In Bradley & Murray (2011) an iterative stochastic procedure is proposed for finding such matrix.

we did not find it to work very well in an online optimization setting, and therefore stick to the original equilibration matrix D E . Although the original motivation for row equilibration is to prevent round-off errors, our interest is in how well it is able to reduce the condition number.


In the most general case, the encoder can update A t and B t in an unconstrained fashion at each timestep t. From the decoder side, we do not know C and therefore we cannot know F C, an estimate of which is needed by the user to update the encoder.

the decoder sets F and can predict updates to [CA CB] directly, instead of to [A B] as the actual encoder does (equation 15).


Note that the proposed RankGAN has a Nash Equilibrium when the generator G θ simulates the humanwritten sentences distribution P h , and the ranker R φ cannot correctly estimate rank between the synthetic sentences and the human-written sentences.

as also discussed in the literature [8,9], it is still an open problem how a non-Bernoulli GAN converges to such an equilibrium.


We give a problem for which the sample complexity of the trivial algorithm is logarithmic in n, whereas it is linear in n for the natural class of algorithms that predicts with the linear combination of instances.

why should we consider learning problems that pick columns out of a random matrix?


The disadvantage of using the binary SVM is that, in general, the 0-1 loss is a poor approximation for the AP loss.

the quality of the approximation is not uniformly poor for all samples, but depends heavily on their separability.


In most cases, especially with a very large vocabulary, V is significantly larger than D, and the additional computation cost is negligible.

as V decreases, the portion of the overhead increases.


2 From the table it is seen that all the samplers perform equally well when the number of items is small (N = 8).

as the number of items increases SM significantly outperforms all other samplers.


Given Φ, we can compute the joint distribution over the prediction range for each time series analytically, as this joint distribution is a multivariate Gaussian.

in practice it is often more convenient to represent the forecast distribution in terms of K Monte Carlo samples, In order to generate prediction samples from a state space model, one first computes the posterior of the latent state p(l T |z 1:T ) for the last time step T in the training range, and then recursively applies the transition equation and the observation model to generate prediction samples.


Besides the superiority of finding good clusters, AP exhibits the surprising ability of handling large-scale data.

aP is computationally expensive to acquire clusters when the number of clusters is set in advance.


Two classes of computable Stein discrepancies-the graph Stein discrepancy [10,12] and the kernel Stein discrepancy (KSD) [7,11,19,21]-have since been developed to assess and tune Markov chain Monte Carlo samplers, test goodness-of-fit, train generative adversarial networks and variational autoencoders, and more [7, 10-12, 16-19, 27].

in practice, the cost of these Stein discrepancies grows quadratically in the size of the sample being evaluated, limiting scalability.


[10] study k-way clustering and show that the eigenvectors of the graph Laplacian are stable in 2-norm under small perturbations.

this justifies the use of k-means in the perturbed subspace since ideally without noise, the spectral embedding by the top k eigenvectors of the graph Laplacian reflects the true cluster memberships, closeness in 2-norm does not translate into a strong bound on the total number of errors made by spectral clustering.


In fact, it can be shown that a more rudimentary form of reweighted 1 applied to this model in [19] amounts to performing exactly one such iteration.

repeated execution of ( 9) is cheap computationally since it scales as O nm x (k+1) 0 , where typically x (k+1) 0 ≤ n, and is substantially less intensive than the subsequent 1 step given by (3).


Point processes are popular models of neural spiking behavior as they provide a statistical distribution over temporal sequences of spikes and help to reveal the complexities underlying a series of recorded action potentials.

the most common neural point process models, the Poisson process and the gamma renewal process, do not capture interactions and correlations that are critical to modeling populations of neurons.


Complementary techniques such as exact covariance thresholding [13,19], and the divide and conquer approach of [8], have also been proposed to speed up the solvers.

as noted in [8], the above methods do not scale to problems with more than 20, 000 variables, and typically require several hours even for smaller dimensional problems involving ten thousand variables.


Batch normalization tackles the issue by normalizing the output of neurons to zero mean and unit variance and then performing dropout independently 1 .

our proposed evolutional dropout tackles this issue from another perspective by exploiting a distribution-dependent dropout, which adapts the sampling probabilities to the evolving distribution of a layer's outputs.


One direct way to address this problem is to score workers using their past performance on similar problems.

this is not always practical, since historical records are hard to maintain for anonymous workers, and their past tasks may be very different from the current one.


Ideally, we would perform maximum likelihood estimation on the parameters, p ✓ (x r , z r )dz r , and compute the posterior p ✓ (z|x).

under a fLDS neither the p ✓ (z|x) nor p ✓ (x) are computationally tractable (both due to the noise model P and the nonlinear observation model f (•)).


The reconstruction error for each instance can be used as an anomaly score.

the reconstruction errors are not reliable because they are calculated from parameters that are estimated using data with anomalies by assuming that all of the instances are non-anomalous.


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

if we add perturbations per iteration or the inherent randomness is non-degenerate in every direction (so the covariance of noise is lower bounded), then polynomial time is known to suffice [Ge et al., 2015].


In fact, the empirical error with a finite margin is shown to converge to zero if , is sufficiently large.

the existence of a weak learner with error 1/2 -, is not always useful in terms of generalization error, since it applies even to the extreme case where the binary labels are drawn independently at random with equal probability at each point, in which case we cannot expect any generalization.


how do I move through the door without bumping into it [11,16,17,20,33,34].

our work focuses on the longer time-scale problem of path following e.g.


Finding large independent sets is a fundamental problem in algorithm design and analysis and computing ALPHA(G) is a classic NP-hard problem which is even very hard even to approximate [11].

the Lovász function ϑ(G) gives a tractable upper-bound and since then Lovász ϑ function has been extensively used in solving a variety of algorithmic problems e.g.


In recent years, the language model Latent Dirichlet Allocation (LDA), which clusters co-occurring words into topics, has been widely applied in the computer vision field.

many of these applications have difficulty with modeling the spatial and temporal structure among visual words, since LDA assumes that a document is a "bag-of-words".


We also observe this phenomenon on English→German translation.

we show that by using value network, such shortage can be largely avoided.


In the more general setting, an instantiation x can change hyperparameters all through the network, leading to different weights.

we believe that a single data instance will not usually lead to a dramatic change in the distributions.


In this case, it is not possible to correctly identify all the features with large probability.

we can show that FoBa can still select part of the features reliably, with good parameter estimation accuracy.


Thus, the eigen-distortion test reveals generalization failures in the CNN and VGG16 architectures that are not exposed by traditional methods of cross-validation.

the models with architectures that mimic biology (On-Off, LGG, LG) are constrained in a way that enables better generalization.


All of the above methods are designed for the batch setting, where all of the data is collected in advance and used at once.

if the training dataset is extremely large or the data are streaming and encountered in sequence, we may want to incrementally update the approximate posterior of the latent function f . Early work by Csató and Opper [6] proposed an online version of GPR, which greedily performs moment matching of the true posterior given one sample instead of the posterior of all samples.


Assuming that EP already yields a good approximation, the computation of a small number of these terms maybe sufficient to obtain the most dominant corrections.

when the leading corrections come out large or do not sufficiently decrease with order, this may indicate that the EP approximation is inaccurate.


All that is needed now is to show a separation of their "-optimal sets for 0 < " < 1 60 d 3 2 , and this is done by showing a separation of the more manageable sets S 1 and S 2 .

indeed, fix 0 < " < 1 60 d 3 2 and observe that for any w 2 S 1 we have and so, for d 4, for any w 2 S 2 we have We see that no w can exist in both S 1 and S 2 , so these sets are disjoint.


The most efficient message update schedule for tree structured models is a two-pass procedure where messages are first sent from the leaves to the root node, and then propagated backwards from the root to the leaves.

as with other message-passing algorithms, for tree structured instances the algorithm will converge with either a sequential or a parallel update schedule, with any initial condition for the messages.


1, we provide NeuralFDR, a practical end-to-end algorithm to the multiple hypotheses testing problem where the hypothesis features can be continuous and multi-dimensional.

the currently widely-used algorithms either ignore the hypothesis features (BH [3], Storey's BH [21]) or are designed for simple discrete features (group BH [13], IHW [15]).


The running time of the algorithm is O nM(r)d where r = min(r 1 , r 2 ).

at smaller scales, where M(r) is comparable with n, it is O n 2 d . since the variance of the estimate also tends to be smaller at smaller scales, the algorithm iterates less for the same accuracy.


The most common way around this is to encourage sparsity during training by way of a penalty function on the expected conditional hidden unit activations given data [10].

this training-time procedure is a heuristic and does not guarantee sparsity at test time.


The metric is often taken to be Euclidean, Manhattan or χ 2 distance.

it is well known that in many cases these choices are suboptimal in that they do not exploit statistical regularities that can be leveraged from labeled data.


Alike AT, β of FT is set to 10 3 in ImageNet and PASCAL VOC 2007.

we set it to 5 × 10 2 in CIFAR-10 and CIFAR-100 because a large β hinders the convergence.


The technique for estimating bandable covariance matrices proposed in [6] is shown to achieve the optimal rate of convergence.

no such theoretical guarantees have been shown for the bandable precision estimator proposed in recent work for estimating sparse and smooth precision matrices that arise from cosmological data [15].


In the literatures of manifold learning, many methods have been proposed to construct these adjacency matrices locally, e.g., via heat kernel function [2].

in the context of manifold alignment, there might be partial alignment cases, in which some points on one manifold might not be corresponded to any points on the other manifold.


With the increasing popularity of machine learning techniques, it has become common to see prediction algorithms operating within some larger process.

the criteria by which we train these algorithms often differ from the ultimate criteria on which we evaluate them.


This establishes minimax optimality of the DS/LOO estimators for functionals of two distributions when s ≥ d/2.

when s < d/2 there is a gap between our upper and lower bounds.


Corel hist 20,000 histograms (64-dimensional) of color thumbnail-sized images taken from the COREL STOCK PHOTO library.

of the 64 dimensions, only 44 of them contain non-zero entries.


Interestingly, because log |Σ| ≤ tr(Σ)−M , the trace norm is the convex envelope for the log-determinant, and thus the two minimization problems are somehow doing similar things.

the framework introduced in this paper goes beyond the two methods by introducing an informative kernel Ω between tasks.


With the notation z i = L • q(i) − ψ i and z 0 = −ψ 0 we re-write the minimax quantity as Observe that without the constraint that p t (i) ≤ 1/L for i > 0 we would put all the probability mass on the maximum of the z i .

with the constraint the maximizer put as much probability mass as allowed on the maximum coordinate argmax i∈{0,...,K} z i and continues to the next highest quantity.


Their approach augmented a traditional supervised learning algorithm with distribution information made available from the unlabeled data.

this paper considers a method for augmenting a traditional unsupervised learning problem with the addition of equivalence classes.


The fixed order of the 441 features can be considered acceptable since any input-output mapping can in principle be learned, assuming we have sufficient training data (and an appropriate network architecture).

if the amount of training data is limited then a better-structured, more compact representation might be of great advantage as opposed to requiring to see most of the possible configurations of co-evolution.


The existence of shift parameters seem to require extra additions/subtractions (see ( 2) and ( 8)).

the binarization operation with a shift parameter can be implemented as a comparator where the shift parameter is the number for comparison, e.g., H v (R) = ⇢ 1, R 0.5 v; 1, R < 0.5 v. (0.5 v is a constant), so no extra additions/subtractions are involved.


There also exists a few works that use GAN to impute the missing values [46].

what these works focused is non-sequential dataset and they have not adopted pertinent measures to process the temporal relations.


As feedback SNR increases, we expect the BER to decrease.

as shown in Figure 4 (Left), the C-L scheme, which is designed for noisy feedback, and S-K scheme are very sensitive to noise in the feedback, and reliability is almost independent of feedback quality.


If this can be achieved, the resulting GIS procedure will be unbiased via the arguments of the previous section.

the G -weights must not only satisfy the constraint (1), they must also be efficiently calculable from a given sample.


For all i ∈ N , all θ i ∈ Θ i and all a i ∈ A i,θi , we have u i (σ Standard BN inference methods could be used to compute E[U ai |θ i ].

such standard algorithms do not take advantage of structure that is inherent in BAGGs.


As noted earlier, the running time of the batch algorithm goes up as t increases (as it has to optimize over the entire past).

the running time of the online algorithm is independent of the past and only depends on the number of documents introduced in each timestep (which in this case is always 1000).


Both of these algorithms were also compared with the SVM equipped with a RBF kernel of variance σ 2 and a soft margin parameter C. Each SCM algorithm used the L 2 metric since this is the metric present in the argument of the RBF kernel.

in contrast with , each SCM was constrained to use only balls having centers of the same class (negative for conjunctions and positive for disjunctions).


While discussing learning the kernel, we showed that L 1 and L 2 cannot be updated simultaneously in a CCCP-style iteration since g is not convex over (S 1 , S 2 ).

it can be shown that g is geodesically convex over the Riemannian manifold of positive definite matrices, which suggests that deriving an iteration which would take advantage of the intrinsic geometry of the problem may be a viable line of future work.


However, a limitation of SDPs is their computational complexity [1], which has restricted their application to small scale problems [6].

an important special case of SDPs are quadratically constrained quadratic programs (QCQP) which are computationally more efficient.


[45] used a deep network to project dense trajectory features from different views into a canonical view.

most of the previous methods require access to 3D human pose information (e.g.


Deep learning has become a ubiquitous technology to improve machine intelligence.

most of the existing deep models are structurally very complex, making them difficult to be deployed on the mobile platforms with limited computational power.


Over the years, several methods have been proposed to solve coupled tensor completion (Acar et al., 2014;Ermis et al., 2015).

many of these methods are non-convex models leading to local optimal solutions.


Also purely feed-forward network architectures were proposed [3].

such networks become unfeasibly large for practical applications.


TiMT, however, follows by a slim margin.

tiWnet explains the similarities exclusively by adding more (unnecessary) edges, which is reflected in its increased, but strongly consistent false positive rate.


At first sight, the difference between move-making algorithms and the LP relaxation appears to be the standard accuracy vs. speed trade-off.

for some special cases of distance functions, it has been shown that appropriately designed move-making algorithms can match the theoretical guarantees of the LP relaxation [14,15,20].


The problem of estimating the sparse precision matrix in Gaussian graphical models has been studied by a large body of literature [23,29,12,28,6,34,37,38,33].

the real world data may not follow a sparse GGM, especially when some of the variables are unobservable.


The introduction of local max-pooling layers in CNNs has helped to satisfy this property by allowing a network to be somewhat spatially invariant to the position of features.

due to the typically small spatial support for max-pooling (e.g.


Although dimensionality reduction can be done posthoc using PCA, [10] shows that this doesn't lead to performance improvement.

we show in §4 that selecting k v can improve the performance of SRM beyond that attained by HA.


The difference of the learner's total reward and the total reward of the optimal strategy is called the (Audibert et al., 2009) of the algorithm and it can be formally written as As compared to the regret, the pseudo-regret has the same expected value, but lower variance because the additive noise ⌘ t is removed.

the omitted quantity is uncontrollable, hence we have no interest in including it in our results (the omitted quantity would also cancel, if ⌘ t was a sequence which is independently selected of X 1:t .) In what follows, for simplicity we use the word regret instead of the more precise pseudo-regret in connection to R n . The goal of the algorithm is to keep the regret R n as low as possible.


In the MAB literature, several recent works consider multi-player MAB scenarios in which players actually compete with each other, either on arm-pulls resources [15] or on the rewards received [19].

we study a collaborative multi-player problem and investigate how sharing observations helps players achieve their common goal.


On the one hand, it is usually acceptable to output a policy that is only locally optimal with respect to the optimization objective.

in many application scenarios where constraints encode safety requirements or the amount of available resources, violating the constraint even by a small amount may have significant consequences.


Column normalization can be viewed as a principled first step towards solving challenging sparse estimation problems.

when non-convex sparse regularizers are used for the image penalty, e.g., p norms with p < 1, then local minima can be a significant problem.


In simple cases, topic models can be used to cluster local textural elements, coarsely representing categories via a bag of visual features [1,2].

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


For example, Node A concerns washbasins for infants, and has two polarized children nodes: reviewers take a positive perspective when their children enjoy the product (Node B: "loves", "splash", "play") but have negative reactions when it leaks (Node C: "leak(s/ed/ing)").

the lowest topics in the hierarchy are often polarized; one child topic of "router" focuses on upgradable firmware such as "tomato" and "ddwrt" (Node E, positive) while another focuses on poor "tech support" and "customer service" (Node F, negative).


The teaching set of a concept c ∈ C is a set of indices (or examples) X ⊆ [n] that uniquely identifies c from C. Formally, given a concept class C ⊆ {0, 1} n (a set of binary strings of length n), X ⊆ [n] is a teaching set for a concept c ∈ C (a binary string in C) if X satisfies c| X = c | X , for all other concepts c ∈ C. The teaching dimension of a concept class C is the smallest number t such that every c ∈ C has a teaching set of size no more than t [GK95, SM90].

teaching dimension does not always capture the cooperation in teaching and learning (as we will see in Example 2), and a more optimistic and realistic notion of recursive teaching dimension has been introduced and studied extensively in the literature [Kuh99, DSZ10, ZLHZ11, WY12, DFSZ14, SSYZ14, MSWY15].


recent work (Dauphin et al., 2014;Choromanska et al., 2014) has brought theoretical and empirical evidence suggesting that local minima are with high probability not the main obstacle to optimizing large and deep neural networks, contrary to what was previously believed: instead, saddle points are the most prevalent critical points on the optimization path (except when we approach the value of the global minimum).


Recent progress in deep generative models has led to tremendous breakthroughs in image generation.

while existing models can synthesize photorealistic images, they lack an understanding of our underlying 3D world.


As expected, Hotelling, Edist and MMD perform best for differences in the Gaussian distribution (column 4).

in all other settings Hotelling's test has poor power, and our approach with minP as the univariate test has more power than Edist and MMD in columns 5-7.


By its definition, the sampler q * (u j ) is computed based on the hidden feature h (l) (u j ) that is aggregated by its neighborhoods in previous layers.

under our top-down sampling framework, the neural units of lower layers are unknown unless the network is completely constructed by the sampling.


In general, the exact form of this pooling function is determined by the complex interaction between the MSR and agent utility, and a closed form of p i from (4) might not be attainable in many cases.

given a paticular MSR, we can venture to identify agent utility functions which give rise to well-known opinion pools.


In particular, it should be possible to increase the number of limited capacity units in a population to form a more precise representation of the sensory signal.

to the best of our knowledge, such a code has not been characterized analytically, even in the simplest case.


[19] use a simple linear algorithm for this step, which takes O(|P|) time.

we propose a more efficient algorithm to maximize δ j (•), which exploits the special structure of this discrete function.


On the one hand, we want to be expressive, and learn all the transitions possible from every o within a horizon h. When o is a high dimensional image observation, this typically requires mapping the image to an extensive feature space [30,12].

however, we want to plan efficiently, which generally requires either low dimensional state spaces or well-structured representations.


by D-softmax is restricted from the start, and may therefore be lacking in terms of expressiveness.

our algorithm first trains words with a full-length vector and dynamically limits the dimension during evaluation.


When constrained to only two labels, their results provide a bipartite SBM.

in the bipartite SBM case, [17] has two drawbacks compared to the results presented here: (1) The data-generating process in [17] rules out certain nested structures of the sets V i .


Discriminator D. In traditional GANs, the discriminator distinguishes between real groundtruth images and fake generated images (which is generated from random noise).

in our conditional network, G2 takes the condition image I A instead of a random noise as input.


For the second category of global landscape analysis, the typical result is that every local minimum is a global minimum.

even for single-layer networks, strong assumptions such as over-parameterization, very special neuron activation functions, fixed second layer parameters and/or Gaussian data distribution are often needed in the existing works.


All prior methods select the local neighborhood based on proximity, and they typically fix its size.

our idea is to predict the set of training instances that will produce an effective discriminative model for a given test instance.


Recent work has shown that randomized value functions can implement something similar to Thompson sampling without the need for an intractable exact posterior update.

this work is restricted to linearly-parameterized value functions [16].


Note that the costs may be either positive or negative.

only their relative values are important.


For GMRFs with n nodes indexing d-dimensional random subvectors, I(x R ; x A ) can be computed exactly in O((nd) 3 ) via Schur complements/inversions on the precision matrix J.

certain graph structures permit the computation via belief propagation of all local pairwise MI terms I(x i ; x j ), for adjacent nodes i, j ∈ V in O(n • d 3 ) -a substantial savings for large networks.


This approach is appropriate when objects can be partitioned into relatively homogeneous subsets.

the properties of many objects are better captured by representing each object using multiple latent features.


The partial derivatives take a standard log-sum-exp form, requiring expectations E p(y A naive computation of this expectation would require summing over D k= d y d configurations.

there are more efficient alternatives: the dynamic programming algorithms developed in the context of Poisson-Binomial distributions are applicable, e.g., the algorithm from [3] runs in O(Dk) time.


In the fully supervised setting, one can sidestep the task of estimating conditional probabilities by directly learning a classifier in a discriminative fashion.

in unsupervised or semi-supervised settings, a reliable estimate of the conditional distributions becomes important.


One possibility is to start at the position of the deleted point, θ i−1 , on the contour constraint, which is independent of the other points and not far from the bulk of the required uniform distribution.

if the Markov chain mixes slowly amongst modes, the new point starting at θ i−1 may be trapped in an insignificant mode.


REINFORCE-OB contributes highly to reducing the variance especially when T is large, which also well agrees with our theory.

pGPE-OB still provides much smaller variance than REINFORCE-OB.


Compared with [12] on subset evaluations, our method significantly improve over [12] on horse-riding and running detection.

[12] provides better detection results than ours on diving detection.


Their runtime is independent of, or even decrease with, the number of training samples [5,6].

because of their simplicity, these methods have a slow convergence rate, and thus may require a large number of iterations.


We find that a CNN augmented with an RN achieves an accuracy above 94% for both relational and non-relational questions.

a augmented with an MLP only reached this performance on the non-relational questions, plateauing at 63% on the relational questions.


To see this, note that the sequence of partitions P 0,bad n becomes arbitrarily ill-balanced, which from (10) implies lim n→∞ Pcut G 0 n (P 0,bad n ) = 1.

the unperturbed graph G n grows in a self-similar fashion as n → ∞ and so the Product Cut of P n remains approximately a constant, say γ, for all n. Thus Pcut Gn (P n ) ≈ γ < 1 for n large enough, and Pcut G 0 n (P 0,good Comparing this upper-bound with the fact lim n→∞ Pcut G 0 n (P 0,bad n ) = 1, we see that the Product Cut of P 0,bad n becomes eventually larger than the Product Cut of P 0,good n . While we execute this program in full only for the example above, this line of argument is fairly general and similar stability estimates are possible for more general families of graphs.


At the beginning of learning when Ja is of small magnitude, the diffusion term, ⟨F 2 a ⟩, has a large impact so that it greatly impedes learning for a large η case.

as the magnitude of the differences JA − JB increases, this effect weakens and the dependence of p A on η becomes quite small.


3.1 Algorithm for Learning the Transitive Reduction of CBNs [13] show that by using O (log n) multiple-vertex interventions, one can recover the transitive reduction of a DAG.

in this case, each set of intervened variables has a size of O( n /2), which means that the method of [13] has to perform a total of O(2 n /2 log n) experiments, one for each possible setting of the O( n /2) intervened variables (see an example of this in Appendix D).


Specifically, we set Q(x) to be sigmoidal with parameter λ (see Figure 2a): As λ → ∞, Q(x; λ) → 1{x > 0}, so R labelwise (w : D) approaches the objective function defined in (7).

r labelwise (w : D) is smooth for any finite λ > 0.


Any nonlinear Wiener functional, for instance, creates infinitely many correlations or cumulants of higher order, and often also of lower order.

a Wiener functional of order n produces only harmonic phase interactions up to order n + 1, but sometimes also of lower orders.


In small or medium networks, we can rely on well-known numerical methods to compute matrix exponentials [24].

in large networks, the explicit computation of Ψ(t) becomes intractable.


Hastie [37] further generalized this approach by assuming that class distributions are a mixture of Gaussians, which has more flexibility than LDA.

both approaches assume a common covariance matrix for all the classes, which is too strict in many practical applications, especially in high-dimensional problems where the covariance matrices of different classes tend to be different.


In such problems it is crucial to identify a nominal or baseline feature distribution with respect to which statistically significant deviations can be reliably detected.

in most applications there is seldom enough information to specify the nominal density accurately, especially in high dimensional feature spaces for which the baseline shifts over time.


Suppose one were to give every layer in the RNN the largest possible skip for any graph with a period of m = 2 d 1 : set s (l) = 2 d 1 in every layer, which is the regular skip RNN setting.

this apparent advantage turns out to be a disadvantage, because time spans of 2  n < m suffer from increased path lengths, and therefore which grows linearly with m. for the proposed DILATEDRNN, where d only grows logarithmically with m, which is much smaller than that of regular skip RNN.


With such limited sampling, UCB1 spends almost all the time exploring and generates almost the same regret of 0.5 per turn as would an algorithm that pulls arms at random.

uCB1K/C is able to obtain a substantially lower regret by limiting the exploration to a subset of the arms.


The recent results in [7,8] suggest coresets that are similar to our definition of coresets (i.e., weighted subsets), and do preserve sparsity.

as mentioned above they minimize the 2-norm error and not the larger Frobesnius error, and maybe more important, they provide coresets for k-SVD (i.e., k-dimensional subspaces) and not for PCA (k-dimensional affine subspaces that might not intersect the origin).


[15] presented mirror descent using the Mahalanobis norm for the proximal function, which is very similar to the proximal function that we show to cause mirror descent to be equivalent to natural gradient descent.

their proximal function is not identical to ours and they did not discuss any possible relationship between mirror descent and natural gradient descent.


Interest in monocular depth estimation dates back to the early days of computer vision, with methods that reasoned about geometry from cues such as diffuse shading [12], or contours [13,14].

the last decade has seen accelerated progress on this task [1][2][3][4][5][6][7][8][9][10], largely owing to the availability of cheap consumer depth sensors, and consequently, large amounts of depth data for training learningbased methods.


As empirically found by [12], perplexities will saturate when n becomes large, because only a small portion of words actually exhibit long-range dependencies.

we can see that the VPYLM performance is comparable to that of HPYLM with much fewer nodes and restaurants up to n = 7 and 8, where vanilla HPYLM encounters memory overflow caused by a rapid increase in the number of parameters.


Mean field variational Bayes (MFVB) is a popular posterior approximation method due to its fast runtime on large-scale data sets.

a well known major failing of MFVB is that it underestimates the uncertainty of model variables (sometimes severely) and provides no information about model variable covariance.


An exact implementation of Bod's parsing method is still infeasible, but Goodman gives an approximation that can be implemented efficiently.

the method still suffers from the lack of justification of the parameter estimation techniques.


The middle panel suggest that 2 -path norm and spectral norm can provide some explanation for this phenomenon.

as we discussed in Section 2, the actual complexity measure based on 2 -path norm and spectral norm also depends on the number of hidden units and taking this into account indicates that these measures cannot explain this phenomenon.


We used 174,577 songs and 14,198 albums to make up the meta-training matrix ¢ , which is dimension 174,577x174,577.

note that the ¢ meta-training matrix is very sparse, since most songs only belong to 1 or 2 albums.


A sufficient condition to satisfy this definition is Hence, the set of misclustered nodes is defined as [6] M n = i ∈ {1, . . . , n} :  In practice, k-means algorithm tries to find a local minimum, and hence, one should run this step with multiple initializations to achieve a global minimum.

empirically we found that good performance is achieved even if we use a single run of k-means.


This is related to recent work on Hough forests for object detection and localization [14], where leaves collect information on locations and sizes of bounding boxes of objects in training images.

they use this evidence to predict a spatial distribution of bounding boxes in a test image, whereas we use the evidence stored in tree leaves to predict the distribution ratios.


From a practical perspective, working in HS(ρ) is not computationally feasible.

our approximation to C has a representation in the finite dimensional space F, as defined here.


Also, SAGA can be analyzed without any additional synchronization per epoch.

there is no qualitative difference in these guarantees accumulated over the epoch.


If the clustering is incorrect the algorithm gets some feedback from the teacher.

the feedback in this case is different from the one in the EQ model.


For example, the bulk of the differential privacy literature has focused on the central model, in which user data is collected by a trusted aggregator who performs and publishes the results of a differentially private computation [11].

google, Apple, and Microsoft have instead chosen to operate in the local model [15,6,2,10], where users individually randomize their data on their own devices and send it to a potentially untrusted aggregator for analysis [18].


For instance, Catoni (2016) constructs a robust estimator of the Gram matrix of a random vector Z ∈ R d (as well as its covariance matrix) via estimating the quadratic form E Z, u 2 uniformly over all u 2 = 1.

the bounds are obtained under conditions more stringent than those required by our framework, and resulting estimators are difficult to evaluate in applications even for data of moderate dimension.


This may superficially seem much too weak.

this condition turns out to be equivalent to boostability.


• Averaging between the parameter vectors of k computers reduces variance by O(k − 1 2 ) similar to the result of [7].

it does not reduce bias (this is where [7] falls short).


During the training phase Gaussian noise can take negative values, so the input to the following layer can be of arbitrary sign.

during the testing phase noise ✓ is equal to 1, so the input to the following layer is non-negative with many popular non-linearities (e.g.


Therefore, in terms of the considered replica symmetric ansatz, a complete solution of the problem seems to be easily obtainable; unfortunately, it is not.

this set of equations ( 15) may be solved numerically for general β, K, and C. there exists an analytical solution of this equations.


These methods scale to large datasets by using noisy gradients calculated using a mini-batch or subset of the dataset.

the high variance inherent in these noisy gradients degrades performance and leads to slower mixing.


This symmetry is generated by a reflection operator, say the function m : R 3 → R 3 that flips the first axis: If S is a shape of a bilaterally-symmetric object, no matter how we align S to the symmetry plane, in general m[S] = S due to object deformations.

we can expect m[S] to still be a valid shape for the object.


While a uni-modal distribution with high variance can also produce both low and high values for the probability β gk , it will also produce intermediate values.

draws from the bi-modal distribution will have a clear gap between low and high values.


In the CIS (Random) model, the first few and the last few levels had little effect on perplexity and the medium-depth levels accounted for most of perplexity reduction.

in the CIS (LearnedRI) model, the effect of a level on perplexity decreased with level depth, with the first few levels reducing perplexity the most, which is a consequence of the greedy nature of the tree-learning algorithm.


at least 1 − δ, we have Such uniform convergence results are fairly common for decomposable loss functions such as the squared loss, logistic loss etc.

the same is not true for non-decomposable loss functions barring a few exceptions [17,10].


In Figure 5, models trained with block_size = 1 and block_size = 7 are both robust with block_size = 1 applied during inference.

the performance of model trained with block_size = 1 reduced more quickly with decreasing keep_prob when applying block_size = 7 during inference.


More recently, [12] proposes an approximate objective for structural SVMs that leads to an algorithm considerably faster than DLPW on problems requiring expensive inference.

the The contribution of this work is twofold.


Therefore, the terminal state ¤ @ is an absorbing state of the finite Markov chain.

the above analysis shows that ¤ @ essentially is composed of multiple absorbing states.


2, are applicable only for special-structured small networks.

common networks used in evaluations of defense methods are wide, which makes prior methods computationally intractable and complicated, which makes some prior methods inapplicable.


Oddly, in our analysis of the strongly convex case, the accelerated method is less sensitive to errors than the basic method.

unlike the basic method, the accelerated method requires knowing µ in addition to L. If µ is misspecified, then the convergence rate of the accelerated method may be slower than the basic method.


by removing whole neurons, filters or layers.

non-adaptive regularization techniques require tuning of a huge number of hyperparameters that makes it difficult to apply in practice.


Finally, note that the above analysis fixes α = O(1/T ), β = 1 − α, but in practice FastRNN learns α, β (which is similar to performing cross-validation on α, β).

interestingly, across datasets the learnt α, β values indeed display a similar scaling wrt T for large T (see Figure 2).


The first source of difficulty is adjusting the notion of effective rank (which the algorithm needs to compute) to compensate for the uncertainty in the knowledge of the eigenvalues of G. A further problematic issue arises because we want to measure the smoothness of f 0 along the eigendirections of G, and so we need to control the convergence of the eigenvectors, given that G converges to G in spectral norm.

when two eigenvalues of G are close, then the corresponding eigenvectors in the estimated matrix G are strongly affected by the stochastic perturbation (a phenomenon known as hybridization or spectral leaking in matrix perturbation theory, see [1,Section 2]).


As shown in Figure 2(a)-(f), elements of M with large values mainly distribute on the upper-left borders if the type of the blur kernel is Gaussian.

elements of M with large values mainly distribute on the diagonal if the input is a motion kernel as shown in Figure 2(g)-(l).


Several papers used multi-agent reinforcement learning [17,18,19] and planning [20,21,22,23] to generate cooperation in this setting.

this approach has not yet demonstrated robust cooperation in games with more than two players, which is often observed in human behavioral experiments.


We say a communication protocol is non-interactive if a message broadcasted by one party does not depend on the messages broadcasted by other parties.

interactive protocols allow the messages at any stage of the communication to depend on all the previous messages.


This makes the tree traversal unpredictable leading to trivial worst-case runtime guarantees.

locality-sensitive hashing [10] based methods approach search in a different way.


We have focussed on product and sigmoidal units as nonlinear computing elements.

the construction presented here is generic.


They therefore have typically wider applicability since they are not tied to any particular classifier family.

wrappers make the classifier an integral part of their operation, repeatedly invoking it to evaluate each of a sequence of feature subsets, and selecting the subset that results in minimum estimated classification error (for that particular classifier).


First order methods are particularly attractive in such problems as they typically enjoy computational complexity linear in the input size.

the convergence of these methods crucially depends on the geometry of the data; for instance, running the same algorithm on a rotated set of examples can return vastly inferior results.


It is known that stress can affect short-and long-term memory by modulating plasticity through stress hormones and neuromodulators [1,2,3,6].

there is no integrative model that would accurately predict and explain differential effects of acute stress.


In such a case, one could resort to within-image methods to further reduce the entropy.

there is a risk that such methods will remove components that actually represent smooth gradations in the anatomy.


These include one-to-one, many-to-one and oneto-many mappings.

existing environments (e.g., OpenAI Gym [6] and Universe [33]) wrap one game in one Python interface, which makes it cumbersome to change topologies.


In Section 4 we will establish the theoretical results on the COCA estimator and will show that it can estimate the latent true dominant eigenvector θ 1 in a fast rate and can achieve feature selection consistency.

we provide another model inspired from the classical PCA method, where we wish to estimate the leading eigenvector of the latent covariance matrix.


Since both q * (u) and ∂L ∂θ/z 1:M depend linearly on q(x) via sufficient statistics that contain a summation over all elements in the state trajectory, we can obtain unbiased estimates of these sufficient statistics by using one or multiple segments of the sequence that are sampled uniformly at random.

obtaining q(x) also requires a time complexity of O(T ).


The negative KL divergence term in Equation ( 5) tries to close the gap between two pipelines, and one could consider allocating more weights on the negative KL term of an objective function to mitigate the discrepancy in encoding of latent variables at training and testing, i.e., −(1 + β)KL (q φ (z|x, y) p θ (z|x)) with β ≥ 0.

we found this approach ineffective in our experiments.


[19,20] -and other related work [6] -assume that each agent votes for a single alternative.

it is potentially possible to design agents that generate a ranking of multiple alternatives, calling for a principled way to harness this additional information.


In these experiments we let both Pegasos and FOBOS employ a projection after each gradient step into a 2-norm ball containing w ⋆ (see [14]).

in the experiment corresponding to the rightmost plot of Fig.


However, none of the existing PID information components described above fits yet the notion of intersection information, as none of them quantifies the part of sensory information I(S : R) carried by neural activity R that also informs the choice C. The PID quantity that seems to be closest to this notion is the redundant information that S and R share about C, SI(C : {S; R}).

previous works pointed out the subtle possibility that even two statistically independent variables (here, S and R) can share information about a third variable (here, C) [23,27].


Ideally, we would want an algorithm that could learn each sub-task and combine them into the complete task, rather than only be able to learn single monolithic tasks.

for many classes of quantitative rewards, "combining" rewards remains an ad-hoc procedure.


We further utilize the dependence between the algorithm input and output and the stochasticity of the algorithm, and we give results for more general processes.

we only obtain upper bounds in this paper.


Specifically, a DBN typically refers to a Bayes' net in which the variables have an explicit notion of time, and past observations have some influence on estimates about the present and future.

marginalizing over unobserved variables at time t−1 typically produces increased complexity in the the model of variables at time t. in both [6] and this work, the emphasis is on performing inference with current information only, and efficiency is obtained by leveraging the similarity between the previous and newly updated models.


We can see that the Bernstein upper bound is much tighter than the TRW upper bound, although at the cost of turning a deterministic bound into a (1 − δ) probabilistic bound.

the Bernstein interval fails to report a meaningful lower bound when the model is difficult (σ p ≈ ±0.5), because n = 10 4 is small relative to the difficulty of the model.


First, the reconstruction error alone is a valid criterion only if one really plans to perform dimensionality reduction of the data and stop there.

pCA is often used merely as a preprocessing step and the projected data is then submitted to further processing (which could be classification, regression or something else).


For instance, for a user uploading a new song, tagging it as 'Rock' may be informative, but will probably only contribute marginally to the song's traffic, as the competition for popularity under this tag can be fierce.

choosing a unique or obscure tag may be appealing, but will not help much either.


3 Due to the implicit nature of the nonlinear mapping, we can not directly evaluate w ij .

we only need its dot product with the transformed input vectors Φ(x).


We assume that each node i can join or leave a given group k according to a Markov model.

since each node can join multiple groups independently, we naturally consider factorial hidden Markov models (FHMM) [8], where latent group membership of each node independently evolves over time.


SPTM has shown impressive results on image-based navigation.

causal InfoGAN's parametric approach of learning a compact, model for planning has the potential to scale up to more complex problems, in which the increasing amount of data required would make the nonparametric SPTM approach difficult to apply.


The trend suggests that, for very large J, close to K measurements per signal should suffice.

with independent CS reconstruction, for perfect reconstruction of all signals the number of measurements per sensor increases as a function of J.


In contrast, using the SAG iterations from the beginning gives the same rate but with a constant proportional to n. Note that this bound is obtained when initializing all y i to zero after the SG phase.

1 in our experiments we do not use the SG initialization but rather use a minor variant of SAG (discussed in the next section), which appears more difficult to analyze but which gives better performance.


When the cardinality of X S increases under infill asymptotics [14, §3.3], This is the limit for the posterior variance at any test location for task T , if one has training data only for the secondary task S. This is because a correlation of ρ between the tasks prevents any training location for task S from having correlation higher than ρ with a test location for task T . Suppose correlations in the input-space are given by an isotropic covariance function k x (|x − x |).

if we translate correlations into distances between data locations, then any training location from task S is beyond a certain radius from any test location for task T . a training location from task T may lay arbitrarily close to a test location for task T , subject to the constraints of noise.


This low-rank structure carries through for purely linear statistics (such as sample means).

non-linearities in the test statistic calculation, e.g., normalizing by pooled variances, will contribute a long tail of eigenvalues, and so we require that this long tail will either decay rapidly, or that it does not overlap with the dominant eigenvalues.


A straightforward and popular approach to optimize L is to use stochastic gradient methods [24,26,28,35].

natural-gradients are preferable when optimizing the parameters of a distribution [3,15,18].


This is because these methods solve the dual optimization problem for a given performance measure; hence the intermediate models do not necessarily yield good accuracies.

(stochastic) gradient based methods directly offer progress in terms of the primal optimization problem, and hence provide good intermediate solutions as well.


Hence, R(s, t) global should be the most important part in this decomposition.

in case of the standard resistance distance the contribution of the global part becomes negligible as n !


We denote the weights of this linear combination as W 2 < NVOX⇥NCELLS , and u t as a vector of size N VOX representing predicted neural activity at each voxel at time t. Thus, For training the model, the predicted neural activity is compared with the actual activity recorded by the scanner.

neural activity is not instantly reflected in the intensity recorded by the scanner, but is delayed according to the haemodynamic response function (HRF; Figure S3).


This algorithm extracts event-related desynchronization (ERD) effects, i.e., event-related attenuations in some frequency bands, e.g., µ/β -rhythm.

the CSP algorithm can be used more generally, e.g., in [11] a suitable modification to movementrelated potentials was presented.


It seems the learning algorithm is suffering from the saddle point problem [8].

the hint may provide an effective guidance to avoid the problem by directly having a guidance at an intermediate layer.


As shown in [28] these frameworks have connections to learning policies in reinforcement learning.

the policies are learned over incomplete configurations.


It is conceivable that one may construct a probabilistic query strategy analogous to the Replicated Bisection strategy by replicating queries in L pre-determined sub-intervals.

it appears challenging to prove that such replications preserve privacy, and still more difficult to see how one may obtain a matching query complexity lower bound in the noisy setting.


Since all histories are of interest, bridging tests are single observations, and T E is exactly equivalent to the original system.

note that in order to make the predictions of interest, one must only know whether the ball is neighboring or on the pixel.


Knowledge of a protein's unique conformation provides insight into the mechanisms by which a protein acts.

no algorithm exists that accurately maps sequence to structure, and one is forced to use "wet" laboratory methods to elucidate the structure of proteins.


The synthetic data sets allow for a controlled evaluation, and for generating training and testing data sets of any desired size.

the data is generated from a distribution that indeed has only a single hidden variable.


This rate can be interpreted as the rate at which unlabeled examples estimate the parameters of the best fitting model and rate at which labeled examples correctly label these estimated decision regions.

for small u estimation of the decision regions will be bad and and corresponding l * u > l * .


Moreover, among those few exceptions that do not use projections onto X i when Π Xi is not easy to compute, only [15,16] can handle agent-specific constraints without assuming global knowledge of the constraints by all agents.

no rate results in terms of suboptimality, local infeasibility, and consensus violation exist for the primaldual distributed methods in [15,16] when implemented for the agent-specific conic constraint sets X i = {x : A i x − b i ∈ K i } studied in this paper.


As an interesting feature, LWR can regress on non-stationary functions, a beneficial property, for instance, in control problems.

it does not provide a proper generative model for function values, and existing algorithms have a variety of manual tuning parameters that strongly influence bias, variance and learning speed of the results.


If this is the case then PickyAdaBoost abstains in that round and does not include h t into the combined hypothesis it is constructing.

(Note that consequently the distribution for the next round of boosting will also be D .) if the current base classifier has advantage γ where |γ| ≥ γ, then PickyAd-aBoost proceeds to use the weak hypothesis just like AdaBoost, i.e.


Use of kernels together with high-order features may lead to further improvements.

we note that the advantage of the higher order features may become less substantial as the observations become more powerful in distinguishing the classes.


Recent work relied on an additional maximum-likelihood estimation (MLE) stage merged with a spectral method to attain good estimates in ∞ error to achieve the limit for the pairwise model.

although it is valid in slightly restricted regimes, our result demonstrates a spectral method alone to be sufficient for the general M -wise model.


The cost function in equation ( 5) is the square of the Frobenius norm of the difference between the empirical matrix ¢ and the fit kernel ¡ c . The use of the Frobenius norm is similar to the Ordinary Least Squares technique of fitting variogram parameters in geostatistics [7].

instead of summing variogram estimates within spatial bins, we form covariance estimates over all meta-training data pairs ¥ .


For example, in the case (d = 3, k = 1) the free parameters are Z12 and Z13, which define a coordinate system for the sphere.

as a function of U, the integrand is simply 1 The density is maximized when U contains the top k eigenvectors of S . the density is unchanged if we negate any column of U.


As a general remark, it appears that there is no globally optimal α parameter across datasets.

the reported training and test MNLL curves appear to be in agreement regarding the optimal choice for α .


GAN can be trained efficiently via back-propagation through the nonlinear function of the generator, which typically requires the data to be continuous (e.g., images).

the discrete nature of text renders the model non-differentiable, hindering use of GAN in natural language processing tasks.


Quantitatively, our algorithm achieves a higher IoU over these methods (MarrNet 0.39 vs. DRC 0.34).

we find the IoU metric sub-optimal for three reasons.


For real datasets, such as image histograms, where minwise sampling is popular [13], the value of this sparsity is of the order of 0.02-0.08 (see Section 4.2) leading to 1 s x ≈ 13 − 50.

the number of non-zeros is around half million.


When from the observations, a red node w ∈ V (r) is connected to at most a single green node, i.e., if v∈V (g) A vw ≤ 1, this red node is useless in the classification of green nodes.

when a red node is connected to two green nodes, say v 1 and v 2 (A v1w = 1 = A v2w ), we may infer that the green nodes v 1 and v 2 are likely to be in the same cluster.


When • R and • C are both Euclidean norms, this oracle can be efficiently computed via the leading left and right singular vector pair.

for most other interesting cases like low rank tensors, such an oracle is intractable [29].


Control was historically among the earliest applications of neural networks, but the recent surge in performance has been in computer vision, speech recognition and other classification problems that arise in artificial intelligence and machine learning, where large datasets are available.

the data needed to learn neural network controllers is much harder to obtain, and in the case of imaginary characters and novel robots we have to synthesize the training data ourselves (via trajectory optimization).


The spike counts are conditionally Poisson distributed given a vector of parameters w and time-dependent vector of covariates x t The log-likelihood of w given the vector of all observed spike counts y is where we have dropped terms constant in w and the t-th row of the design matrix X is x t . The methods in this paper apply both when using the canonical log link function such that the nonlinearity is f (x) = exp(x) and when using alternative nonlinearities.

with moderate amounts of data, first or second order optimization techniques can be used to quickly find point estimates of the parameters w. inference can be prohibitive for large datasets, as each evaluation of the log-likelihood requires passing through the entire design matrix.


In RVM, the "dictionary" used for signal representation is the collection of values from the "kernel function".

sRSC roots in the standard sparse representation and recent developments of harmonic analysis, such as curvelet, bandlet, contourlet transforms that show excellent properties in signal modelling.


For example, any F . With this scenario in mind, it is unsurprising that low-rank approximation guarantees fail as an accuracy measure in practice.

we ran a standard sketch-and-solve approximate SVD algorithm (see Section 3) on SNAP/AMAZON0302, an Amazon product co-purchasing dataset [22,23], and achieved very good low-rank approximation error in both norms for k = 30: the approximate principal components given by Z are of significantly lower quality than A's true singular vectors (see Figure 1).


Note that this is different from Figure 2(b), as now we take the effect of random sampling and SVD into account.

the trend in both figures are the same: SMP-PCA always outperforms SVD( e A T e B) and can be arbitrarily better as ✓ goes to zero.


However, their algorithms are prone to local optimal issues and the recovered tensor might be very different from its true value.

our main results, Theorem 1 and Theorem 2, guarantee that a convex program can exactly or accurately recover the pairwise interaction tensors from O(nr log 2 (n)) observations.


The assumption refers to the fact that the value of a slate is a linear function of its feature representation.

note that this linear dependence is allowed to be completely different across contexts, because we make no assumptions on how φ x depends on x, and in fact our method does not even attempt to accurately estimate φ x .


Unfortunately, β is typically unknown to the learner.

using the tools to design self-tuning algorithms, e.g.


Table 1 shows that for the first three sets of data (Gaussians, Circles, AI) maximum margin and spectral clustering obtained identical small error rates, which were in turn significantly smaller than those obtained by k-means.

maximum margin clustering demonstrates a substantial advantage on the fourth data set (Joined Circles) over both spectral and k-means clustering.


Because according to Algorithm 1 in [11], the output of input Θ weighted by the scalars s = Φ g can be approximated to first glance, the scalars s is totally erased by BN in this mathmatical process.

the de facto operation of a convolutional module has a process order to aggregate the features.


Summary In our framework, SGLD and SGRLD take Q(z) = 0 and instead stress the design of the diffusion matrix D(z), with SGLD using a constant D(z) and SGRLD an adaptive, θ-dependent diffusion matrix to better account for the geometry of the space being explored.

hMC takes D(z) = 0 and focuses on the curl matrix Q(z).


This is like the Type-II transformation in [31], and we found that it worked better than Type-I for our experiments.

we aim to minimize F (x) in a novel way, so first we review the submodular vertex-cover problem.


However, to achieve this their algorithm runs the entire junction tree algorithm in each iteration, and does not reuse messages between iterations.

sample Propagation reuses all but one of the messages between iterations, leading to a greatly reduced "constant factor".


From high level, our proof constructs an estimation sequence { w (t) , M (t) , t } such that t → 0 and w * − w (t) 2 + M * − M (t) 2 ≤ t . In conventional matrix sensing, this construction is possible when the sensing matrix satisfies the Restricted Isometric Property (RIP) [Candès and Recht, 2009]: When A is 2 -norm δ k -RIP for any rank k matrix M , A A is nearly isometric [Jain et al., 2012], which implies M − A A(M )/n 2 ≤ δ.

then we can construct our estimation sequence as following: in gFM and symmetric rank-one matrix sensing, the 2 -norm RIP condition cannot be satisfied with high probability [Cai and Zhang, 2015].


However, in the real-world problems, it is hard to identify the conditions that unlabeled data can help.

it is interesting to explore the relation between the low density assumption and the manifold assumption.


Namely, one can find other simple mediators that satisfy these two properties.

we show that the Shapley mediator is the unique mediator to satisfy the fairness, economic efficiency and stability requirements.


[21] have shown that this strategy can improve modern language models like recurrent networks without retraining.

their model assumes that the data distribution changes smoothly over time, by using a context window to improve the performance.


Most of the existing analyses of multiarmed bandits with side information has focused on the adversarial (worst-case) model, where the sequence of rewards associated with each state-action pair is chosen by an adversary.

many problems in real-life are not adversarial.


Phase regularisation could be useful for tasks with a target phase, or where something is known about the phase characteristics of the system involved.


Results show that the proposed 20 informative regions yield comparable matting performance to a fine-labelled trimap in terms of quality.

generating a fine trimap costs much users efforts, and it takes about 3 minutes to obtain a good alpha matte.


The objective of image retrieval is to quickly index and search the nearest images to a given query.

our goal is to localize objects in every single image of a dataset without supervision.


[9] demonstrates the speedup many orders of magnitude faster than the previous state of the art in the context of computing aggregates over the queries (such as the LSCV score for selecting the optimal bandwidth).

the authors did not discuss the sampling-based approach for computations that require per-query estimates, such as those required for kernel density estimation.


Unlike the other works [29,28] that use explicit attention parameters, MRN does not use any explicit attentional mechanism.

we observe the interpretability of element-wise multiplication as an information masking, which yields a novel method for visualizing the attention effect from this operation.


Finally, we exemplified our work by using KD-trees as the tree-consistent partition structure for generating the component-specific partitions in CS-EM, which limited its effectiveness in high dimensions.

any hierarchical partition structure can be used, and the work in [8] therefore suggest that changing to an anchor tree (a special kind of metric tree [15]) will also render CS-EM effective in high dimensions, under the assumption of lower intrinsic dimensionality for the data.


In the Gaussian setting, the minimum sample complexity can be improved to n = Ω(∆ 2 log p), i.e., when J min = Θ(1/ √ ∆) where the maximum degree scales as ∆ = Θ(log p log c) [7].

for Ising models, the minimum sample complexity can be further improved to n = Ω(c 4 log p), i.e., when J min = Θ(J * ) = Θ(1/c).


In particular when f (S * ) = f (∅) = 0, it returns large sets with large positive cost.

the deviation of the approximate edge weights ν i from the true cost is bounded [18].


WAGE [19] quantizes weights, activations, errors and gradients to 2, 8, 8 and 8 bits respectively.

all of these techniques incur significant accuracy degradation (> 5%) relative to full-precision models.


Economists and computer scientists are often concerned with inferring people's preferences from their choices, developing econometric methods (e.g., [1,2]) and collaborative filtering algorithms (e.g., [3,4,5]) that will allow them to assess the subjective value of an item or determine which other items a person might like.

identifying the preferences of others is also a key part of social cognitive development, allowing children to understand how people act and what they want.


We now define the expected reward to be the adaptive value of information of extracting the a'th set of features given the system state and budget B: Intuitively, (3) says that each time we add additional features to the computation, we gain reward equal to the decrease in error achieved with the new features (or pay a penalty if the error increases.)

if we ever exceed the budget, then any further decrease does not count; no more reward can be gained.


Thus, computing The value of Q t depends on the reward parameters θ t , the model, and the planning depth.

as we present below, the process of computing the gradient closely resembles the process of planning itself, and the two computations can be interleaved.


In general, it is hard to show an explicit separation result for ḡJ .

in simple models, we can do explicit computations to show separation.


'S' is a singleview anomaly since 'S' is located far from other instances in each view.

both views of 'S' have the same relationship with the others (they are far from the other instances), and then 'S' 30th Conference on Neural Information Processing Systems (NIPS 2016), Barcelona, Spain.


TensorLog establishes a connection between inference using first-order rules and sparse matrix multiplication, which enables certain types of logical inference tasks to be compiled into sequences of differentiable numerical operations on matrices.

tensorLog is limited as a learning system because it only learns parameters, not rules.


Participants are required to choose one out of four possible materials.

it can still be challenging to distinguish between materials, especially when sampled ones have similar damping and specific modulus.


The auditing complexity of this algorithm can also be as large as Θ(log 2 (m)).

auditing allows us to beat this barrier.


Although fMRI is the most popular method for functional brain imaging with high spatial resolution, it suffers from poor temporal resolution since it measures blood oxygenation level signals with fluctuations in the order of seconds.

dynamic neuronal activity has fluctuations in the sub-millisecond time-scale that can only be directly measured with electromagnetic source imaging (ESI).


In higher dimensions (d ¸4), SMC did not Þnd all of the regions.

the MCMC algorithm found all of the regions, and did so in a reasonable amount of time.


Thus, a distributional assumption on P (X) does not restrict the set of covariate functions in any way.

specifying the conditional distribution, P (X|Y ), naturally entails restrictions on the form of P (Y |X).


We use partially pre-trained agents because random agents see few rewards in some of our domains.

this means we have to account for the budget (in terms of real environment steps) required to pretrain the data-generating agent, as well as to then generate the data.


These developments have made it possible to apply RNNs to new domains such as language translation [1,40] and parsing [44], and image and video captioning [7,45].

the current RNNs are designed to output each time one "token" in the input sequence, they can not handle properly the segment detection task in which each time a continuous chunk of the inputs is selected.


1BitSGD was experimentally observed to preserve convergence [35], under certain conditions; thanks to the reduction in communication, it enabled state-of-the-art scaling of deep neural networks (DNNs) for acoustic modelling [37].

it is currently not known if 1BitSGD provides any guarantees, even under strong assumptions, and it is not clear if higher compression is achievable.


Recently, requirements for various non-Gaussian convolutions have emerged and are continuously getting higher.

the handmade acceleration approach is no longer feasible for so many different convolutions since it is a time-consuming and painstaking job.


To extract convolutional features for source D s and target D t , the input source and target images (I s , I t ) are first passed through fully-convolutional feature extraction networks with shared parameters W F such that D i = F(I i |W F ), and the feature for each pixel then undergoes L 2 normalization.

in the recurrent formulation, at each iteration the target features D t can be extracted according to extracting each feature by transforming local receptive fields within the target image I t according to T i for each pixel i and then passing it through the networks would be time-consuming when iterating the networks.


Exact computation in these cases is often computationally intractable, which has led to many approximation algorithms, such as variational approximation [5], or loopy belief propagation.

most of these methods still rely on the propagation of the exact probabilities (upstream and downstream evidence in the case of belief propagation), rather than an approximation.


Distributions over matrices with exchangeable rows and infinitely many columns are useful in constructing nonparametric latent variable models.

the distribution implied by such models over the number of features exhibited by each data point may be poorly-suited for many modeling tasks.


A sufficiently weak dependence results in a monotonically increasing Bayes factor which favors the absence of the edge A +-B at any finite value of 0:.

given a sufficiently strong dependence between A and B, the log Bayes factor takes on positive values for all (finite) 0: exceeding a certain value 0:+ of the scale parameter.


As alluded to above, for the purpose of establishing analytic properties of the algorithm, we will assume comparisons are governed by the BTL model of pairwise comparisons.

the algorithm itself operates with data generated in arbitrary manner.


For example, [15] demonstrates that on USPS, using lasso and group lasso regularizations together outperforms models with a single regularizer.

they only consider the squared loss in their paper, whereas we consider a logistic loss which leads to better performance.


These estimators enjoy the parametric rate of O n −1/2 when β > d/4, and work by optimally estimating the density and then applying a correction to the plug-in estimate.

our estimator undersmooths the density, and converges at a slower rate of O n −β/(β+d) when β < d (and the parametric rate O n −1/2 when β ≥ d), but obeys an exponential concentration inequality, which is not known for the estimators of [8].


We can also derive upper bounds on the difference between LSIF and uLSIF and show that uLSIF gives a good approximation to LSIF.

we do not go into the detail due to space limitation.


In practice, their model is defined by the same forward equations as ours.

equation 3 which computes the backward vectors is instead: Incorrect "@Hannah Sunder: The Walking Dead is just a great tv show" its bad ass just started to watch the 2nd season to catch up with the 3rd Figure 4: Examples of predictions made by the GB-RNN for twitter documents.


Note that the GP does not guarantee that the predicted Q has rank P . Therefore, we do not truly guarantee that Z satisfies the constraints.

as shown in our experiments, the violation of the constraints induced by the factorization is much smaller than the one produced by doing prediction in the original variables.


In most cases, both Robust PCA and AMMC perform quite similarly (see Figure 5 in Appendix E).

in one case AMMC achieves 87.67% segmentation accuracy (compared with the ground truth, manually segmented), while Robust PCA only achieves 74.88% (Figure 3).


In contrast, neural networks employ massively-parallel, graded processing that can search out many possible solutions at the same time, and optimize those that seem to make graded improvements in performance.

the discrete character of structured representations requires exhaustive combinatorial search in high-dimensional spaces.


Empirical simulations showing that the other forward algorithms also suffer this regret are in Appendix F. An attractive feature of forward algorithms is that they generalize to partial orders, for which efficient offline optimization algorithms exist.

in Section 4 we saw that FAs only give a Õ(t − 1 2 ) rate, while in Section 3 we saw that Õ(t − 2 3 ) is possible (with an algorithm that is not known to scale to partial orders).


In [5], the consistency of SVM with additive kernel is established, where the kernel-norm regularizer is used.

the sparsity on variables and the learning rate are not investigated in previous articles.


We can see that OLS and SOLS require approximately the same number of iterations for comparable decrease in objective function value.

since the SOLS instance has a much smaller size, its per iteration computational cost is much lower than that of OLS.


We are focussing here on the same problem but using CSP extracted features and arrive at similar results.

in a theoretical part we show that using more classes can be worth the effort if a suitable accuracy of all pairwise classifications is available.


Furthermore, when some of the singular values of M fall below the "noise level" √ dσ, one can show a tighter bound, with a nearly-optimal bias-variance tradeoff; see Theorem 2.7 in [5] for details.

when M is full-rank, then the error of M depends on the behavior of the tail M c . We will consider a couple of cases.


When µ 1 = 1, µ 2 = 0, the attacker is interested in increasing the RMSE of the collaborative filtering system and hence reducing the system's availability.

when µ 1 = 1, µ 2 = −1 the attacker wishes to increase RMSE while at the same time keeping the rating of specific items (j 0 ) as low as possible for certain malicious purposes.


A more recent work proposes an architecture that resembles the structure of the hippocampus to facilitate continual learning for more complex data such as small binary pixel images [15].

none of them demonstrates scalability to high-dimensional inputs similar to those appear in real world due to the difficulty of generating meaningful high-dimensional pseudoinputs without further supervision.


In opposite, for subject one the maximum is achieved at 4.9 seconds, yielding a low steepness value.

a low value is also found for the submission of all other competitors.


Note the explicit incorporation of the reconstructive and discriminative component into sparse coding, in addition to the classical reconstructive term (see [9] for a different classification component).

since the classification procedure from Eq.


The very concept of a "reaction" can be ambiguous, as it corresponds to a macroscopic abstraction, hence simplification, of a very complex underlying microscopic reality, ultimately driven by the laws of quantum and statistical mechanics.

even for relatively small systems, it is impossible to find exact solutions to the Schrödinger equation.


Unfortunately, both variants suffer from a polynomial time complexity with a super-linear dependence on the dimensionality d (at least a power of 4), which renders them not practical for optimizing problems of high dimension.

second-order information carried by the Hessian has been utilized to escape from a saddle point, which usually yields an almost linear time complexity in terms of the dimensionality d under the assumption that the Hessian-vector product (HVP) can be performed in a linear time.


Thus, according to these schemes, patterns are stored wholesale in the hippocampus when they first appear, and are continually read back to cortex to cause plasticity along with the new information.

if the hippocampus is permanently required to prevent a catastrophe, then, first, there is no true consolidation: if neocortical plasticity is not inhibited by hippocampal damage, 20 then its integrity is permanently required to prevent degradation; and, second, what is the point of consolidation -couldn't the hippocampus suffice by itself?


It was shown by [8] that such clusterings are readily detected offline by classical batch algorithms.

we prove (Theorem 3.8) that no incremental method can discover these partitions.


In the example of Figure 3c with binary random variables, the model has 11 parameters.

these parameters are determined by the environment: To be adaptive in nonstationary environments, the model must be updated following each experienced state.


[2013] is closest to ours in also presenting a framework with three criteria related to discrimination control (group fairness), individual fairness, and utility.

the criteria are manifested less directly than in our proposal.


We agree with the general consensus that fast learning involves the feedforward connections.

by considering positional invariance for discrimination, we show that there is an inherently non-linear component to the overall task, which defeats feedforward algorithms.


Thin junction trees (graphs with low tree-width) are extensions of trees, where inference can be solved efficiently using the junction algorithm [7].

learning junction trees with tree-width greater than one is NP-complete [6] and tractable learning algorithms (e.g.


Existing approaches to clustering HMMs operate directly on the HMM parameter space, by grouping HMMs according to a suitable pairwise distance defined in terms of the HMM parameters.

as HMM parameters lie on a non-linear manifold, a simple application of the k-means algorithm will not succeed in the task, since it assumes real vectors in a Euclidean space.


A range-EEG feature has been proposed [23], which measures the peak-to-peak amplitude.

our approach learns frequency bands of interest and we can deal with long time series evaluated in our experiments.


All units and parameters at all levels of the network are engaged in representing any given input and are adjusted together during learning.

we argue that one-shot learning of new classes will be easier in architectures that can explicitly identify only a small number of degrees of freedom (latent variables and parameters) that are relevant to the new concept being learned, and thereby achieve more appropriate and flexible transfer of learned representations to new tasks.


Therefore EM algorithms can converge to local optima.

this problem can be alleviated using deterministic annealing as described in [9,10].


The statistical properties of PEM (and Maximum Likelihood) methods are well understood when the model structure is assumed to be known.

in real applications, first a set of competitive parametric models has to be postulated.


One line of work [3,4] divides game images into patches and applies a Bayesian framework to predict patch-based observations.

this approach assumes that neighboring patches are enough to predict the center patch, which is not true in Atari games because of many complex interactions.


The resulting model, called BicyleGAN, effectively achieves one-to-many image translations.

there are several differences with our method.


The AltMin technique has also been applied to many other estimation problems, such as matrix completion [19], phase retrieval [27], and mixed linear regression [44].

the current theoretical understanding of AltMin is still incomplete.


In numerical analysis this is typically a much-desired feature, leading to methods with improved stability and accuracy.

it is still a three-part procedure, analogous for example to paired Adams-Bashforth and Adams-Moulton integrators used in PEC mode (Butcher, 2008).


Like Nash equilibrium, a QPE and EFPE can be computed in polynomial time in the size of the input game.

the big-O complexity hides dramatically larger constants in the case of a QPE or an EFPE, and the algorithms known so far thus do not scale beyond small instances [ Čermák et al., 2014;Ganzfried and Sandholm, 2015].


The slope for LMC and SGLDFP is −1 which confirms the convergence of θn − θ to 0 at a rate N −1 .

we can observe that θn − θ converges to a constant for SGD and SGLD.


They primarily focus on nonlinear dynamics and an RNN-based variational family, as well as allowing control inputs.

the approach does not extend to general graphical models or discrete latent variables.


Under more realistic assumptions, i.e., more classes have increasing pairwise classification error compared to a wisely chosen subset it is improbable to increase the bit rate by increasing the number of classes higher than three or four.

this depends strongly on the pairwise errors.


Such strength and specialization is in agreement with data on climbing fibers in the cerebellum [18][19][20], who are believed to bring information about errors during motor learning [21].

in this model, the specificity of the error signals are defined by a weight matrix through which the errors are fed to the neurons.


That NoSDE games exist is surprising, in that randomness is needed even though actions are always taken with complete information about the other player's choice and the state of the game.


(2015), we use the method of moments for estimating latent-variable models.

those papers use it for parameter estimation in the face of non-convexity, rather than as a way to avoid full estimation of p(f v | y).


When (A2) holds, uniform confidence intervals of f on its level sets are easy to construct because little statistical efficiency is lost by slightly enlarging the level sets so that complete d-dimensional cubes are contained in the enlarged level sets.

when regularity of level sets fails to hold such nonparametric estimation can be very difficult or even impossible.


If the ith sensor is not involved in a reward communication event at that time, its global reward estimate is updated according to Y i (k) = αY i (k − 1) + r i (k).

at any time k that there is a communication event, its global reward estimate is updated according to , where j is the index of the sensor with which communication occurs.


Q*bert presents an interesting difference between human and synthetic preferences: on short timescales, the human feedback does not capture fine-grained reward distinctions (e.g., whether the agent covered one or two tiles) which are captured by the synthetic feedback.

on long timescales this does not matter much and both models align well.


Our model treats objection as a more challenging decision, thereby deserving higher weight.

the middle two sequences receive alternating votes.


The Diffusion Network(DN) is a stochastic recurrent network which has been shown capable of modeling the distributions of continuous-valued, continuoustime paths.

the dynamics of the DN are governed by stochastic differential equations, making the DN unfavourable for simulation in a digital computer.


Note that an adversarial divergence is not necessarily a metric, and therefore does not necessarily induce a topology.

convergence in an adversarial divergence can still imply some type of topological convergence.


Our design of the move kernel K t are based on two observations.

first, we can make use of U and σ V as auxiliary variables, effectively sampling this move would be highly inefficient due to the number of variables that need to be sampled at each update.


Adaptive schemes, where tasks are assigned based on the data collected thus far, are widely used in practical crowdsourcing systems to efficiently allocate the budget.

existing theoretical analyses of crowdsourcing systems suggest that the gain of adaptive task assignments is minimal.


This demonstrates that naively learning from synthetic images can be problematic due to a gap between synthetic and real image distributions -synthetic data is often not realistic enough with artifacts and severe texture losses, misleading the network to overfit to fake information only presented in synthetic images and fail to generalize well on real data.

with the injection of photorealistic and identity preserving faces generated by DA-GAN without extra human annotation efforts, our method outperforms b1 by 1.00% for TAR @ FAR=0.001 of verification and 1.50% for FNIR @ FPIR=0.01, 0.50% for Rank-1 of identification.


In the presence of a single agent, such problems have been studied in the context of offline policy learning [6,51] and online bandits (with imperfect information) [22,25,38].

the multi-agent learning setting is again under-explored; we leave that for future work.


Since in LCC each data is encoded by some anchor points on the data manifold, it can model the decision boundary of an SVM directly using f (x) ≈ v∈C γ v (x)f (v).

then by taking γ x as the input data of a linear SVM, f (v)'s can be learned to approximate the decision boundary f . OCC learns a set of orthogonal basis vectors, rather than anchor points, and corresponding coding for data.


One the one hand, MDS is using the pseudo-distance defined in equation 1, whose relationship with the real distance between two pixels in the original image is linear only in a small neighborhood.

isomap uses the geodesic distances in the neighborhood graph, whose relationship with the real distance is really close to linear.


an undirected network with n nodes where each couple of nodes (i, j) ∈ V 2 belongs to E independently of the others with probability p), the exact influence of a set of nodes is not known.

percolation theory characterizes the limit behavior of the giant connected component when n → ∞.


Specifically, because of the assumed independence of the {v i }, the EM method requires one to repeatedly maximize the Q-function such that the estimate of α at the (m + 1)th iteration is: Like the compound Dirichlet likelihood, the compound shadow Dirichlet likelihood is not necessarily concave.

note that the Q-function given in ( 7) is concave, because log p(v i |α) = − log |det(M )| + log p D,α M −1 v i , where p D,α is the Dirichlet distribution with parameter α, and by a theorem of Ronning [11], log p D,α is a concave function, and adding a constant does not change the concavity.


1, the activation of the last layer is therefore equal to where we defined the total weight matrix product W in the last expression, equal to the chain of matrix multiplications along all layers 1, 2, . . . , L. This expression makes obvious the uselessness of having multiple, successive linear layers, as their combined effect reduces to a single one.


PERSPECTIVE is the fastest among all methods and is 60% faster than SPHCONV, followed by DIRECT which is 23% faster than SPHCONV.

both baselines are noticeably inferior in accuracy compared to SPHCONV.


The two estimated masks achieve similar accuracy around 90%.

it is clear that the DNN mask misses significant portions of unvoiced speech, e.g., between frame 30-50 and 220-240.


The runtime of PDMM decreases as K increases from 21 to 61.

the speedup from 61 to 81 is negligable.


Technically speaking the parameters of both the component and corresponding cluster has to be updated for exact inference.

updating cluster parameters for every data instance removed will significantly slow down inference.


Variational methods are typically fast, and often produce high-quality approximations.

when the variational approximations are poor, estimates can be correspondingly worse.


So far, we have assumed the smoothness t of the true distribution P is known, and used that to tune the parameter ζ of the estimator.


CP-VTON [29] learns a thin-plate spline transformation for transforming the in-shop clothes into fitting the body shape of the target person via a Geometric Matching Module (GMM).

all methods above share a common problem, ignoring the deep feature maps misalignment between the condition and target images.


The GAN Generator is a deep non-linear transformation from latent to image space.

each GMM component is a simple linear transformation (Az + µ).


If only a single plastic synapse is taken into consideration, covariance learning rules seem to make matching behavior a steady state of learning.

under certain situations where a large number of synapses simultaneously modify their efficacy, matching behavior cannot be a steady state.


Unfortunately, this approximate equivalence between excitatory and inhbitory neurons is inconsistent with the anatomical observation that only about 15% of cortical neurons are inhibitory.

the original architecture could probably work if we had larger populations of map neurons, more synapses, and/or NMDA-like synapses with longer time constants.


Then we have a formula for f and a subgradient: f@xA a n k=1 x@kA@f@S k A f @S k 1 AA; @ f@xA Q n k=1 e (k) @f@S k A f @S k 1 AA: Equation (2) was used to show that submodular minimization can be achieved in polynomial time [16].

algorithms which directly minimize the Lovasz extension are regarded as impractical.


. . , a n . We will analyze the following popular non-convex objective, (1.1) Previously, Ge et al.

[GHJY15] show that for the orthogonal case where n ≤ d and all the a i 's are orthogonal, objective function f (•) have only 2n local maxima that are approximately ± 1 the technique heavily uses the orthogonality of the components and is not generalizable to over-complete case.


We think of X as "public," while and are private and only needed at the time of compression.

even with = 0 and known, recovering X from X requires solving a highly under-determined linear system and comes with information theoretic privacy guarantees, as we demonstrate.


The advantages of such formulation are twofold: the dimension of the optimization variable is reduced, and positive semidefiniteness is naturally enforced.


recently [9] propose to use Variational Autoencoder as a heuristic way to recover the latent confounders from multiple proxies.

matrix factorization methods, despite stronger parametric assumptions, address the problem of missing values simultaneously, require considerably less parameter tuning, and have theoretical justifications.


Options are temporally-extended actions that, like HRA's heads, can be trained in parallel based on their own (intrinsic) reward functions.

once an option has been trained, the role of its intrinsic reward function is over.


3b shows that the condition number of A becomes worse as the degree d becomes larger, and as more probability mass is assigned to the dense part G d of the transition matrix T , providing some weak evidence for the necessity of Condition 3.

also, recall that Theorem 1 shows that HMMs where the transition matrix is a random walk on an undirected regular graph with large degree (degree polynomial in n) cannot be learned using polynomially many samples if m is a constant with respect to n. such graphs have all eigenvalues except the first one to be less than O(1/ √ d), hence it is not clear if the hardness of learning depends on the large degree itself or is only due to T being ill-conditioned.


( 1), we need to marginalize over all possible global transformations T . In our current implementation we used only global shifts, and assumed uniform distributions over all shifts, i.e., P (T |H ref ) = 1/|ref |.

the algorithm can accommodate more complex global transformations.


The second factor is mixing filters: algorithms typically seek, and directly optimize, a transformation that would unmix the sources.

in many situations, the filters describing medium propagation are non-invertible, or have an unstable inverse, or have a stable inverse that is extremely long.


To date, matrix and tensor decomposition has been extensively analyzed, and there are a number of variations of such decomposition (Kolda and Bader, 2009), where the common goal is to approximate a given tensor by a smaller number of components, or parameters, in an efficient manner.

despite the recent advances of decomposition techniques, a learning theory that can systematically define decomposition for any order tensors including vectors and matrices is still under development.


The proposed framework is motivated by the operator-theoretic view of nonlinear dynamical systems.

learning a generative (state-space) model for nonlinear dynamical systems directly has been actively studied in machine learning and optimal control communities, on which we mention a   9) and white Gaussian observation noise and (right) the estimated Koopman eigenvalues.


By choosing w = (1, • • • , 1) we obtain a trivial (k, 0)-coreset.

in a more efficient coreset most of the weights will be zero and the corresponding rows in A can be discarded.


First, the accuracy of the belief model β(τ ) in Equation 1 is highly dependent on the performance model P (U |τ, π), which evaluates the policy π behaving against the opponent using policy τ , named response policy.

the performance model of a response policy against different strategies might be the same in multiagent domains, resulting in indistinguishability of the belief model and thus inaccurate detection.


This has been formalized by "differential privacy", which provides bounds on the maximum disclosure risk [15].

differential privacy hinges on the benevolence of an organization to which you give your data: the privacy of individuals is preserved as long as organizations which collect and analyze data take necessary steps to enforce differential privacy.


It behaves like e y for y < 0, but grows linearly for positive y.

it exhibits grave problems for latent state forecasting.


If G is a tree, this is obviously satisfied.

the result holds on any graph for which: the subgraph induced by Pu:v is a chain; and every i ∈ Pu:v separates N (i) \ Pu:v from Pu:v \ {i}, where N (i) {j : {i, j} ∈ E} is the neighbor set of i.


The cover tree, which is designed exclusively for NNS, shows slightly better query performance than ours.

the MS-distance is more general and flexible: it supports addition of a new vector to the data set (our data structure) in O(d) time for computing the mean and the standard deviation values of the vector.


If the algorithm guarantees a zero regret against the competitor with zero L 2 norm, then there exists a sequence of T vectors in X , such that the regret against any other competitor is Ω(T ).

if the algorithm guarantees a regret at most of > 0 against the competitor with zero L 2 norm, then, for any 0 < η < 1, there exists a T 0 and a sequence of T ≥ T 0 unitary norm vectors z t ∈ X , and a vector u ∈ X such that The proof can be found in the supplementary material.


The learning process is an iterative algorithm that alternates between fixing latent values and optimizing the latent SVM objective function.

we case part learning as finding maximal cliques in a weighted graph of image patches.


To point out a few, random averaging projection method [28] handles multiple constraints simultaneously but cannot deal with regularizers.

accelerated stochastic gradient descent with proximal average [29] can handle multiple regularizers simultaneously, but the algorithm imposes a Lipschitz condition on regularizers, and hence, it cannot deal with constraints.


Deep multi-layer neural networks have many levels of non-linearities allowing them to compactly represent highly non-linear and highly-varying functions.

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


There are various general notions about their roles, such as regulating sleeping and waking [13] and changing the signal to noise ratios of cortical neurons [11].

these are slowly giving way to more specific computational ideas [20,7,10,24,25,5], based on such notions as optimal gain scheduling, prediction error and uncertainty.


The bandit algorithm of Garber (2017) additionally requires a certain boundedness property of barycentric spanners, namely: max q > i Q 2 q i  .

for certain bounded sets this quantity may be unbounded, such as the two-dimensional axisaligned rectangle with one axis being of size unity, and the other arbitrarily small.


The weights reflect the similarities between the target therapy and all training therapies.

the therapy-specific approaches do not address the bias originating from the different treatment backgrounds of the samples, or the missing treatment history information.