in a pre-processing step, we store the rows of F in each processor apriori.

short-Dot is a generalized framework that can achieve a wider variety of pre-specified sparsity patterns as required by the application.


(Full details are found in [9], and the supplementary materials, §4.1.)

agents interact by making choices that restrict or broaden the range of actions available to others.


There are no current approaches available that simultaneously learn both the user and item factors by sampling from the posterior in a bandit setting.

for the sake of theoretical analysis, we assume that PTS can sample from the full posterior.


Given a p n ⇥ p n binary image x 0 2 {+1, 1} n , we generate a corrupted version of the same image y 2 {+1, 1} n . We then try to denoise y by maximizing the following objective function: U (x) = X (i,j)2E x i x j + ✓ 0 X i2V y i x i , (4.1) U and N represent uniform and normal distributions.

the dimension of the above optimization problem is O(r P m `=1 |R `|2 ), which is O(nr) if the regions have bounded size; this will be the case in our implementation.


Given k ≥ 1, number of iterations T , step sizes η t , design matrix X and response Y = y, 1.

to establish some notation, we will write P L for the projection to any linear subspace L ⊆ R n , and P ⊥ L for the projection to its orthogonal complement.


From here we can see that if we let L go to infinity and set k(n) = λ −n , 0 ≤ λ ≤ 1, then we obtain the λ-return estimator in equation ( 4), since .

this leads to TD γ for episodic tasks (given in Algorithm 1), which eliminates the eligibility trace parameter λ.


As long as the eigenvalues of the blocks are different each eigen-vector will have non-zero values only in entries corresponding to a single block/cluster: where x (c) is an eigenvector of the sub-matrix L (c) corresponding to cluster c. However, as was shown above, the eigenvalue 1 is bound to be a repeated eigenvalue with multiplicity equal to the number of groups C. Thus, the eigensolver could just as easily have picked any other set of orthogonal vectors spanning the same subspace as X's columns.

it highlights the different patterns of distribution of eigenvalues for different data sets.


We focus on convex optimization problems [2] of the form minimize f (x) subject to c(x) ≤ 0, where c(x) is a vector of inequality constraints, f (x) and c(x) have continous partial derivatives, and measurements y k of the gradient at x k are noisy.

careful analysis [7] has shown that poor conditioning is not the problem-rather, it is a deficiency in the search direction.


Hamming also lends itself to SIMD parallel processing unlike Cayley which is inherently serial.

this set of comparisons can be modelled as a directed acyclic graph (DAG) with m nodes, one for each pixel in the vectorized image patch, and m 2 edges.


Then, this positive definite ⌃ can be seen to satisfy our Condition (C3), since each row has only 4 non-zeros.

for example, consider ⌃ where ⌃ SS = 0.95I 3 + 0.051 3⇥3 for a matrix 1 of ones, ⌃ SS c is all zeros but the last column is 0.41 3⇥1 , and .


The moments of the target RBMs were computed exactly, and moment matching was performed with conjugate gradient using the exact gradients.

the former source of variance is well modeled by the perfect transitions analysis and can be made small by adding more intermediate distributions.


Each rule r is of the form f < v, where f ∈ f i and v is a value for f . The vector C is used during classification only when the corresponding node has one or more ∅ children.

the theory we present here holds for any hypothesis, input and output space that may be handled by a computer with infinite resources (see [11; 12] for more precise descriptions).


If the binary classification learning algorithm outputs scores that are probability estimates, they do not satisfy the first requirement because the probability estimates are all between 0 and 1.

for this reason, we propose an algorithm analogous to the Hastie-Tibshirani method presented in the previous section to find the best approximate probability estimates pi (x) such that the Kullback-Leibler distance between rb x and r b x is minimized.


We can find that our DBH method achieves much lower replication factor than Random and Grid.

unfortunately, existing vertexcut methods, including those in PowerGraph and GraphBuilder, make rarely use of the power-law degree distribution for GP.


For the logistic bandit, previous bounds for Thompson sampling [7] and upper-confidence-bound algorithms [5] scale linearly with sup x φ (x)/ inf x φ (x), where φ is the logistic function φ(x) = e βx /(1 + e βx ).

even for problems with infinite action sets, like the linear bandit with a polytopic action set, Thompson sampling is known to obey gracious regret bounds [6].


Being differentiable, our new self-expressive layer provides a simple but effective way to learn pairwise affinities between all data points through a standard backpropagation procedure.

for the same reason, it also remains difficult to directly train a network with millions of parameters from scratch.


A more detailed description of Wasserstein++ can be found in Appendix C, and the relation of Wasserstein++ to existing approaches combining GANs and autoencoders is discussed in Section 6.

entries distributed uniformly on [0, 1].


In terms of learning dynamics, one approach is to solve stochastic differential equations (SDE) [20].

this natural constraint on x t leads to a linearly truncated state space that realistic events lie.


Our work outlines the general class of graphical models for exponential family distributions, but there are many avenues for future work in studying this model for specific distributional families.

in the case of discrete random variables, sufficient statistics can be taken as indicator functions as in the Ising or Potts model.


The L 1 -norm provides a convenient way of measuring such a distance, leading to the classical AUC criterion (AUC standing for area under the ROC curve): The popularity of this summary quantity arises from the fact that it can be interpreted in a probabilistic fashion, and may be viewed as a distance between the locations of the two distributions.

for any pair of distributions (G, H), the centered random variable √ N {U n1,m1 (s) − AUC(s)} is asymptotically normal with limit variance σ 2 s (G, H) = Var(H s (s(X + 1 )))/p+Var(G s (s(X − 1 )))/(1−p) under P (G,H) .


Define the polyhedral set The set Φ(X) consists of matrices C that approximately locate a factorization of X.

then Algorithm 1 finds a rank-r nonnegative factorization F Ŵ that satisfies the error bound the AGKM algorithm computes the factorization exactly when = 0.


The resulting algorithm enjoys essentially the same regret bound, and can be implemented efficiently whenever efficient sampling is possible from the resulting distribution.

then, there exists an algorithm such that for any T > 0, knowing T , the regret satisfies by choosing ↵ = 1/(T L), we have We note in passing that the the dependence of the algorithm on the time horizon T can be alleviated, using, for example, the doubling trick.


indeed the black circles and blue dots of Figure 3 coincide.


Tractable learning [1] is a promising new machine learning paradigm that focuses on learning probability distributions that support efficient querying.

many other important and interesting queries do not conform to this structure, including the following: • Consider the task of predicting the probability that a legislative bill will pass given that some lawmakers have already announced how they will vote.


Scaling model capacity has been vital in the success of deep learning.

between each E-step, there are many gradient updates for both θ and φ.


We use a linear combination of the reconstruction error for 'input', 'conv1_2', 'conv2_2', 'conv3_2', 'conv4_2' and 'conv5_2' layers of VGG-19; {α l } are updated online during training to normalise the expected contribution from each layer as in [4].

this generalises significantly from the training examples, which only consist of pairs of digits sampled from the same house number instance, sharing a common style.


Several existing API methods [4,5] can provide both local optimality guarantees and global guarantees under strong assumptions regarding the way samples are generated (e.g., access to a reset distribution that is similar to the optimal policy's state distribution).

1 in high level follows GPS's iterative procedure of alternating reactive policy improvement and MBOC, the main difference between Alg.


4.1), a greedy but not unreasonable choice is to set λ A (x N (A) ) to be the current Monte Carlo estimate of the marginal p(x Happily, the number of terms in ( 15) is now on the order of the number of the particles.

mean field remains a popular tool for statistical inference, mainly because it applies to a wide range of problems.


Our exemplar based clustering experiments involve DISCOVER applied to the clustering utility f (S) described in Section 3.2 with d(x, x ) = x − x 2 .

while Algorithm 1 successfully finds a distributed solution A dc [m] with f (A dc [m]) ≥ Q, (c.f.


Figure 1 (f) is a zoomed plot of this region and shows that the SD and CQ tests commit too many false positives at low thresholds.

for example, when thresholding p-values at 0.01, SD has an actual FPR of 0.03, and an even more excessive FPR of 0.02 when thresholding at 0.001.


For example, in the case of compounds and proteins, each x has a chemical graph structure and each y has a sequence structure, so the data structures completely differ between x and y.

note that the criterion can be used for extracting one-dimentional feature of the objects.


Note that although H(n i ) is only an upper bound on the statistical error, Bottou and Bousquet remark "it is often accepted that these upper bounds give a realistic idea of the actual convergence rates" [BB07], in which case balancing the sub-optimality with H(n i ) asymptotically minimizes the total error.

instead of choosing new points from a static training set, such as in DYNASAGA, STRSAGA chooses new points from the dynamically changing buffer Buf.


Subsequently, a semidefinite relaxation of the original problem was presented which does not suffer from local minima.

finding the dual leaves us with the following min max saddle point problem that will be subsequently relaxed and transformed into a semidefinite program: where 1 is a vector of ones, y is a vector of the labels, Y = diag( y) is a matrix with the labels on its diagonal with zeros elsewhere, and X is a matrix with x i in the ith column.


While the risk-neutral policy finds a shorter route (with average cost equal to 18.137 on successful runs), it is vulnerable to perturbations and fails more often (with over 120 failed runs).

furthermore, it will be used to show that a linearinterpolation of V (x, y) in the augmented state y has a bounded error.


Note that there is no hope of distinguishing distinct hidden nodes without this non-degeneracy assumption.

we can identify A up to a canonical form defined as: Definition 2 (Canonical form).


If the automaton is in the last state s α M (α) of an amino acid state list, it changes to the positive end state s + with probability 1 since the parent mass constraint is satisfied.

an ideal spectrum is composed of the masses of all prefix and suffix sequences of the peptide.


Now let k be the largest number such that d(S k ) ≤ 1 2 d(V), and assume i∈ Sk λ i ≥ 1 2 i λ i .

as we shall see below, it is always non-negative on superlevel sets.


Although our result does not strictly dominate the result for HOGWILD!

if the total number of workers is bounded by O( K/M ), the linear speedup is achieved.


This work was partially supported by NSF grant #IIS-1514253 and ONR grant #N00014-15-1-2339.

we consider a recently proposed arithmetic circuit representation, the Probabilistic Sentential Decision Diagram (PSDD).


Specifically, the area of the ellipse is proportional to the average power of the audio signal (computed over the same periodogram window) while the eccentricity is controlled by the the entropy of the normalized periodogram.

surprisingly, in our limited experiments, the noise reduction approaches what is possible using a priori knowledge of the audio signal (using Weiner filtering).


an advantage of the variational framework is the introduction of auxiliary variables which weaken the strong dependency between X and F. the variational approximation is only applicable to Gaussian observations; with Poisson observations, the integral over F remains intractable.


We are interested in whether our method can successfully capture the nonlinear property of this pendulum data.

for our SSM, the traditional sampling importance resampling (SIR) particle filter will introduce the unnecessary computational load due to the fact that (5) in the SSM is a linear structure given θ t . This inspires us to apply a more efficient marginalized particle filter (also called Rao-Blackwellised particle filter) [9,11,12,13] to deal with the estimation problem by combining Kalman filter into particle filter.


Note that in both cases the (dense) population firing rate λ = m λ m (x) will be given by λ = √ 2πpφ/|∆θ|, where ∆θ is the separation between neighbouring tuning centres θ m . The Ornstein-Uhlenbeck (OU) process controlled by a process U t is given by the SDE Equation (7) can then be solved by simulating the dynamics of Σ s . This has been considered extensively in [13] and we refer to the results therein.

we present examples that show two possible reasons for different optimal coding strategies in estimation and control.


A simple argument shows that the family of continuous functions with compact support is no longer dense in L 1 in infinite-dimensional spaces.

we show that by the structure of the construction, combined with the packing and covering properties of γ-nets, we have that in any γ-net, the total measure of all these "bad" cells goes to 0 when γ → 0, thus yielding a consistent classifier.


For MVC, MIS, and MC, we report the size of the set identified by the evaluated approaches.

it generalizes from synthetic graphs to real ones, from SAT graphs to real-world social networks, and from graphs with roughly 1,000 to graphs with roughly 100,000 nodes and more than 10 million edges.


The next step is to go towards combinatorial studies in which tissues measured by two or more of such devices are simultaneously analyzed.

[4]), the tradeoff problem is solved between the understandability (sparsity of factor-loadings) and the reproducibility of the covariance matrix from the sparsified factor-loadings.


Such problem can be resolved when using a different     Stanford 3D Indoor Semantic Dataset (S3DIS) [2] is a collection of real scan data of indoor scenes with annotations of instance segments and their semantic labels.

we also report the average mean IoUs when finding the best correspondences between part labels and the indices of dictionary atoms per category.


Scalable software packages for GLASSO have been developed, such as huge (Zhao et al., 2012).

from a computational perspective, (3.1) can be viewed as a convex relaxation of (3.2).


The labels of outliers are generated by y o = sign( −β, x o ).

since y i is deterministically related to β * , x i , the expected correlation Ey β, x achieves the maximal value in this setup (ref.


Up to now we have considered the output of the semantic segmentation as "hard facts", and hence ignored uncertainty in the class labeling.

the synthetic question-answer pairs are automatically generated question-answer pairs, which are based on the templates shown in Table 2.


Furthermore, we show that in the stochastic setting the algorithm achieves an O a:∆a>0 Kε 2 ∆a pseudo-regret guarantee.

sODA is safe against an unrestricted oblivious adversary and provides improved regret guarantees for at least two different types of "easiness" simultaneously.


GBN significantly outperforms the state-of-the-art algorithm on Q 1 2 (we obtain the p-values of the paired t-tests for all the above differences on the test sets of queries, all these values are less than 0.005).

this accuracy gives the required accuracy δ of the inexact first-order oracle for f (ϕ) on each step of the inner cycle of the Algorithm 2.


In [15], similar results are obtained for M-estimators using AMP.

the study in [25] is more limited than ours, in the sense that it only establishes universality of the expected value of the optimal cost when the LASSO is restricted to an arbitrary rectangular ball.


Given no collision, the quality of an arm (channel) always has a continuous measure like the SNR or the channel gain.

we conclude that, for some additive constant C, where (a) follows since completing the last epoch to a full epoch increases Rk , and (b) is (13).


Similarly, γ M (A 3 ) is the sum of weights of length 3 walks with no self-loop, which leads to (6).

it is known that the original matrix is close in spectral norm to the sampled one where the missing entries are filled in with zeros and properly rescaled under certain incoherence assumptions.


, where each subspace corresponds to one of ten classes.

with the WideResNet backbones, in most cases, the error rates are reduced with an increasing capsule dimension c on all datasets, where the smallest error rates often occur at c = 8.


Uniform averaging is not invariant to adding redundant agents; concretely div(A) = 0 whereas div(A 0 ) = ( 1.15, 1.15, 0, 0), falsely suggesting agent B is superior.

suppose n agents play a series of pairwise matches against each other.


It is known from Vapnik's cross-validation bound in [11] (Theorem 10.7) that by using the large margin idea alone, one can derive an expected misclassification error bound that is of the order O(l/n), where the constant is margin dependent.

we first consider the following inequality which follows from the definition of w. (A):  It is well-known that every bounded sequence in a Hilbert space contains a weakly convergent subsequence (cf.


Parameters of the updated FSC, π � i,l , are obtained by summing and normalizing the weights.

the DBNs differ by including models of other agents in a special model node.


We thank Charles Kemp and Michael Lee for useful comments.

the key point of this statistical approach is that we are not restricted to using R(X): we have a measure of the randomness of X for any choice of P (X|regular).


. . , a M }, and each latent vector is subject to a ∼ N H (0, I H ).

we assume that the prior covariance matrices C A and C B are diagonal and positive definite, i.e., Without loss of generality, we assume that the diagonal entries of the product C A C B are arranged in the non-increasing order, i.e., c Throughout the paper, we denote a column vector of a matrix by a bold smaller letter, and a row vector by a bold smaller letter with a tilde, namely, The Bayes posterior is written as where is the marginal likelihood.


We compare primal suboptimality and feasibility in the plots.

coordinate descent methods have been increasingly deployed to tackle huge scale machine learning problems in recent years.


We can write the gradient as: For a plasticity rule to be biologically plausible it must be local, so only information encoded in the states of the pre-synaptic j and the post-synaptic i neurons must be considered to update ǫ ij .

fluctuations around the reached state, slightly above η = 1, are approximately one order of magnitude bigger than for κ = 0.01.


As an approximation, the VB framework was proposed [2][4].

in regular statistical models, 2λ is equal to the number of parameters and m = 1, whereas in non-regular models such as mixture models, 2λ is not larger than the number of parameters and m ≥ 1.


More iterations alternate: the third refits the meanfield (green) and the fourth refits the copula (cyan), demonstrating convergence to the true posterior.

the gradient of a latent variable z i is evaluated over both the marginal q(z i ) and all pair copulas which model correlation between z i and any other latent variable z j .


Royer and Wright [17] proposed an algorithm that utilizes the negative gradient direction, the negative curvature direction, the Newton direction and the regularized Newton direction together with line search in a unified framework, and also analyzed the time complexity of a variant with inexact calculations of the negative curvature by the Lanczos algorithm and of the (regularized) Newton directions by conjugate gradient method.

lemma 3 provides a similar guarantee to Lemma 2 and can be used to derive a similar convergence to Theorem 1.


This favors similar distances between source phrases and their aligned slots.

. . , x n ) ∝ exp ( r θ r (x r )) , where r ⊂ {1, ..., n} is a subset of variable indices, which we use to restrict the domain via x r = (x i ) i∈r .


sequences, where n=1 is a sequence of N (i) observed variables.

in addition, the idea of boosting KL-divergence regularization is complimentary to our model, which can be potentially integrated for better disentanglement.


To emphasize the dependence of the function r u (t) on τ u , we will also write r u (t) as r u (t|τ u ).

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


This is due to the fact that n IFO calls correspond to one PO call in PROXGD, while one IFO call in PROXSVRG corresponds to one PO call.

an alternative to PROXSVRG is the algorithm proposed in [4] (popularly referred to as SAGA).


The latter quantity is available to the presynaptic neuron through its inward fast recurrent connections, as shown for the autoencoder in Fig 1D .

this local representation of network's the global performance is crucial in the supervised learning scheme we describe in the following sections.


Spending a long time finding the most accurate circuit may be worthwhile, since the cost is amortized over all queries.

the KL divergence can be computed by adding the expected divergence of each local factor, where the expectation is computed according to the global probability distribution.


We clearly outline and handle such issues and design novel prior-and/or penalty-weighted GAI++ algorithms that control the penalty-weighted FDR at any time.

this achieves the best of both worlds (guaranteeing FDR control, and handing out the largest possible reward of ↵), as posed by the above dilemma.


To produce Figures 1a and 1b, we reimplemented the toy experiment of Bishop [5,Section 3.5.1].

14), converges to the expected loss, but it provides good guarantees only for large training sample (n & 10 5 ).


Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way.

we propose a new class of stochastic optimization algorithms to cope with large-scale OT problems.


is unable to traverse the environment in one step, optimization is taken over a small ball in R 2 centered at current location g t . In practice, the set of controls needs to be discretized and entropy computed for each action.

"Random-walk" strategy was unable to find the object unless it was visible initially or became visible by chance.


As observed before, we can reduce the problem to the L different labelings.

we are now ready to prove the main theorem.


That way, the system is not restricted to the designer's choice of feature maps, but learns relevant structure from the data.

their model explains only about 10% of the "simplest" fixations in the data.


Experimental results have shown that this model outperforms the standard tfidf bag of words model on a well known data set.

since uc never occurs in d and Pu-+x ~ pv-+x, the u --+ x Fisher score entry for a document d becomes tf( ux, d) The Fisher kernel is subsequently defined to be k(d,d') = UJrIUd', where Ud is the Fisher score vector with ux-component a~n P( d) and I = Ed[UdUdTJ .