We can simplify this MLN by replacing R by a predicate J having one argument such that D(1 Decomposition.

given an MLN M and its associated schematic MLN S, the optimum solution to the Integer Polynomial Programming problem returned by SMLN-2-IPP(S) is the MAP solution of M . In the next three examples, we show the IPP output by Algorithm 2 on some example MLNs.


Next, we extend our experiments to cases that are increasingly more difficult to manually batch.

our contention is that operation batching is increasingly becoming another aspect of model coding that is error prone and amenable to automation.


As this set contains all possible joint-utilities, it will contain the optimal joint-utility for any definition of optimal (the bargaining solution F bs will select the utility vector it deems optimal).

when computing the Pareto frontier during the backup the algorithm relies on no points except those of the previous step's Pareto frontier.


For models with ReLU activation, we use pretrained models provided by [20] and also evaluate the same set of 100 random test images and random attack targets as in [20] (according to their released code) to make our results comparable.

fast-Lin is a special case under our framework.


Next, we define a prior over the vectors {a L }, {a R }, and {R}.

the dataset is a fully observed matrix-so there is only one relation.


Although other approaches to optimal controller design exists, we argue now that the SLS parameterization has some appealing properties when applied to the control of uncertain systems.

again by using standard concentration arguments.


We examine the efficiency of our MCMC method with approximate metric on a well studied toy example, the Fitzhugh-Nagumo model, before examining a realistic, nonlinear and highly challenging example describing enzymatic circadian control in the plant Arabidopsis thaliana [22].

it has been shown that such chains may still be usefully employed as long as they satisfy some technical conditions, namely diminishing adaptation and bounded convergence [2].


The solution length varies between three and six words.

to pass the typical visual CAP TCHA, a user must correctly type the characters displayed in an image of distorted text.


Then, the differences in bounds reflect the intrinsic differences between risk minimizers.

[7] has shown that we can estimate R(g) without any bias if satisfies the following symmetric condition: Specifically, let R u,− (g) = E X [ (g(X), −1)] = πE + [ (g(X), −1)] + (1 − π)R − (g) be a risk that U data are regarded as N data.


One challenge in building AI agents that learn from experience is how to set their goals or rewards.

r, the task-specific reward, could reward the agent for successfully completing parallel parking.


Finally, instead of choosing a new random projection in each cell, a dictionary of a few random projections is chosen at the outset.

the design goal of VQ is to minimize the error introduced by replacing vectors with their representative.


Under this assumption, learning f i,j (t) is equivalent to learning a real number, α i,j .

here, we adopt a method similar to [15] and approximate (4) by discretizing the integral: Intuitively, if δ is small enough and the triggering functions are bounded, it is reasonable to expect that i,t (λ).


We initialize the templates using a simple scaled K-means clustering model, which we in turn initialize with prototypical spikes determined from the data.

no discrimination boundary can be identified orthogonal to which the oversplit cluster appears bimodal.


Hierarchical multidimensional recurrent neural networks containing Long Short-Term Memory [11] hidden layers and a CTC output layer [8] have proven effective for offline handwriting recognition [9].

if the prior P (α) is uniform and a single weight sample is taken for each element of D, then minimising L(α, β, D) is identical to minimising L N (w, D) with weight noise or synaptic noise [13].


If f can be written as a product of log-concave potentials over a hypergraph G, we say that f is log-concave decomposable over G. Proof.

these two classes are not equivalent: twice continuously differentiable functions are supermodular if and only if all off diagonal elements of the Hessian matrix are non-negative.


We learn a matrix of weights W ∈ d * p . In this model, each output is treated independently, so we can solve all of them quickly in one matrix operation (even with thousands of semantic features): where I is the identity matrix and λ is a regularization parameter chosen automatically using the cross-validation scoring function (Hastie et al., 2001) 3 .

l( f) will take the prediction of features and return the closest point in a given knowledge base according the Euclidean distance (L 2 ) metric.


In some of the results below, we will be interested in deriving specific rates of convergence.

we will additionally make use of the following notions.


Given an input query q, we represent this query according to its DAG structure, then we use Algorithm 1 to generate an embedding of the query based on this DAG.

the example on the left shows a path query on the Reddit data; note that there are multiple nodes that satisfy this query, as well as multiple paths that reach the same node.


With this setup, we present an assumption as follows: Assumption 1.

this hierarchal framework depicted in Figure 1 has been presented in [25] as Meta-Learned Shared Hierarchies (MLSH).


Our proposed method significantly outperforms the correlation-based classifier which is unable to consistently track the attentional modulation of the listener over time.

the complete data log-posterior, where the unobservable sequence {n k,r } K,R k=1,r=1 is given, takes the form: The log-posterior of the parameters given the complete data has a tractable functional form for optimization purposes.


For tractability and fast computation of messages in the forward-backward algorithm for eq.

as each model is only fit to one trial, the parameter-estimates are very noisy since they are not sufficiently constrained by the data from each trial.


In doing so, our notion helps to incentivize the collection of better features, that depend more directly on the target rather then the protected attribute, and of data that allows better prediction for all protected classes.

that for all values of the protected attribute, the conditional behavior of the predictor is at exactly the same point in this space.


Then, for any δ > 0, with probability at least 1 − δ, the following holds for h ∈ H: Furthermore, if H has a VC dimension of d, then the following holds with probability at least 1 − δ: where e is the natural number.

the xaxis of the figures are in logarithmic scale.


Now we provide a matching algorithmic lower bound on the expected regret, showing that the analysis presented in Section 3.1 is sharp as a function of T . Moreover, our lower bound characterizes how much regret must be accrued in order to achieve a specified estimation rate for the system parameters (A , B ).

after each epoch, OFU requires optimizing a non-convex objective to O(T −1/2 ) precision.


Alternatively, the MAP problem can be solved in a lifted manner by leveraging various lifted inference rules such as the decomposer, the binomial rule [6,9,22] and the recently proposed single occurrence rule [13,19].

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


In this paper, we deviate from this classic pipeline and propose to modulate the entire visual processing by a linguistic input.

given a mini-batch B = {F i,•,•,• } N i=1 of N examples, BN normalizes the feature maps at training time as follows: where is a constant damping factor for numerical stability, and γ c and β c are trainable scalars introduced to keep the representational power of the original network.


With the same assumptions, [2] proves that for a single-hidden ReLU network with a single non-overlapping convolutional filter, all local minimizers of the population loss are global; they also give counter-examples in the overlapping case and prove the problem is NP-hard when inputs are not Gaussian.

in these problems the inputs are labeled examples {(x i , y i )} n i=1 ∈ R d × R which are guaranteed to satisfy y i = f (⟨w, x i ⟩) for some w ∈ R d and nondecreasing (Lipchitz continuous) f ∶ R → R. The goal in this problem is to find a (nearly) accurate such f and w. An interesting polynomial-time algorithm called the Isotron exists for this problem [12,11].


Using the PASCAL VOC action classification and object detection datasets, we empirically demonstrate that each of our approaches greatly reduces the training time of AP-SVM while not decreasing the testing accuracy.

during training, the parameters of an SSVM are estimated by minimizing a regularized convex upper bound on a user-specified loss function.


Hence, the nullspace of ∂ ∂x consists of the set of horizontal lines.

the general algorithm is found in the Supplementary material of this paper.


Each task is expressed using a cost function consisting of two point target cost terms.

it should be noted that although the targets are equally spaced in task space and results are shown with respect to movement distance in task space, the distances in joint space scale non linearly.


The reduction of the convolutional structures of the three gates in ConvLSTM brings no side effects to spatiotemporal feature map fusion.

( 22) corresponds to the maximum element chosen within the channel c of Z t . the normalization in Eq.


Accordingly, there have been various lines of work on high dimensional inference based on imposing different types of structure constraints such as sparsity and group sparsity [15] [5] [21].

it is worth noting that in the standard Lasso the factor 1 2 is omitted.


Conditioned on σ = σ (j) , we define an HMM over G with the following transition and observation probabilities, respectively: L(z where φ(v, e; z1, .

as we discuss in Section 5, the parametric assumptions made in the most basic form of ALPACA can be considerably relaxed without impacting the computational complexity of learning.


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

here the expectation is defined with respect to randomness introduced by Markov kernel of MDP as well as the policy ⇡.


2 Contextual relationships between foreground objects (i.e., C o and C m ) may be beneficial (e.g., people found on bicycles), but are not considered in this work.

the method does not attempt to understand the scene semantics.


By the induction hypothesis, rounds 2 to n of the loop determine a cue permutation π ′ with INCORRECT(π ′ , L ′ ) ≤ (n − 1) • opt I ′ (L ′ ).

in addition, we show that TTB does not have this property, concluding that the greedy method of constructing cue permutations performs provably better than TTB.


There is an increasing tendency to consider machine learning as a problem in optimization: define a loss function, add constraints and/or regularizers and formulate it as a preferably convex program.

hence, our approach can be thought of as a middle ground that borrows from both learning philosophies.


Finally, we continue to investigate whether other techniques from the robust statistics and machine learning literatures can be incorporated in the general framework while preserving desired properties.

since is closed and convex by assumption, we know that (r) = sup ν νr − ν * (ν), where * is the Fenchel conjugate of [22].


On the word similarity task, SPPMI yields better results than SGNS, and SVD improves even more.

we note that M PMI 0 is inconsistent, in the sense that observed but "bad" (uncorrelated) word-context pairs have a negative matrix entry, while unobserved (hence worse) ones have 0 in their corresponding cell.


Figure 2(f) illustrates how the optimal choice of η depends on parameters defining the population Laplacians and sample Laplacians.

. . , λ(n − 1) lies in the unit simplex.


The running time for this experiment was 59 seconds.

while this hierarchical clustering method can be applied to any latent variable model that can be learned with the tensor method of moments (e.g.


Because the pool of available modules is shared between processing stages (or time steps), modules can be used at multiple locations in the network.

our architecture differs from [25] in that we don't assign a probability to every of the M modules and pick the K most likely but instead we assign a probability to each composition of modules.


Nevertheless, several questions remain open: whether there is an intrinsic information-theoretic obstacle to bridging this gap; whether our convergence rate estimates hold with high probability (and not just in expectation); and whether our analysis extends to a fully decentralized setting where the players' updates need not be synchronous.

as we discussed above, the aggregate bias in the algorithm after n stages is O( ): if the conditions (5.2) are satisfied, both error terms vanish, but they might do so at very different rates.


The experiments were carried out with the following parameters settings.

the statistics of locally selected image contrasts, appropriately captured by the Weibull distribution, explain up to 75 percent of occipital EEG activity for natural images and almost 83 for artificial dead leave images.


It is known that when n = ⌦(s ⇤2 log d), one could obtain the optimal statistical rate of O( p s ⇤ log d/n) by nonconvex method [37].

in the low-dimensional setting, for two-layer neural network [14] propose a tensor-based method for estimating the parametric component.


Another important question is whether current decisions have long-range effects, or if it suffices to simply learn policies that optimize immediate reward.

to cite a prominent example, the US Congress recently mandated a study of the power efficiency of servers, including a feasibility study of an Energy Star standard for servers and data centers [16].


Thus, if we can obtain lower bounds on accuracy for functionalities involving only a single bit at each of the parties, we obtain lower bounds on accuracy for all non-trivial general functionalities.

a similar technique of transforming a non-linear optimization problem into an infinite dimensional LP has been successfully applied in [26], where optimal privatization mechanisms under local differential privacy has been studied.


Similar pooling operations can also be employed to gain tolerance to other image transformations, including those induced by changes in viewpoint or illumination.

for example, a face can be encoded invariantly to translation as a vector of similarities to previously viewed template images of any other objects.


In figure 1 we show the logarithm of the exact partition function , the first order or mean field bound, the upper bound (which is roughly quadratic) and the third order lower bound.

the section is concluded by explaining how these bounds on the partition function can be used to bound m eans and correlations.


• per category preprocessing establishes the required detector data-structure.

as c gets large, we expect the approximation to improve.


[2017] then use an EM-type approach illustrated in figure 2 iteratively optimizing parameters and the variational lower bound L Q(θ).

this pathwise solution of RODEs implies that a massive amount of deterministic ODEs have to be solved efficiently.


The data emission model for state i is set as N (i, σ 2 ), where σ varies under different noise level settings.

it could be beneficial to visualize the relationship between clinical, imaging, and biochemical markers as the pathology evolves, in order to better understand AD progression and develop treatments.


( 6):  See Figure 1 for the plots of ρ * .

the theory [11] behind LSH still works if we use hash function h 1 for preprocessing x ∈ S and a different hash function h 2 for querying, as long as the probability of the event {h 2 (q) = h 1 (x)} increases with Sim(q, x), and there exist p 1 and p 2 with the required property.


Let us assume that each image of the database has been represented by a number of low-level features, and that a (dis)similarity measure has been defined so that the proximity between pairs of images represents some kind of "conceptual" similarity.

it is interesting to note that while relevance feedback mechanisms have been first introduced in the information retrieval field [2], they are receiving more attention in the CBIR field (Huang).


Such variables are then treated as part of learning using the technique presented in [13].

the purpose is to provide a better initial guess for the object pose, which is then refined by optimizing over the latent variables.


when trying to limit the error introduced, a significant amount of time is needed for such optimization.


imagine we have a large corpus, containing unlabeled pictures of animals, and our task is to build a generative probabilistic model of the data.


In this work, we analyze three such algorithms which are based on convex relaxations.


The problem of sampling k n columns in a matrix also arises in network controllability.


This setup replaces one N -way choice by a sequence of O(log N ) binary choices.

when the responsibilities of both components for a datapoint are close to 0.5, we cannot be sure that the datapoint should be in one component but not the other.


In the following, we give an analysis which shows that under certain conditions it is however possible to guarantee the convergence of a gradient-descent type algorithm to a global minimum.

for each domain, the parameters λ and Λ were chosen via 10-fold cross validation on 1,000 points.


Let Γ be a probability distribution on (0, +∞) (the inverse density prior).

the compression set and the message string.


We pad and clip reviews to a length of 200 tokens, and learn 50-dimensional word vectors from scratch for a vocab size of 5,000.We train an LSTM with 64 hidden dimensions on this data.

we did not observe the same behavior when turning off the corresponding component of the GLC, and believe it may be due to variance introduced during training by the difference in signal provided by the Forward method's C estimate and the clean labels.


. . , π T −1 ), where each π t : S → A is a (stationary) policy, we define the value V πt,...,πT −1 (s) ] as the expected (normalized) sum of rewards attained by starting at state s and the "clock" at time t, taking one action according to π t , taking the next action according to π t+1 , and so on.

if θ * = arg min θ T (θ), then [1] presents a polynomial time algorithm that finds θ so that T (θ) ≤ (n + 1)T (θ * ).


Moreover, the learned parameters of such compressible priors are dimension agnostic.

some of these new algorithms are variants of the popular iterative re-weighting schemes [3,[6][7][8].


The DAE log-likelihood bound with and without walkback is respectively -116 and -142, confirming visual inspection suggesting that the walkback algorithm produces less spurious samples.

algorithm 2: THE WALKBACK ALGORITHM is based on the walkback corruption process C( X|X), defined below in terms of a generic original corruption process C( X|X) and the current model's reconstruction conditional distribution P (X| X).


Zettlemoyer and Collins [11] perform similar work based on lexical learning with lambda-calculus language.

the image features are detected by the Kadir-Brady operator [13], and their appearance is calculated by the SIFT operator [14].


Figure 5 shows examples of generated images.

pixelwise comparison of the generated images requires that not only the input but also the output representations are aligned, which is ensured in our case since at the beginning of training both have the same parameters.


Exact learning is known to be NP-hard (c.f.

in the greedy M step, specific training cases are chosen as exemplars.


Both algorithms produced similar results thus we focused on [10] while replacing the normalization with the three schemes presented above.

the Frobenius norm normalization is a new formulation and is based on a simple iterative scheme.


However, they tend to struggle when data is scarce or when they need to adapt to new tasks within a few numbers of steps.

the key idea behind MetaGAN is that imperfect generators in GAN models can provide fake data between the manifolds of different real data classes, thus providing additional training signals to the classifier as well as making the decision boundaries much sharper.


Despite only requiring weak feedback, our TPP learning algorithm has provable regret bounds and empirically performs well.

we further observe, generalizing to tasks with both new environment and object is harder than when only one of them changes.


We extend the classic Hamiltonian Monte Carlo (HMC) with the scheme of continuous tempering stemming from the recent advances in physics [8] and chemistry [15].

( 6), and the mini-batch noise is absorbed into the thermostats from the system dynamics in Eq.


LDA with 200 topics does improve upon LDA-50, achieving a perplexity of 1142.

the LDA with 200 topics performed much better on this dataset compared to the LDA-50, but its performance only slightly improved upon the 50-dimensional Replicated Softmax model.


4 (a) and (b) show the image and the implicit shape representation: the pyramid's lowresolution shape and the shape recipes used over the top four scales.

stereo often fails to provide the shape of image regions with complex shape details, where the shape recipes succeed.


To overcome the above drawback, recent work has focused on stochastic proximal gradient methods (SPG), which exploit the additive nature of the empirical risk function F(✓).

end for e ✓ (s) The MRBCD method with variance reduction is summarized in Algorithm 2.


Now, regard the transformation variables {Φ i } as well as the cluster memberships {z i } as being hidden.

our approach is to formulate models for both the clustering and alignment sub-problems and integrate them into a unified probabilistic framework that allows for the derivation of consistent learning algorithms.


For any v ∈ V , For any v ∈ V and l ∈ Lemma 1, which can be proved by FKG inequalities, suggests that given p l−1 (u → v), we may compute an upper bound on the influence.

we take this approach of generating a subnetwork from the original network, yet we avoid the significant gap between the bound and the influence by considering the following directed acyclic subnetwork, in which there is no backtracking walk.


Recall that λ ě λ max yields βpλ,Ωq " 0, in which case ρ :" y ´X βpλ,Ωq " y is the optimal residual and y{λ max is the dual solution.

the dual solution θpλ,Ωq is unique, while the primal solution βpλ,Ωq might not be.


It is well-known that f * (z) = 1 2 z 2 .

we show that for each X T g θ ∈ D α g , Fenchel's duality naturally leads to an explicit decomposition X T g θ = b 1 + b 2 , with one belonging to α √ n g B and the other one belonging to B ∞ .


This is possible because the persistence inside A ⇤ sampling focuses the refinement on the regions that are important for accepting the current sample.

in this work, we introduce a generic sampling algorithm that returns exact independent samples from a distribution of interest.


Note that k (⌧ ) k 1 is the average length of a document with topic ⌧ .

binomial dropout trains on perturbed features x(i) instead of the original features , where x(i) during training, we randomly thin the j-th feature x j with binomial noise.


To get even better initialization, we perform our initial optimization with a large degradation noise estimate (σ n = 2.5) and then perform the optimization with a lower estimate (σ n = 1).

we explicitly use the Gaussiansmoothed natural image distribution as a prior, and we show that we can learn the gradient of its logarithm using a denoising autoencoder.


Therefore, there exists a correct process ζ(i) which is farther from i than every neighbor j of i (including the Byzantine neighbors).

as seen above, Krum slows down learning when there are no Byzantine workers.


With a prescribed sequence of edges γ 1 , .

loss suffered after T rounds of play is at most (0).


The detailed data generating process is shown in supplementary section D. The root node Y is a binary variable, while other variables are continuous.

we would find tractable Q-distributions over q (x ft |x f<t , y).


In each pass, each sample can be randomly transformed or the hidden nodes can be randomly activated.

the proposed loss function is completely unsupervised and can be used along with supervised training as a semi-supervised learning method.


a search engine's ranking of the documents is more critical than the accuracy of its classification of all documents as relevant or not.


Applications include collaborative filtering [23], system identification and realization [19,21], multi-task learning [28], among others.

in essence, we turn (5) into an unconstrained problem by giving up on satisfying the linear constraint exactly.


We denote their entries by a i , a i,j , a i,j,k , etc., depending on the number of dimensions.

for any t such that λ t+1 < λ t , we have (σ t , {w  We evaluate the effectiveness and efficiency of our method SURF through numerical experiments on both synthetic and real data, and compare with various state-of-the-art regression methods, including LASSO, Elastic Net (ENet), Regularized multilinear regression and selection (Remurs) [Song and Lu, 2017], optimal CP-rank Tensor Ridge Regression (orTRR) [Guo et al., 2012], Generalized Linear Tensor Regression Model (GLTRM) [Zhou et al., 2013], and a variant of our method with Alternating Convex Search (ACS) estimation.


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

the Discriminator block and the training procedure are unchanged.


The cluster size is varied from n min = 20 to n min = 200 in steps of 20 and r is varied from 0.05 to 1 in steps of 0.05.

we observed 15% of the total number of entries.


(2), which measures the cosine distance between n i and n j .

we refer readers to the original papers for detailed definition due to limited space.


If a 'state vector' is now defined to be the n-dimensional vector it is readily seen that x(t) is a basis for the stationary oblique predictor space X t := Y φ+ t / U φ+ t P φ t , which, on the basis of general geometric principles, can be shown to be a minimal state space for the process φ y (y), as in the linear case [3,5].

( 20)) and define the following matrices consisting of N − 1 columns: Xl+1 = Xl (:, 2 : N ), Xl = Xl (:, 1 : N − 1).


In gene expression analysis, we are interested in recovering a matrix of expression levels for various genes across a number of conditions.

so our algorithm is applicable for all these settings.


The distribution of ODCs strongly depends on the disparity and does not vary significantly between runs for a given disparity.

disruptions appear at ODC boundaries in the runs with disparate stimuli, these disruptions becoming more distinct with increasing disparity due to the increasing sharpness of ODC boundaries.


We make this comparison with continuous variables by discretely relaxing continuous priors using a discrete prior with a finite support set that contains much of the structure and information as its continuous analogue.

we can go beyond this to additionally reduce computational and energy demands for the evaluation of Φ ¦ W. One approach is to constrain the elements of s w to be 0 or a power of 2 so that multiplication operations simply become efficient bit-shift operations [25][26][27].


However, since x is arbitrary, ∂g(P f (x)) = ∂g(z) ⊇ ∂g(x) if g is not linear.

since both P f and P g are increasing and nonexpansive, it follows easily that so is P f • P g , hence the existence of h ∈ Γ 0 so that P h = P f • P g . In a general Hilbert space H, we again easily conclude that the composition P f • P g is always a nonexpansion, which means that it is "close" to be a proximal map.


After we construct this P , we can run LEARNHIST at a centralized server, and simply output the resulting hypothesis distribution.

. . X m ) of m independent samples from P and sequence R of uniformly and independently distributed random bits, and outputs a hypothesis distribution P := θ( X, R).


During learning, a set of Mahalanobis metrics, one for each source, are learned together.

in the preprocessing step all the features are standardized in all the data sources.


features for speakers within a phone differ not only because of different speaker characteristics but also different phonetic contexts.


We evaluate jungles on a number of challenging labelling problems.

the task of learning the current level of a DAG can be written as: Maximizing the Information Gain.


Refinement: Temporally Constrained Clustering Spectral clustering methods are designed for an unordered "bag" of feature vectors, but, in our case, the temporal ordering of image is an important source of information.

let C 1 (t) denote the class label for image t, and g(c) = f (ID(c)); c = 1 . . . n denote cluster centers.


B: Spike pair example for differential Hebbian learning.

our analysis indicates that both cortical as well as hippocampal STDP is most susceptible for modulations in the theta frequency range.


Two common factors make the global VB solution attainable in PCA and LRSC: first, a large portion of the degrees of freedom that the VB approximation learns are irrelevant, and the optimization problem can be decomposed into subproblems, each of which has only a small number of unknown variables; second, the stationary condition of each subproblem is written as a polynomial system (a set of polynomial equations).

bayesian learning is often obstructed by computational difficulty: the rigorous Bayesian learning is intractable in many models, and its variational Bayesian (VB) approximation is prone to suffer from local minima.


Let q be our ideal distribution for q given by q(x, y, z|`= 1) = f X,Y,Z (x, y, z), q(x, y, z|`= 0) = f CI X,Y,Z (x, y, z) and q(`= 1) = q(`= 0) = 0.5.

if the classifier has accuracy close to random guessing, then f X,Y,Z (.)


It is also interesting to study how it can be generalized to the case with undirected network or even continuous covariate space.

we discussed three operations: superposition, subsampling, and point transition, which produce DPs depending on others.


In FPGAs and ASICs, the total number of computational units in a network has a significant impact on the power consumption and speed of inference.

we chose CIFAR-10 to allow quick experimentation.


Let X be the event that for all p I § p , X w vs in the OAL algorithm in a given state.

it is sufficient to only prove that the OAL algorithm will converge to the optimal policy over individual state games w.p.1.


Further improvements through conjugate gradient methods and Krylov sub-spaces are available.

we experimented on two commonly used GLM optimization problems, namely, Logistic Regression (LR) and Linear Regression (OLS).


While such approximations have recently been used successfully in a variety of works [21,9,18] the specific form of our model poses two additional difficulties.

we achieve this by performing probabilistic inference using a recurrent neural network that attends to scene elements and processes them one at a time.


Comparison with Sample Complexity of Proposed Method: For Ising models, under uniform sampling of observed nodes, we established that the sample complexity of the proposed method scales as n = Ω(∆ 2 ρ −2 (log p) 3 ) for regular graphs with degree ∆.

we employ latent graphical models for topic modeling.


In addition, it is unclear if parameters in each model can capture the individual differences in learning.

no change of the environmental statistics) is optimal in this condition.


LWF CGs were given a causal interpretation in [6].


let z (t) be chosen via uncertainty sampling with the parameters θ: ).


Just as in the analyses of particle dynamics in dissipative quantum mechanics [4] we anticipate that the time-course of α(t) may exhibit qualitatively different types of behavior depending on the strength of the non-local terms.

it is well known that, at least in some regimes, the problem with dissipation has a phase transition to a truly localized state.


Each iteration either samples a mini-batch of links or samples a mini-batch of non-links.

to maintain a correct stochastic optimization algorithm of the variational objective, the subsampling method must be valid.


Note that the first of the above terms involves the data while the second one only involves the prior.

a temporal latent function x(t) ∈ R Q (with Q D), governs an intermediate hidden layer when generating the data, and the dth feature from the data vector y n is then produced from x n = x(t n ) according to where f d (x) is a latent mapping from the low dimensional space to dth dimension of the observation space and β is the inverse variance of the white Gaussian noise.


The strongest results of this kind establish Õ(S Ô AT ) regret for particular algorithms [4,5,6] which is close to the lower bound ( Ô SAT ) [4].

the vast majority of e cient reinforcement learning has focused upon the tabula rasa setting, where little prior knowledge is available about the environment beyond its state and action spaces.


For any choice of parameters (θ, g), there is a resulting vector of marginals µ The marginal polytope M is now the set of all such vectors µ that are realizable under some distribution P (x), and the partition function can equally be expressed in terms of the marginals [7]: where H(µ) is the entropy of the distribution, ∆(µ) is the vector of disagreement probabilities with entries ∆(µ) i,j = xi =xj µ ij,xixj , and stack(θ, g) adds the elements of θ and g into a single vector so that the sum can be written as an inner product.

the result are inference schemes that optimize rigorous bounds on the partition function.


light-tailed distribution) is one whose tail decays at least as fast as a Gaussian distribution (i.e., exponential decay).

since ReLU operation is pointwise, we have the identity y " AGpzq " AσpW 2 σpW 1 zqq " σpAW 2 σpW 1 zqq.


DBCD and PROXCOCOA+ adopt a coordinate distributed strategy to partition the data.

another branch of the distributed proximal stochastic methods is based on block coordinate descent [3,20,7,16].


K subspaces (each of dimension at most r): U k denotes the basis spanned by k-th estimated subspace and O d⇥r ⇢ R d⇥r denotes the set of orthonormal matrices, i.e., U T U = I if U 2 O d⇥r .

when initialized within a small constant distance to the true subspaces, our method converges to the global optima (and recovers true subspaces) in time linear in the number of points.


The standard goal of nonconvex optimization with provable guarantee is to find approximate local minima.

the amount of objective decrease -i.e., f (y k ) − f (x) if x moves out of the safe zone-must be proportional to the distance x − y k 2 we travel in space.


The time axis is discrete, with index n = 1, 2, .... At stage n, the following events occur: (i) the input instance is presented to the classifiers (but not to the agent); (ii) each classifier a ∈ A outputs f n (a) ∈ [0, 1], which is the probability of the input to belong to class 1, and simultaneously the agent chooses a classifier a n ; and (iii) the correct label of the instance, b n ∈ {1, −1}, is revealed.

we have two classifiers, and we assume that the outputs of these classifiers lie in the set ≥ λ such that γ 1 > γ, γ 2 < γ, and λ ≥ 0.


In the generative process, the hidden variable of feature f m for an object y t , F m t ∼ Bernoulli(a To compute the probability of the feature matrix F 6 , in which the parameters a and b are integrated out analytically, we use the counting variables c 00 m , c 01 m , c 10 m , and c 11 m to record the 0 → 0, 0 → 1, 1 → 0, and 1 → 1 transitions f m has made in the binary chain m. The stochastic process that derives the probability distribution in terms of these variables is defined as follows.

to employ the H&K's model for tasks that require clustering objects with rich linguistic features (such as event coreference resolution), or to extend this model in order to enclose additional observable properties is a challenging task [22,25].


Furthermore, in special cases, a subset of the interaction network may be known with a high confidence using Capture-C [12].

notice that when applying alternating optimization to solve this problem, we can simply use the same approach used to solve (OPT2).


We use both CIFAR and SVHN datasets in experiments to evaluate the performance.

we use the lengths of capsules to score the presence of entity classes corresponding to different subspaces, while their orientations are used to instantiate the parameters of entity properties such as poses, scales, deformations and textures.


For stochastic optimization problems, another important evaluation criterion is the confidence level of the objective value.

to obtain tighter bounds, we strengthen the basic assumption of the stochastic subgradient in Eq.


More generally, one could replace slate spaces by arbitrary compact convex sets, as done in linear bandits.

replacing θ µ,x with θi motivates the following estimator for V (π), which we call the pseudoinverse estimator or PI: In Eq.


As in several existing metric learning methods, we restrict ourselves to learning a Mahalanobis distance function over our input data, which is a distance function parameterized by a d × d positive definite matrix A.

in many real applications, constraints are only available incrementally, thus necessitating methods that can perform online updates to the learned metric.


It deals with bounding the performance of algorithms that result in a set output when given training data.

note that we are interested in data-independent priors over the space of classifiers 2 , and hence, we consider our prior Π to be the same as the volume measure P over the classifier space yielding π as unity.


r t (π) = E[ρ t ] where ρ t is drawn from the distribution r(s t ).

restricting D to probability measures on (0, 1) and applying Lemma 1, we get To finish the proof, we note that γ < 1 and, by definition, We use the MDP of the previous section with a different policy class which we now describe.


If the primate visual system uses recurrence in lieu of greater network depth to perform object recognition, then a shallower recurrent model with a suitable form of recurrence should achieve recognition accuracy equal to a deeper feedforward model [Liao and Poggio, 2016].

cNNs trained to recognize objects in the ImageNet dataset predict the time-averaged neural responses of cortical neurons better than any other model class.


Then the exposure process is given by E(t) = B N (t).

suppose Ψ : [0, T ] → R n×n is a non-increasing matrix function, then for every fixed constant intensity if and only if Ψ(t) satisfies if where The next theorem shows that if Ψ(t) satisfies ( 7), then one can calculate η(t) for piecewise constant intensity µ : [0, T ] of form (9).


The complexity of ECOC with a code of length l and code-distance δ is at most Õ(dl) and at least dδ/2.

in many practical applications, we will prefer not to employ kernels (either because of shortage of examples, which might lead to a large estimation error, or due to computational constraint), and in such cases we expect to see a large difference between the methods.


In addition, as analyzed in Section 2, the approximation in [1,14] drops the rank constraint of the matrix y y, which does not lead to a tight approximation.

course-l 1800 50 1000 To evaluate the effectiveness of the proposed CTSVM method, we choose the conventional SVM as our baseline method.


we feel that tightening this gap is a particularly exciting open problem.


The other options can be encoded via the "On" and "Off" positions respectively.

hence, positive rewards are sparse, arising only when sending and interpreting are properly coordinated, which is hard to discover via random exploration.


Amazon.com requires its sub-services to report and optimize performance at the 99.9 th percentile, rather than in expectation, to make sure that all of its customers have a good experience, not just the majority [1].

we have used on-time statistics for February 2011.


Finally, given the forces acting on the bodies at time t, f t , and the collision coefficient c, the constrained dynamics can be formulated as the following mixed LCP  where [a, , ⇣] T are slack variables for the inequality constraints, and [v t+dt , e , c , f , ] T are the unknowns.

the model is able to learn the paddle parameters quickly from random trajectories, improving the control precision, and leading to high reward, as shown in Figure 6 Figure 5: Even though the baseline is able to achieve lower MSE over one-step predictions of the dynamics of the Cartpole environment (left), the physics engine-based controller is able to achieve a higher reward very quickly (right).


When averaging across all trials, this effect was very significant for the pets and vegetables group (p < 0.001), and less significant for the hazard group (p = 0.05) (Figure 2b).

it is still an open question whether humans are prone to similar mistakes.


Furthermore, often desired features like zero truncation or zero inflation can also be naturally incorporated by modifying the g(0) value [22,23].

we define the generalized count distribution as the family of count-valued probability distributions: where θ ∈ R and the function g : N → R parameterizes the distribution, and is the normalizing constant.


Naive-MKL works only 0.56 ms on Netflix and 1.42 ms on MovieLens, which is fast enough for most of applications.

prior work on non-metric similarity search on graphs.


Mixture models and nonparametric family [Jaakkola and Jordon, 1999, Gershman et al., 2012, Dai et al., 2016a are the natural generalization.

the most important difference is that CVB couples the adversarial component with original models through optimization embedding, which is flexible enough to approximate the true posterior and promote the learning sample efficiency.


An intuitive way of achieving this is by studying the odds of r t+1 ∈ {0, r + 1} conditional on r t = r: p(r t+1 = r + 1|y 1:t+1 , r t = r, m t ) p(r t+1 = 0|y .

conversely, as β → 0, one recovers the KLD which cannot treat any observation as an outlier.


Hence H satisfies this weak-learning condition.

let C ⊆ R m×k and matrix B ∈ R m×k , which we call the baseline; we say a weak classifier space H satisfies the condition (C, B) if In ( 2), the variable matrix C specifies how costly each misclassification is, while the baseline B specifies a weight for each misclassification.


One can now further optimize over the choice of ϑ to obtain the best constant in the bound.

then if u t * ≤ M for all t and η t = η t −β , then Assuming h is bounded, optimizing over β yields a rate of R t (x) = O(t κ 1+κ ).


Notice that existing methods, which do not incorporate the dynamic of data for summarization, perform similar to each other for most tasks.

as we will show, { i } and {u t i 0 ,i } are related to {z i,t }, hence, the final optimization only depends on {z i,t }.


An alternative strategy followed by some other methods relies on selecting a subset of the MRF nodes at each scale (based on some criterion) and then fixing their labels according to the optimal solution estimated at the current scale (essentially, such methods contract the entire label set of a node to a single label).

here we will also make use of a pruned solution space S(M, A), which is defined based on a binary function A : V × L → {0, 1} (referred to as the pruning matrix hereafter) that specifies the status (active or pruned) of a label for a given vertex, i.e., During optimization, active labels are retained while pruned labels are discarded.


This extends learning kernel ideas and helps explore kernel combinations leading to better performance.

for any such stationary point µ ⋆ , F (µ ⋆ ) = y ⊤ (K µ ⋆ + λI) −1 y = y ⊤ y λ , which is clearly a maximum.


So, with high probability this overcomes the at most γ 8 m x incorrect bias of neighbors that have already updated, and so the points will indeed update correctly as desired.

because of the high noise rate, learning this function directly would require a very large number of queries to be made (for noise rate η, one would necessarily require Ω( paper is to what extent this difficulty can be alleviated by providing the agents the ability to engage in a small amount of local communication among themselves.


. . , t k }, and a collection of binary and vertical compatibility relations between tiles H, V ⊆ L × L. A tiling is a mapping of board locations to tile-types, t : {0, . . . , n − 1} × {0, . . . , n − 1} → L; such a tiling is consistent just in case (i) the origin location of the board receives tile-type 0 (t(0, 0) = tile 0 ); and (ii) all adjoint tile assignments are compatible: (∀x, y) t(x, y), t(x + 1, y) ∈ H & t(x, y), t(x, y + 1) ∈ V. The TILING problem is thus to decide, for a given instance, whether such a consistent tiling exists.


where f (x) = c T x and g(y) is the indicator function as defined before.

the key challenge in designing a first-order algorithm is that LPs are usually non-smooth and non-strongly convex optimization problems (may not have a unique solution).


Understanding why a model makes a certain prediction can be as crucial as the prediction's accuracy in many applications.

to validate the importance of Theorem 1, we compared explanations from LIME, DeepLIFT, and SHAP with user explanations of simple models (using Amazon Mechanical Turk).


The gradient of the likelihood can be computed in terms of the empirical covariance and the covariance of s i and s j as produced by the current model: The second term on the right hand side is difficult to compute, as it requires sampling from the model.

the solid diagonal line corresponds to a perfect match between model and ground truth.


Following [5], we can model the linear term directly in the quadratic term if we augment all data points with an extra feature of value 1, i.e., x T ← [1, x T ].

when Ω(•) = • 1 , we need to solve It is well known that the optimal solution of max h∈H |h T Γ c h| is the dominant eigenvector of Γ c . we simply need to find the dominant eigenvector h c of each Γ c and select ĥ as the h c with largest singular value |h T c Γ c h c |.


We thus evaluate our method in two different settings using existing datasets: (1) we validate our 3D pose predictions using Human3.6M [13] which provides accurate 3D and 2D poses for 15 different actions captured in a controlled indoor environment; (2) we evaluate on Leeds Sport dataset (LSP) [16] that presents in-the-wild images together with full-body 2D pose annotations.

we train an end-to-end CNN classifier for 3D pose estimation and show that, with our synthetic training images, our method outperforms state-of-the-art results in terms of 3D pose estimation in controlled environments and shows promising results for in-the-wild images (LSP).


Asymptotically (as k 1 and k 2 increase), the inequality becomes an equality where f 1 and f 2 are the numbers of non-zeros in u 1 and u 2 , respectively.

conditional Random Sampling (CRS) combines the advantages of both sketching and random sampling.


Inhibitive interaction, Θ = π/2 Excitatory interaction, Θ =0 Physiological experiments [2][3] have demonstrated that the neuronal activities in the classical receptive field are suppressed by responses outside the CRF to stimuli with similar motions including both directions and speeds on the center and surrounding regions.

the phase tuning can give a good classification of velocity differences.


Castro and Nowak [9] study a framework in which the learner also queries arbitrary domain points.

note that the margin threshold explicitly depends, through λ, on additional information about the data-generating process.


To provide for an expressive dynamics model, we can represent the parameters of this distribution (e.g., the mean and covariance of a Gaussian) as nonlinear, parametric functions of the current state and action, which can be arbitrarily complex but deterministic.

these approaches can be categorized by how they represent the state distribution: deterministic, particle, and parametric methods.


In Steps 2-3, UCRL2 computes estimates pk (s |s, a) and rk (s, a) for the transition probabilities and mean rewards from the observations made before episode k. In Step 4, a set M k of plausible MDPs is defined in terms of confidence regions around the estimated mean rewards rk (s, a) and transition probabilities pk (s |s, a).

when a learner explores suboptimal actions, this may take him into a "bad part" of the MDP from which it may take about D steps to reach again a "good part" of the MDP.


moreover, we analyze the convergence of AMPE in another norm ( • 2 instead of • A ).


4 Cutting-Plane Algorithm using Belief Propagation In the previous section we established that BP on a carefully designed GM using non-intersecting odd-sized cycles solves the MWM problem when the corresponding MWM-LP relaxation is tight.

initially, set m 1→0 , m 0→1 by n 1→0 , n 0→1 .


While the sequential rollout still only performs classification on single images, the streaming rollout can integrate over two input images due to the skip connection that bridges time (see Fig.

due to the pipelined structure of computations in the streaming case, outputs are more frequent.


Now, using the Hammersley Clifford theorem [1] and assuming only up to pairwise clique potentials to be nonzero, the joint distribution over the labels x given the observations y can be written as, where Z is a normalizing constant known as the partition function, and -A i and -I ij are the unary and pairwise potentials respectively.

the MAP estimates of the labels were obtained using graph-cuts for both the models.


Variational upper bounds on MAP and the partition function, along with algorithms for providing fast, convergent optimization, have been widely studied in the last decade.

because of the fully decomposed form, the gradient w.r.t.


After training, first-and second-layer mappings were inferred from the first three frames of the test sequences.

a natural way of training the model on sequential data is to replace the reconstruction task with the objective of predicting future frames as we discuss next.


Its definition follows for any vertex i ∈ V (s) and any label l ∈ L : Local energy variation This feature represents the local variation of the energy around the current solution x (s) .

as in [11], we remove the local energy of the current solution as it leads to a higher discriminative power.


We then define the concentration matrix , where Λ is the diagonal matrix of L −1 (used to normalize the diagonal of Σ = Θ −1 ).

when considering simulated results for validation, we use the model by Barabási & Albert (1999) to generate graphs with this property.


Next, we provide the sampling conditions.

our results ensure that the sample size can be fixed to guarantee the convergence of Algorithm 1.


In contrast, using stochastic search methods or descent methods to find the global minimum will generally incur a computational cost scaling which is exponential in the sample size times the parameter space dimensions.

in the following section, we modify L 2 Boost for fitting mixture models.


This expectation can be computed in closed form for GPs.

due to space constraints, we will only describe the key ideas and defer all details to Appendix B.


Otherwise, the extrapolation (3) is used.

again, PSA achieves the best single-pass accuracy for both tasks.


Ideally, we want the LML error to be of order 1 of less, since much larger errors could severely affect the results of a comparison (e.g., differences of LML of 10 points or more are often presented as decisive evidence in favor of one model [26]).

we have shown on both synthetic and real model-fitting problems that, given a contained budget of likelihood evaluations, VBMC is able to reliably compute valid, usable approximations in realistic scenarios, unlike previous methods whose applicability seems to be limited to very low dimension or simple likelihoods.


It is this pruning mechanism that naturally chooses the number of active dipoles.

the optimal X (with Γ and Z fixed) is just the standard weighted minimum-norm solution given by for each i.


3 It is worth pointing out that in the tabular case, IMLinUCB reduces to CUCB [7], in the sense that the confidence radii in IMLinUCB are the same as those in CUCB, up to logarithmic factors.

for ray graphs with ω = 0.8 and ω = 0.7, our estimated growth are respectively O(L 2.488 ) and O(L 2.467 ), which are again close to the expected O(L 4 ).


Suppose that the agent follows policy 1 and uses Sarsa updates to learn weights £ , and suppose that 1 4$ &© 0' i %) y A for all © and .

for any y A , let denote the set of -soft policies.


Note that, exchanging the role of the primal and dual problem in (3), we can obtain the dual version of both ADMM and ACLD, which can be used to tackle the primal or dual sparse problem.

in this paper, we proposed a new variable splitting method to solve the linear programming problem.


In the noiseless setting, we can take = 1 and recover the original QBC update.

we consider a broader class of updates, where `(•, •) is a general loss function.


Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

to control the program lengths of the training and test data, we develop a pCFG-based program generator and a subset of the core CoffeeScript grammar.


It follows that O::i = 00 is thus a minimum.

the learning procedure in [6] relied upon heuristic re-estimation equations for the hyperparameters, the behaviour of which was not well characterised.


Algorithms in [12,26] are unlikely to be practical for most vision problems, which typically have tens of thousands of variables.

one of these formulations was called a roof dual.


We gave ADMM and PGD an advantage by optimally tuning them for each individual problem-instance tested.

we will later use Lemma 3.7 as a criteria to find the critical values.


9) using these samples: which is also log-concave and thus efficiently maximized for φ.

the conditional intensities for the two cells are then given by where k y and k z are linear filters representing each cell's receptive field, h yy and h zz are filters operating on each cell's own spike-train history (capturing effects like refractoriness and bursting), and h zy and h yz are a filters coupling the spike train history of each neuron to the other (allowing the model to capture statistical correlations and functional interactions between neurons).


Domain experts derive knowledge from previous tasks: They learn about the performance of machine learning algorithms.

formally, this AutoML problem can be stated as follows: Definition 1 (AutoML problem).


Unfortunately, only one of the paired comparisons was statistically reliable by a two-tailed Bonferroni corrected t-test: (0, 1) versus x * (p = .027).

figure 3b uses the PPF mean to estimate the optimum duration, and this duration is plotted against n requires a strategy for selecting the next experiment.


However, extremum distribution operation on decision nodes is very time-consuming because it must consider over all the child nodes.

the ability to include prior information provides important flexibility and can be considered an advantage of the approach.


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

we use the encoder from unsupervised learning for action recognition.


Intuitively, adaptive averaging increases the weights w(t) on portions of the trajectory which make progress.

these heuristics are known to empirically improve the speed of convergence, but provide few guarantees.


The off-policy evaluation problem satisfies the absolute continuity assumption if µ(s | x) > 0 whenever π(s | x) > 0 with probability one over x ∼ D. Using Assumption 1, we can now apply the techniques from the combinatorial bandit literature to our problem.

1 from the introduction shows that PI provides a consistent multiplicative improvement in RMSE over IPS, which suffers due to high variance.


Then, many tasks in computer vision can be naturally formulated in terms of energy minimization where the energy function has the form: , where θ p and θ p,q are univariate and pairwise potentials.

proposition 1 provides the lower bound As stated in Section 4.5, T k can be deleted from further consideration when β k = ∞ or µ.


Three classes (squares, triangles, and circles) should be separated from the rest.

another common approach, all-versus-all (AvA) [HT98], is a more expressive alternative which assumes the existence of a separator between any two classes.


I.e., we now have a family of policies that take as input a trajectory, and that attempt to make the helicopter fly that trajectory.

in the invention of the helicopter, it was necessary to add a tail rotor, which blows air sideways/rightwards to generate an appropriate moment to counteract the spin.


Besides, for the different random walk, we compute the corresponding transition matrix P t based on features from the different layer of similarity branch which represent different semantic levels, thus the information will be propagated gradually according to different levels' semantic similarities.

this work was supported by the grants of National Natural Science Foundation of China (61702301), China Postdoctoral Science Foundation funded project (2017M612272), Fundamental Research Funds of Shandong University, National Natural Science Foundation of China (61332015) and National Basic Research grant (973) (2015CB352501).


For our network we obtained results for up to 100 components of size 16 × 16.

the encoding of image patches investigated in this study separates feature and position information of visual components.


Best-boundfirst search can quickly discard unpromising nodes, but should not be used frequently at the top levels of the tree since the bound estimate is not accurate enough yet.

similarly, we set Gurobi's node limit to the average number of nodes explored by our algorithm.


There are many existing methods, such as pitch perception model based methods, and probabilistic approaches [4,15,16,17].

the original algorithm is extended in the following ways: Firstly, not all peaks exceeding the given threshold are detected, only the significant ones are selected by an edge detection procedure.


When this expected difference is large enough, we can make the same approximation as Eqn.

when log R tot (T ) reaches the target present threshold (Θ 2 ), with probability P (C = 2|T ), the target is present and with probability P (C = 1|T ) the target is absent, i.e.


We ensure that by setting λ, the standard deviation of their prior, fixed to one in all experiments.

a possible solution, which we propose in this paper, is to treat word information as features rather than as explicit constraints and to adjust a smoothing prior over topic distributions for words such that correlation is emphasised.


First, we have focused on the SAGA method as the basic iteration loop, but this approach can likely be extended to other proximal incremental schemes such as SGD or ProxSVRG.

we emphasize that a straightforward combination of this sparse update rule with the proximal update from the Standard SAGA algorithm results in a nonconvergent algorithm: the block-wise reweighting of h is a surprisingly simple but crucial change.


The most interesting aspect of the Bayesian optimal policy is that these immediate and future reward components in (3) can be interpreted as automatically balancing exploitation (immediate utility) and exploration (expected future utility given the information revealed by the present batch).

we conduct a paired t-test for each other policy against the best one, and also emphasize those that are not significantly worse than the best with significance level α = 0.05 in blue italics.


The algorithm next generates new features Φ (s, a) from the data trajectories using the current DRL network with weights w k . This step guarantees that we do not use samples with inconsistent features, as the ER contains features from 'old' networks weights.

rL tackles the curse of dimensionality by approximating terms in the DP calculation such as the value function or policy.


Then we can approximate Inf Sec by the empirical infimum of the sectional curvatures inf 1≤i≤t Sec xi (u i , v i ).

we typically assume T 0 to be known in advance in some other way.


Figure 1 (bottom) shows results when comparing multiple models.

because of the weighting factors, Equation 3 defines a consistent risk estimate (see [4], Chapter 2).


Moreover, we note that spectral algorithms have been also used in rating estimation in the context of crowdsourcing [49,53].

whether the gains characterized in both works are the maximally achievable remains open.


θ u = 0 for all u) and a common (unknown) edge parameter θ (i.e., θ uv = θ iff nodes u and v are adjacent in the grid, and 0 otherwise).

we observed qualitatively different results for The Beatles, the fourth most popular artist, being a favorite of 480 users.


The ill-posed nature of the MEG/EEG source localization problem requires the incorporation of prior assumptions when choosing an appropriate solution out of an infinite set of candidates.

this produces approximate posteriors on W and Z but the result cannot be integrated to form the posterior on S. the posterior mean of W , Ŵ , is used as an estimate of the source correlation matrix (using Ŵ Ŵ T ) to substantially improve beamforming results that were errantly based on uncorrelated source models.


We encode this prior knowledge by choosing Ω(β|Λ) with This method constraints the sum of the sets to be nonincreasing and may be interpreted as the composition of the wedge set with an average operation across the sets P i , see the discussion at the end of Section 3.

the utility of (2.2) is that upon inserting it into (2.1) results in an optimization problem over λ and β with a continuously differentiable objective function.


In our implementation we chose to break such ties arbitrarily.

for k ≤ d, let U k , Σ k , and V k contain only the top-k singular vectors and associated singular values.


Once we have detected the pairwise conversations we can identify the communication that occurs within the community and map the links between individuals.

finally, we have shown a strong correlation between a person's aggregate influence value and her betweenness centrality score.


In Figure 1 (right), we considered frustrated grid networks where p = 1 10 , where REC-BP converged in only one of 10 networks generated.

before we discuss the general case where we relax multiple equivalence constraints, we highlight first a few properties shared by both REC-BP and REC-I compensations, that shall follow from more general results that we shall present.


When A 22 approaches zero, the estimation error for A 11 approaches infinity.

we depend on rank one only in the sense that we understand the combinatorial-algebraic structure of rank-one-matrix completion exactly, whereas the behavior in higher rank is not yet as well understood.


We let the family of conditional densities for y be Gaussian for simplicity, that is, we assume that f j,k = N (µ j,k , σ j,k ) with µ j,k ∈ R and σ j,k ∈ R + .

. . , x ip ) T ∈ X for i ∈ [n], the graph construction follows via computing all pairwise distances using ρ(x u , x v ) = xu − xv 2 , where x is the whitened x (i.e., mean subtracted and variance normalized).


Corollary 1 shows that the left singular vectors P (k) can be recovered under mild conditions; thus the span of the right singular vectors can also be recovered.

. . , R): (5) If the core tensor C = (β i1...i K ) ∈ R R×•••×R is superdiagonal, the above decomposition reduces to the canonical polyadic (CP) decomposition [9,15].


In this construction, rather that drawing the ✓ ⇤ i ⇠ G 0 once as in (5), one may draw ✓ ⇤ i ⇠ G 0 for the first block of time, and then a simple Gaussian auto-regressive model is employed to allow the {✓ ⇤ i } drift a small amount between consecutive blocks.

the research reported here was supported under the DARPA HIST program.


When T is as small as 25, the sparse least-square method shrinks all the eigenvalues but still keep most of them non-zero, while Lyap with a non-sequence sample of size 1600 over-estimates the first few largest eigenvalues in modulus but shrink the rest to have very small modulus.

both models are stable, and the stationary distribution for each model is a zero-mean Gaussian.


It should be noted that for this work we will be working within a model-based framework and as a result will require knowledge of the transition model (although it could be learned).

we will focus the discussion on a different MCMC approach based on trans-dimensional simulation.


We also explicitly avoid discussing tapes and registers in our computational cost model.

the most natural question is how to develop algorithms that satisfy the mixed stability criterion: the algorithm should give "nearly the right answer to nearly the right problem" (as in [Trefethen and Bau III, 1997]).


9 and 11 are valid for any transformation T . I v/.

next, we show how to relax the constraint that the transformed density q .


Results using the full model are reported in Table 3, which shows 3D estimation is still under satisfactory, despite the efforts to maintain a good 2D-3D consistency.

we formulate the learning objective of the projection from 3D to 2D as where f (•) denotes a differentiable projection function which projects a 3D bounding box to a 2D bounding box, and X I * j ∈ R 2×4 is the 2D object bounding box (either detected or the ground truth).


Some simple algebra (omitted for the sake of brevity) shows that the weight matrix of the product graph can be written as Performing a random walk on the product graph G × is equivalent to performing a simultaneous random walk on the graphs G and G [4].

[1] count the number of nodes in the random walk which have the same label.


Section 4 shows that the jointree approach is a special case of the arithmetic-circuit approach, and discusses some practical implications of this finding.

finally, it multiplies the computed message into the table of cluster j: Φ j = Φ j M ij .


Direct optimization is combinatorial because of what we call the global zero attraction property: Whenever any individual coefficient x i goes to zero, we are necessarily at a local minimum with respect to this coefficient because of the infinite slope (discontinuity) of the ℓ 0 norm at zero.

this bound holds for all v with equality when v = x.


Their estimators are sub-optimal even assuming X is Gaussian.

throughout the experiment we vary n and fix d = 500 and s ⇤ = 5.


We then show an equivalence between low-density rejection and a constrained two-class classification problem where the other class is the uniform distribution over Ω.

we introduce an additional variable, z, to represent the max-min rejection rate.


frame-synchronous processing, because the sequence lengths, |X| and |V |, should be known beforehand.

the linear time-warping function takes the form as where x is the ceiling function which gives the smallest integer that is greater than or equal to x.


These overestimations result from a positive bias that is introduced because Q-learning uses the maximum action value as an approximation for the maximum expected action value.

the use of the technique of optimism in the face of uncertainty can be thought of as an orthogonal concept to the over-and underestimation that is the topic of this paper.


theorem 2 Assume that updates are performed with a delay bounded by τ , also assume that we apply a random skip filter on pushing gradients and a significantly-modified filter on pulling weights with threshold O(t −1 ).


Rather, we consider a step of the form ¡ ¢ where ¡ £¢ # ¢ ¢ H . It is easy to see that the first order theory of gradient boosting and the line search solution apply to this formulation as well.

our implementation of the boosting algorithm, therefore, does indeed limit to include probability distributions only, in this case those that can be represented by "simple" Bayesian networks.


These representations show promising results for learning a mapping between visual data [22] the same way that it was shown for text [23].

we did not pose any restriction about the view-point of the objects.


We define the regret incurred by a reinforcement learning algorithm π up to time T to be where ∆ k denotes regret over the kth episode, defined with respect to the MDP M * by .

we demonstrate through a computational study in Section 6 that PSRL outperforms the optimistic algorithm UCRL2 [4]: a competitor with similar regret bounds over some example MDPs.


For each value of p and sparsity level of Ω, n = 1.2p and n = 0.2p were tested, to represent both the n < p and n > p cases.

the existence of such constants follows directly from Theorem 1, as Θ t lie in the bounded domain {Θ ∈ S p ++ : f (Θ) + g(Θ) < f (Θ 0 ) + g(Θ 0 )}, for all t. it is possible to specify the constants a and b to yield an explicit rate; this is done in Theorem 2.


Various propositions were made to implement the model but only the simplest ones were tested in this paper.

multimodal information processing is currently a very challenging framework of applications including multimodal person authentication, multimodal speech recognition, multimodal event analyzers, etc.


We introduced the modular gated recurrent unit, a modified GRU that enables minimalistic sequence-to-sequence models based on modular computation.

we then apply our modular networks to language modeling and image classification.


Clearly this permanently assigning blocks to agents avoids these issues.

in this part, we present convergence results for the bounded delays.


Denoting by exp q : T q N → N the exponential map at q, the simple gradient descent based optimization scheme can be written as • choose a random point q 0 from N , • while stopping criteria not fulfilled, 1. compute gradient ∇F at q k 2. one has: q k+1 = exp q k − α∇F | q k 3. determine stepsize α by Armijo rule [19].

the discussion of a robust median-type estimator, that is Γ(x) = x, has been done recently in [8].


It is well-known that minimizing the 1 norm can lead to sparse solutions [52].

to evaluate the accuracy of the output h (T ) , we compute C f Rh (T ) with the true f , and declare successful recovery if , e j > 0.95.


Since the mean absolute error (MAE) is commonly used in this setting, we choose to work with the A-optimality criterion.

when α < 1, f is said to be approximately supermodular.


For a problem TI, its p,-relaxation refers to the problem obtained by considering the margin value P,n for inputs of dimension n. A main tool for proving hardness is the notion of p-Iegal input instances.

the following definitions focus on separation problems, but extend to densest set problems in the obvious way.


Let Gaussian with mean µ t and variance σ 2 t . Assume that the noise is also Gaussian with variance σ 2 , so F (x) = Φ( x σ ).

forcing the MM to maintain a Gaussian belief over the true value at each time t should give a good approximation to the true state space evolution, and the resulting optimal actions should closely match the true optimal actions.


It may happen because punctuation marks are significantly smaller than characters.

the IAM database [29] is made of handwritten English texts copied from the LOB corpus.


This variational family is indexed by parameters η, which are fit to minimize the KL divergence between the variational and true posteriors.

in the 111th House, the per-lawmaker improvement Imp u = D (J ud − I ud ) was invariably positive or negligible, because each lawmaker has many more parameters in the issue-adjusted model.


This three-stage approach is similar to the one used in [7] to learn trees over words.

8, the maximum is achieved at where N i is the number of times item i occurs in the training set.


Similarly, temporal receptive fields were chosen randomly from functions bandlimited to 4 kHz.

several examples include conductance-based models such as Hodgkin-Huxley, Morris-Lecar, Fitzhugh-Nagumo, Wang-Buzsaki, Hindmarsh-Rose [20] as well as simpler models such as the ideal and leaky integrate-and-fire (IAF) neurons [15].


Other invariant kernels have been proposed: In [19] authors introduce transformation invariant kernels, but unlike our general setting, the analysis is concerned with dilation invariance.

tIDIGITS (Figure 3): We use a subset of TIDIGITS consisting of 326 speakers (men, women, children) reading the digits 0-9 in isolation, and so each datapoint is a waveform of a single word.


Kernel methods provide a principled framework for nonlinear data modeling, where the inference in the input space can be transferred intactly to any feature space by simply treating the associated kernel as inner products, or more generally, as nonlinear mappings on the data (Schölkopf & Smola, 2002).

for instance, in cases where only inner products of the input data are involved, kernel learning is equivalent to the learning of a kernel matrix.


New algorithms are described for dealing with pattern recognition problems with very different pattern distributions and dealing with unlabeled data.

in general, one can construct the VRM functional using any estimate dPest (x, y) of the density dP(x, y) , instead of restricting our choices to pointwise kernel estimates.


The main question we sought to answer with this study is whether mathematical decoding algorithms that can make use of the temporal evolution of movement parameters, that can incorporate uncertainty, and that can also incorporate prior knowledge, would provide improved decoding results compared to an existing algorithm that utilized only the instantaneous relationship.

the duration of certain movement patterns will deviate from the distribution described by Equation 1.


Then, SGD is both β Z -uniformly stable and β Z -pointwise hypothesis stable with respect to L and P, with When T = Θ(n), Equation 1 is Õ(n −1 ), which is acceptable for proving generalization.

in certain situations, it may be advantageous to sample according to a data-dependent distribution.


handling spatial transformations explicitly using data-augmentation or a special network structure have been shown to be more successful in many tasks [13,15,16,17].


Applying Lemma 3.1 and Theorem 3.1 in (11), one obtains an upper bound for KL divergence, In the problem of minimizing the KL divergence g(µ, CC T ), one needs to iteratively update µ and C, since they are coupled.

we derive an upper bound for the Kullback-Leibler divergence, which yields a fast closed-form solution via decoupled optimization.


We derive a block coordinate descent algorithm for optimizing our bound over both the cost-shifting parameters (reparameterization) and weights (fractional counting numbers), which generalizes dual decomposition and enjoy similar monotonic convergence property.

we can apply power sums with different weights τ i to each variable x i along a predefined elimination order (e.g., [x 1 , .


Much of the utility, however, in using sequential sampling models to understand decision-making, and their application to practical problems [10], requires making inferences about variations in parameters across subjects, stimuli, or experimental conditions.

we thank Jeff Rouder for supplying the benchmark data, and Scott Brown, E.-J.


If P = {1, 2} and u 1 = −u 2 , the game is two-player zero-sum.

in this paper we introduced a new method of pruning that allows CFR to avoid traversing highregret actions in every iteration.


To address this issue, numerous machine learning methods have been developed to deal with each of the previous specific situations.

in the following section, we propose a generalization of the empirical surrogate risk, called the empirical surrogate β−risk, which can be employed in the context of weakly labeled data instead of the standard one under some linear conditions on the margin.


Our objective is to find the set of voxel time courses S defined as where S * denotes a subset of the entire collection of voxels time courses S extracted from a single fMRI scan.

in most of these approaches, a classifier is trained directly on the fMRI data to discriminate between known different brain states.


Instead of performing any single domain-specific task such as clustering or estimating an expectation, we can simply compute the barycenter of the inputs and process it later any arbitrary way.

full experiment details are given in Appendix D. As the input distributions are moved along parallel paths on the sphere, the barycenter accurately tracks the new locations as shown in the final three figures.


The probability that a field moves from state x i to state x i + 1 with d i = 1 is set to be , where ε and p are parameters and n i is the number of the neighbors of i that are infected.

our first topology type are random, regular graphs with three neighbors per node.


We would like to guarantee, with probability 1 p for a small p > 0, that the confidence interval around this estimate contains the value x > w ⇤ given by the optimal w ⇤ 2 W. To estimate such an interval without parametric assumptions, we use Chebyshev's inequality which-unlike other concentration inequalities like Hoeffding or Bernstein-does not require independent samples.

for covariance, because the covariance of the weights is The goal for computing variances is to use a concentration inequality.


This assumption about the auxiliary process {W t } is the same as our Bootstrap assumption.


Dual smoothing (dual-smooth): Instead of the primal, the dual (6) may be smoothed, e.g., by entropy [8,38] applied to each g j as gε j (λ j ) = min x∈[0,1] n f j (x) + εh(x) where h(x) is a negative entropy.

as we will see, its convergence is so slow to counteract any benefit that may arise from not using projections.


Note that when α ≤ 1, the most expensive edge cost is bounded by 2a √ n, where a is the edge cost constant.

in this section we briefly describe dynamical simulations on a 100 × 100 grid (which has 10 8 possible edges).


Finite differencing, where the perturbation directions d are the n standard basis vectors, is a default approach for Jacobian estimation.

• Optimize: Solving a compressed convex optimization problem to minimize (or find a feasible) l p reconstruction.


The value of executing o upon entering state s is given by: Q U and U both depend on θ and φ , but are omitted from the notation for clarity.

actually learning a deep hierarchy of options end to end has received surprisingly little attention to date.


Unlike A* search with an inflated heuristic, each search iteration in ARA* is guaranteed not to expand states more than once.

the OPEN list can be viewed as a set of states from which we need to propagate local inconsistency.


Given z i t−1,P and β i t , the transition to z i t,P is deterministic with linear combination: z i t,P = f (z i t−1,P , β i t ).

finally, we show how we learn the DDPAE by optimizing the evidence lower bound in Section 3.3.


Conversely, excitable neurons (such as those with low thresholds) spike early in the theta cycle.

place cells employ a phase code: the timing at which a neuron spikes relative to the phase of the inhibitory theta rhythm (5-12Hz) conveys information.


l), the independence is guaranteed also for whole column vectors of u.

the top row shows the row vectors of n sorted by the logarithm of their norm.


We hope to explore many promising applications of these ideas in the future.

lWTA may be a step forward towards models that do not forget easily.


This is known as the source recovery problem.

before proceeding, we should clarify the notion of fixed point convergence in Algorithm 1.


2 We now present a simple poisoning attack on transfer learned networks.

the first dimension is along the vector joining the centroids of the base and target classes (u = µ base − µ target ), while the second dimension is along the vector orthogonal to u and in the plane spanned by u and θ (the weight vector of the penultimate layer, i.e.


There remain several limitations to our framework that we would like address in the future.

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


2 Lepski's procedure for estimating the Laplace-Beltrami operator All the Riemannian manifolds considered in the paper are smooth compact d-dimensional submanifolds (without boundary) of R m endowed with the Riemannian metric induced by the Euclidean structure of R m . Recall that, given a compact d-dimensional smooth Riemannian manifold M with volume measure µ, its Laplace-Beltrami operator is the linear operator ∆ defined on the space of smooth functions on M as ∆(f ) = − div(∇f ) where ∇f is the gradient vector field and div the divergence operator.

cross validation [AC + 10] is the standard approach for tuning parameters in statistics and machine learning.


It is also possible to include various side constraints: soft constraints can be applied by penalizing the rewards, or hard constraints such as time windows can be enforced through a masking scheme.

next, we introduce our model, which is a simplified version of the Pointer Network.


Note that for a sequence-to-sequence model, there can be four variants to handle different input-output formats.

in the following, we call the node being expanded the expanding node.


The key intuition is that we stack L GNN modules and learn to assign nodes to clusters at layer l in an end-to-end fashion, using embeddings generated from a GNN at layer l − 1.

this research has been supported in part by DARPA SIMPLEX, Stanford Data Science Initiative, Huawei, JD and Chan Zuckerberg Biohub.


The proof of Theorem 3 is based on the following lemma, which is at the base of all PAC-Bayesian theorems.

the PAC-Bayes-Bernstein inequality is expressed in terms of the true expected variance, which is rarely accessible in practice.


In addition, the obtained estimator attains the optimal statistical properties in parameter estimation: Recall that b ✓ {1} is obtained by the warm initialization (3).

moreover, for some constant M > 0, at least one of the following two conditions holds: (I) The Hessian of the cumulant function is uniformly bounded: Then Assumption 1 ⇠ 3 hold with high probability.


Then F 1 (y, ȳ) = 2 2+t1+t2 , and So we can pick ȳ as ( ) which only misclassifies x k+1 , and get which can be verified by ∂J k+1 (w k+1 ) = w k+1 + k+1 i=1 α i a i : α ∈ ∆ k+1 0 (just set all as claimed in Theorem 6.

it is usually much harder to establish SLB than WLB.


Compared to handcrafted methods [25,17,36,7], most CNN-based methods have better performance.

to deal with geometric variations within CNNs, STNs [15] offer a way to provide geometric invariance by warping features through a global transformation.


In this work we take an alternative approach based on an information theoretic formulation of the problem of sharing and hiding intentions.

in many scenarios, it might be worthwhile for an agent to give up some reward if it means large gains in the ability to hide or share information.


We also refer to the output p t = f t (b 0∶t−1 ) as the strategy of the player at time t. Now that we can refer to algorithms simply as functions (or distributions over functions), we introduce the notion of a stable algorithm.

if the algorithms played by player 1 in the form of f t and player 2 in the form of g t give sub-linear policy regret sequences, then the sequence of product distributions converges weakly to the set S. In particular if both players are playing MWU or Exp3, we know that they will have sublinear policy regret.


As mentioned in the introduction, the sample complexity of margin-error minimization can be upperbounded in terms of the average norm Alternatively, we can rely only on the dimensionality and conclude m(ǫ, γ, D) ≤ Õ(d/ǫ 2 ) [7].

our tight characterization, and in particular the distribution-specific lower bound on the sample complexity that we establish, can be used to compare large-margin (L 2 regularized) learning to other learning rules.


We now replace each occurence of Pu-+ c in P(d) by 1 -LaEA\{ c }Pu-+ a .

a more flexible approach would be to consider different length subsequences as features, depending on their frequency.


In our case B is a block-diagonal matrix (not a fully-dense Gaussian matrix), and the SD only provides an estimate of the PTC.

in our case the calcium signal is sparse in the non-orthogonal basis described by the matrix G from (4).


Let B be a K × K matrix where B ab ≥ 0 for all a, b.

[12]) removes the ancillary effects of heterogeneous degrees under the DC-SBM.


we note that any bounded function is sub-Gaussian.


One could argue that object segmentation masks can be obtained by a stand alone segmenter like Mask-RCNN [8] and just in-paint this masked region to achieve removal.

our model learns to find and remove objects from general scene images using image-level labels and unpaired data in a generative adversarial network (GAN) framework.


The reason for this, theoretically, is that the sample complexity of MOD-SULQ scales with d 3/2 p log d whereas PPCA scales with d. Because PPCA uses the exponential mechanism with q F (•) as the utility function, it is not surprising that it performs well.

our theoretical results apply to the special case k = 1.


Theorem 7 essentially implies that by exploiting the multi-stage convex relaxation framework, our proposed DC proximal Newton algorithm gradually reduces the estimation bias for "strong" signals, and eventually obtains an estimator with better statistical properties than the `1-regularized estimator.

we terminate the iterations when the following approximate KKT condition holds: where " is a predefined precision parameter.


The loss function is defined as: where [Pred(x 0 + δ)] i is the i-th class prediction score of x 0 + δ.

our explanation for the digit in row 1 of Figure 1 to be a 3 would be: The row 1 digit is a 3 because the cyan pixels (shown in column 2) are present and the pink pixels (shown in column 3) are absent.


At each iteration, we get a new draw corresponding to the draw of T j and M j .

we run one long chain rather than multiple starts.


Only recently, similar results are starting to be proved for realistic neural network models .

to examine this prediction of ultra slow diffusion and find the value of α, in Figure 2a, we examine w t − w 0 during the initial training phase over the experiment shown in Figure 1.


Altogether, these results suggest that several observed features of cortical dynamics, such as excitatory-inhibitory balance, integrate-and-fire dynamics and Hebbian plasticity, are signatures of a robust, optimal spike-based code.

we set L V = V 2 /2, and calculate the gradient: We can simplify this equation considerably by observing that the contribution of the second summation is largely averaged out under a wide variety of realistic conditions 4 .


We can now state the definition of the lower envelope for the CMH minimum attainable p-value: Definition 1 Let S ∈ I P P be a potentially prunable feature subset.

analogously, we consider as potentially prunable the set of feature subsets I P P = {S | x S,j ≤ min(n 1,j , n 2,j ) ∀ j = 1, . . . , k}.


. . , x d+1 ), so the Bayes classifier predicts 0 for all x in the simplex.

first, the nearest neighbor rule (also called 1-nearest neighbor, in the context of the general family of k-nearest neighbor rules) is a well-known interpolating classification method, though it is not generally consistent for classification (and is not useful for regression when there is significant amount of label noise).


The smallest bounding box of X is defined as B (X) := B (a, b) where the lower bound a is given by the pointwise infimum of X and the upper bound b is given by the pointwise supremum of X, that is a α := inf{x α : x ∈ X} and b α := sup{x α : x ∈ X} for all α = 1, . . . , d. Note that B (X) = B (conv (X)).

lemma 2 Let (A t ) t=1,...,T be disjoint subsets of V. For each t = 1, . . . , T , let Ξ t ⊆ M At be convex with a finite number of extreme points.


The present paper is related to a recent publication targeted at a neuroscience audience [14].

generating a corrective control signal can be detrimental, because: 1) the noise in the motor system is known to be multiplicative [13] and therefore could increase; 2) the cost being minimized most likely includes a control-dependent effort penalty which could also increase.


Given an input vector of dimension d, we consider a neural network with L layers of neurons for binary classification.

(iii) Similar to Corollary 1, we will present the following corollary to show that at every local minimum θ * = (θ * , θ * exp ), the neural network f with augmented exponential neurons is equivalent to the original neural network f . Corollary 2 Under the conditions in Theorem 2, if θ * = (θ * , θ * exp ) is a local minimum of the empirical loss function Ln ( θ), then two neural networks f (•; θ * ) and f (•; θ * ) are equivalent, i.e., f (x; θ * ) = f (x; θ * ), ∀x ∈ R d . Corollary 2 further shows that even if we add an exponential neuron to each layer of the original network f , at every local minimum of the empirical loss, all exponential neurons are inactive.


In such situations, we believe that the only avenue is an unsupervised method.

these quantities are instrumental to both human detection and the pose classification problem.


We give three such examples, described briefly below.

we claim that Φ(∅) can always be achieved by an adversary for any algorithm w (•).


The learner's objective is to maximize cumulative reward, which is equivalent to minimizing regret: the extra reward a learner would have received by always choosing the best available action.

a randomized algorithm A for the contextual bandit problem is (ε, δ)-jointly differentially private (JDP) under continual observation if for any t and any pair of t-neighboring sequences S and S , and any subset S >t ⊂ D t+1 × D t+2 × • • • × D n of sequence of actions ranging from day t + 1 to the end of the sequence, it holds that P(A(S) ∈ S >t ) ≤ e ε P(A(S ) ∈ S >t ) + δ.


One type determines global stability and the other type determines whether or not multistability is possible.

there exists an input b such that there is more than one stable steady state.


It has been shown that mixture of trees admit a decomposable prior [20].

although the structure of the trees for a particular character are similar, they vary considerably in the parameters.


Even when blocks have balanced difficulty, and the computing nodes have equal computing power, this dependence persists.

indeed this turns out to be the case in practice.


In the proposed approach, model contours 2 and 3 in Fig.

a more powerful class of MCMC methods could also be used [7].


This implies that Next we present our key result, Theorem 4.5, which can be viewed as a 'Neyman-Pearson lemma' for binomial data under ( , 0)-DP.

for this reason, it is natural to consider a test which post-processes X + L. we know by classical UMP theory that since X + L is discrete, a randomized test is required.


By comparing the plots for AD and NC, we can observe the following two distinct phenomena: First, in AD, between-lobe connectivity tends to be weaker than within-lobe connectivity.

various algorithms for achieving SICE have been developed in recent year [ 17]- [22].


Next we used the d561102 data from hc-1, which consists of 4 extracellular recording and 1 intracellular recording.

we used 5000 burn-in samples and 5000 collection samples in the Gibbs sampler, and we choose the collection sample with the maximum likelihood when presenting below example clusterings.


The proposed algorithms address the two limitations explicitly.

in this case, ∇g(X) only requires computing the minimum eigenvector of a matrix, which is cheaper than a full eigenspectrum computation required at each iteration of the standard SGD algorithm to restore feasibility.


Unlike C s , the covariance C sf is no longer diagonal.

these independent priors neglect a statistical feature of many real-world regression problems, which is that non-zero weights tend to arise in clusters, and are therefore not independent a priori.


We next show that a model of the TE system can make predictions for all tests t ∈ T in all histories of interest h ∈ H I .

[1]), though these ideas have been applied in dynamical settings as well (e.g.


The resulting equations are more concise, but harder to read.

they are easier to analyze and compare to polynomial kernels.


A naive approach towards approximating D would be to just pick a subset C uniformly at random.

in order to construct a coreset for the union of two (weighted) coresets, we use a weighted version of Algorithm 1, where we consider a weighted point as duplicate copies of a non-weighted point (possibly with fractional weight).


For a document d we denote by z d ∈ {1, . . . , k} the tier storing d. Define as the number of cache levels we need to traverse to answer query q.

figure 2: Left: maximum flow problem for a problem of 4 pages and 3 queries.


cannot be compactly described by piecewise linear functions or other "simple" local representations).


( 2) Histograms: sums of the intensities in random image patches, histograms of (oriented and non oriented) gradients at different locations, Haar-like features.

at every Boosting step, our first algorithm MAS Naive models G q with a Gaussian mixture model fitted on the edges estimated at the previous iteration, computes from that density model the pair (Q, T ) maximizing e(Q, T ), samples the corresponding number of examples and features, and keeps the weak-learner with the highest approximated edge.


some important caveats -and directions for necessary future work -should be emphasized.


Let Z u be an N u ×K feature-assignment matrix for pseudo-images only; then the number of pseudoimages, N u , determines the influence of relevance feedback.

kumar and Udupa presented a cross-view similarity search [10] by generalizing spectral hashing [1] for multi-view data objects.


For an RKHS based on a Gaussian kernel, the entropy condition (10) holds for any γ > 0 [23].

lemma 3. min w J has the following dual form: Proof.


Finally, note that the cluster assumption might also be useful in a purely supervised learning task.

to make use of unlabeled data, one needs to formulate assumptions.


In this paper, we consider collaborative filtering as a ranking problem.

we present the first effort to optimize this measure for collaborative filtering.


K(x l , •) in the RKHS, and is therefore a negative number.

the set S defines the support of the classifier, namely, the set of examples that actively participate in the classifier's definition.


CoR-3 improves the overall accuracy of the state-of-the-art Dual-MFA from 66.49% to 69.38%.

reasoning plays an essential role in Visual Question Answering (VQA).


The range of α for which this bound results in a reduction in effective sample size beyond the trivial reduction to αn depends on Vol(Z).

the loss function is , and thus only depends on θ.


Obviously, for all exact k-NN algorithms, E = 0, for all approximate algorithms, E ≥ 0.

it takes O(n 2 ) time to find the optimal v.lpv and v.rpv.


For a cleaner presentation, we assume that all the mixture weights are 1/k, but our results hold with general weights as long as an appropriate center separation condition is satisfied.

the streaming Lloyd's method is agnostic to the data distribution and can in fact be applied to any mixture of sub-Gaussians problem.


The generative adversarial network (GAN) [3] employs a generative model in which the code is drawn from a simple distribution (e.g., isotropic Gaussian), and then the code is fed through a sophisticated deep neural network (decoder) to manifest the data.

vAEs [12,13] represent one of the most successful deep generative models developed recently.


We evaluate scaling with problem dimensionality by running the various solvers on problems of different dimensionalities and computing various metrics on the solver runs as described below for each experiment.

it is more scalable and provides the ability to trade off computation for more approximate solutions.


Note that the IC oracle never generalizes beyond the level from which the examples are drawn, and thus, exhibits very different generalization results compared to the human participants in our experiment.

as no existing challenge data tests this paradigm, we collect and make available a new, large-scale dataset for visual concept learning using the ImageNet hierarchy as the source of possible concepts, with human annotators to provide ground truth labels as to whether a new image is an instance of each concept using a paradigm similar to that used in experiments studying word learning in children.


x * in Proposition 11 can be chosen to be a local minimum.

given a real-valued continuous function h on X × Y , define the point-to-set map Ψ : X → P(Y ) by Then, Ψ is closed at x if Ψ(x) is nonempty.


We can use our algorithm for estimating ρ(f, x * ) to compute adversarial examples.

the algorithm in [21] can also be used to approximate ρ(f, x * ); we show experimentally that our algorithm is substantially more accurate than [21].


Finally, we like to mention that, if the conditional distributions are not equal modulo translations, then the situation may become more involved.

in order to prove the remaining assertions it suffices to show that lim t→±∞ C L ,P( • |x) (t) = ∞ for P X -almost all x ∈ X.


Our work is organized in the following manner: we describe in Section 1 the problem of bandit optimization.

we also emphasize the fact that the dependency in √ K is expected, and optimal, in bandit setting.


In this paper, we study how pre-trained sentence representations, obtained by general purpose sentence encoders, can be leveraged to train better models for text generation.

in both these sets of experiments, we use a conditional GAN with our generators and discriminators as MLPs that use conditioning information in their input layers.