Then, up to first order, matrix Then, to the extent that the above approximation holds, we can write: 5 Now, y t v k−1 x t is the margin of the (first-order) Perceptron vector v k−1 over a mistaken trial for the Higher-order Perceptron vector w k−1 .

the same analysis also suggests a simple (but principled) way of switching on the fly between higher-order and first-order updates.


We replaced the exact Group Lasso optimization problem by a smooth dual forward-backward algorithm with Bregman distances.

we also denote by argmin h the set of minimizers of h or the minimizer of h when it is unique.


The above result clearly implies that for a probability measure ν on K, TV(δ 0 P t , νP t ) ≤ .

itô's formula then gives , ν t ≥ 0 on the support of L, and ∇g(X t − X t ), ν t ≤ 0 on the support of L . Moreover ∇ 2 g(X t − X t ) = 1 |Xt−Yt| P (Xt−Yt) ⊥ where P x ⊥ denotes the orthogonal projection on x ⊥ .


As in the language recognition task, we used EER as the performance measure.

quantitatively, we show that the method produces keywords which are good discriminators between classes.


It depends very much on the form of f and ∆ which choice of Γ is easier to handle.

as our loss function, we used ∆(y, y ) = 1 − recall (where recall is the proportion of base-pairs in the reference structure y that are recovered in the predicted structure y ).


Expectation Propagation (EP) is a popular approximate posterior inference algorithm that often provides a fast and accurate alternative to sampling-based methods.

the error measure that we optimize is the average KL divergence We differentiate this objective analytically for the appropriate output distribution type and compute gradients via back-propagation.


This is related to the previous question.

if η is chosen so that normalizers are penalized for distance from log µ(Y) (e.g.


On high dimensional data, subspace structures are usually designed in statistical models with reduced numbers of free parameters, leading to improvement on both learning efficiency and accuracy [3,11,24].

the capacity control is essential to generalization ability, for which we proceed to deliver a variational Bayesian inference on PCSA.


We argued that not only the search space of the loss function among neural networks can easily be nearly convex, but also regularizers, such as dropout, make the search space smooth, and the point in the search space have good accuracy.

in the untuned hyperparameter setting, mean-IMM performs worse when more transfer techniques are applied.


If an attacker can associate a pseudonym with a human identity, the attacker may learn the user's transaction history.

that satisfies is a constant that depends only on degree d, and I 1/2 (a, b) is the regularized incomplete Beta function, i.e., the probability a Beta random variable with parameters a and b takes a value in [0, 1 2 ).


One preferred interpretation for a T-junction is occlusion (6b).


Viewing n as an asymptotic parameter and γ as a fixed constant, we have  1)) , which holds for 0 < α < 1 2 , we see that any setting of γ such that α is bounded above zero by a constant gives an exponential gap between the error rate of PickyAdaBoost (which is (1/2−γ) n ) and the lower bound on AdaBoost's error provided by (7).

to simplify the exposition, we have assumed that POPBM can exactly determine quantities such as Z t and the accuracies of the weak hypotheses.


The GT model is an enhancement of the stochastic Blockstructures model [7]  the extended model of Kemp et al.

unlike [3], since our goal is to cluster entities based on the similarity of their voting patterns, we are only interested in whether a pair of entities voted the same or differently, not their actual yes/no votes.


This is specifically of great interest for the neurodegenerative disease diagnosis, where the features from different regions of the brain are extracted, but not all the regions are associated with a certain disease.

in the training stage, they denoise the feature values using a strategy similar to robust principle component analysis (RPCA) [7] and build the above LS-LDA model using the de-noised data.


The data basis contained in total 14 signals, with a length of 8000 time points each.

many applications like the modeling of acoustic signals, EMG signals, or movement trajectories, require temporal shift-invariance of the extracted components.


The task of selecting the "best" feature subset, known as feature selection (FS), is therefore an important task.

several issues require further work: weakly relevant features (in the sense of [12]) are not removed by the first algorithm while the second approach relies on a good initial clustering.


For most of the categories the modes found by our algorithm were indeed verified by a human observer as representing a true mode in view space.

if we have an image descriptor so that the distance between descriptors for two images approximates the similarity of views between the objects, we can calculate the Parzen density without ever computing the views.


Barry and Hartigan [10,11] used product partition models as distributions over possible segmentations of time-series data.

it seems that each learner reaches the boundary of its favored range of reactivity or stability when further changes in that direction cause it to either be so reactive that it often assigns relatively high probability of drift to many time steps for which there was no drift, or so stable that it cannot react to actual drift.


In contrast to previous work, we provide guarantees on the quality of the approximation as n increases.

we define the n-inverse covering radius of compact K ⇢ X as the value ✏ n (K) = inf{✏ > 0 : N ✏ (K)  n}, when n is large enough so the infimum exists.


1 also indicates that, as the feature dimension (and the number of nodes in each level) increases, MLFre identifies more inactive nodes, i.e., 3 i=1 r i ≈ 100%.

to the best of our knowledge, MLFre is the first screening method that is applicable to TGL.


For example, in a street scene, a car may be adjacent to regions belonging to a number of objects, such as building, person, road, etc.

the extent is over adjacent horizontal and vertical neighbors.


Moreover, the arithmetic circuit is decomposable and deterministic.

definition 2 (Arithmetic Circuit) An arithmetic circuit AC(X) over variables X is a rooted DAG whose internal nodes are labeled with + or ⇤ and whose leaf nodes are labeled with either indicator variables x or non-negative parameters ✓.


Section 6 presents experimental results on a challenging benchmark dataset.

it is not plausible to learn a huge number of parameters in deep networks reliably in this scenario.


Even if d is very large, the kernel can be a good choice if each training instance contains only a few non-zero elements.

when m = 2, this is the same cost as the SG algorithm implemented in libfm.


Each of these networks is formed by taking the largest connected component in the social circle of a specific user.

as a second example, random walk-based graph embeddings (e.g.


Theorem 3 Suppose that A is generated by a Gaussian distribution, x 0 is i.i.d.

for this, we require strong convexity and bounded third derivatives.


Basically, if the parameter ✓ could be included into the grid ⇥ 0 , Theorem 2.1 would turn into a bound on the regret R T (✓) with respect to ✓.

in the adversarial setting, we develop an algorithm BOA+ whose cumulative excess risks is controlled by several bounds with different trade-offs between sparsity and rate for strongly convex loss functions.


There exists a PTAS for the offline K-MAX problem.

although it bears conceptual similarities with stochastic CMAB, the techniques used are different.


In general, good targets are those that minimize the loss computed in the output layer if they had been realized in feedforward propagation.

for additional details see Tables 3 and 4 in the Appendix.


The work of Manilla & Meek (2000) considers the problem of learning the structures and estimating the parameters of mixtures of these series-parallel RIM models using a local greedy search over recursive partitions of elements.

while our experiments had at most n = 33 this was not due to the running time of the algorithms.


Within the first 3 4 N updates, with high probability they will all update correctly as argued above.

in large part this is because the effectiveness of active learning is known to quickly degrade as noise rates become high [5].


. . , a m ) , diag(a) represents the m×m diagonal matrix with a 1 , .

we relax EΘ in (1) as a sample scoring matrix Y and define the following penalized model: under the constraints The following theorem provides a solution for this problem.


The general experiment settings are as follows.

suppose y λ / ∈ F , i.e., λ ∈ (0, λ max ).


The reducibility of MaxEnDNet to M 3 N renders many existing convex optimization algorithms developed for learning M 3 N directly applicable as subroutines for learning our proposed model.

we can apply the same convex optimization techniques as being used for solving the problem P1.


We conclude by noting that while the transition point from the early stage to the late stage for Q-ThS is near optimal in the heavily loaded regime, it does not yield optimal regret performance in the early stage in general.

after a critical point when the algorithm has learned the system parameters well enough to stabilize the queue, the queue-length goes through regenerative cycles as the queue become empty.


For any u × v matrix M we note M i,j its (i, j)-th entry.

none of these methods is applicable directly to the p > 1 setting since they all rely on specific properties of the p = 1 case, such as the fact that the solution is piecewise-affine in λ and that the set of change-points is monotically decreasing with λ.


With this notation, we have by the triangle inequality and Jensen's inequality that The bound (7) shows that solving the empirical minimization problem to accuracy sufficient to have guarantees the same convergence rates provided by Theorem 1.

our second contribution is to develop a novel extension of simple averaging; it is based on an appropriate form of bootstrap [6,7], which we refer to bootstrap average mixture (BAVGM) approach.


[14] show how SINR-optimal demixing can be approximated with extra sensors when assuming a white additive noise, and Koldovskỳ and Tichavskỳ [16] discuss how to achieve asymptotically low bias ICA demixing assuming white noise within a fixed ICA model.

despite the significant work on noisy ICA algorithms, they remain less efficient, more specialized, or less practical than the most popular noise free ICA algorithms.


We also require a more restrictive condition -namely that D X can be rotated to a product distribution over the axes of R d . A distribution can always be rotated so that its coordinates are uncorrelated.

we present the γ-adapted-dimension k γ (D).


. . , w y sy ∈ R d . 6 Let s = � n y=1 s y , and let , where b yj is 1 if the j-th column of A came from {w y 1 , .

now Q 0-1 1 can be written as , where e n−1 , e n denote the (n − 1) × 1 and n × 1 all ones vectors, respectively, and I n−1 denotes the (n − 1) × (n − 1) identity matrix.


Following [6,2], we consider a space of input-output pairs (x, y) ∈ X × Y endowed with a probability distribution P (x, y).

when η = 1/λ max , this algorithm requires O(κ log(1/ρ)) iterations to reach accuracy ρ.


If the parameters k, ⌘, and are chosen such that 12k⌘d  then .

( 3), with the perturbation matrix A t set to (r 2 R(x t )) 1/2 , the root of the inverse Hessian of R at the point x t . the distribution of y t is supported on the Dikin ellipsoid centered at x t , scaled by .


In Lemma 1 it only requires for every w ∈ W there exists one w * that could be different for different w such that ( 5) and ( 6) hold.


To speed up convergence of SVM-Rank, we do not include rank constraints for memorability scores that lie within 0.001 of each other.

we can compute the expected distance E(D j |v j ) of an image as: This represents the expected number of modifications in v from 1 to 0 (α) or from 0 to 1 (β).


Now, it can be checked that for a, b ∈ A, we have L(V, a)/ L(V, b) = i∈{2,...,m} (p i /p 1 ) SC APP (b)−SC APP (a) .

but this low-cost, large-scale data may require compromising quality: the workers are often unqualified or unwilling to make an effort, leading to a high level of noise in their submitted labels.


The agent receives the reward X i,s when he pulls arm i for the s th time.

despite being in a Bayesian setting, it makes sense to view it as a learning problem and to evaluate the agent's performance through its Bayesian regret.


Let K be the final learned number of clusters on n data points.

we presented a new algorithm called PG-means for learning the number of Gaussian clusters k in data.


Despite the simple generation process, there exist strong nonlinearities in the resulting dataset because the moving digits can exhibit complicated appearance and will occlude and bounce during their movement.

for our spatiotemporal sequence forecasting problem, we use the structure shown in Fig.


Calculating a best response to a fixed strategy is computationally cheap (in games of perfect recall), costing only a single traversal of the game tree.

we could (in principle) store Player 2's strategy for each iteration between t+1 and t+1000, and on iteration t+1000 calculate a best response to each of them and announce that Player 1 played those best responses following action a on iterations t + 1 to t + 1000 (and update the regrets to match this).


31st Conference on Neural Information Processing Systems (NIPS 2017), Long Beach, CA, USA.

his bound depends on the nuclear norm of the underlying matrix which may be √ n times larger than our result.


We note that near optimality of our algorithm does not depend on convexity property, or tree-like structure as many of the previous works; but only relies on geometry of the graphical structure which is present in many graphical models of interest such as those arising in image processing, wireless networks, etc.

equivalently, from the optimization point of view, we wish to find an optimal assignment of the problem maximize H(x) where For completeness and simplicity of exposition, we assume that the function H is finite valued over Σ n . results of this paper extend for hard constrained problems such as the hardcore or independent set model.


In Section 3 we show that by making use of the "kernel trick" we are able to compute the sample covariance matrix in feature space in linear time in the number of samples.

we tested all three algorithms on a very simple generative model on 3 binary nodes, where nodes ¥ through 3 % ¥ point to node 3 .


a symmetric probability density p(x) ≡ exp(−g(x 2 )) can be represented in the convex variational form, ) is increasing and concave on (0, ∞).


This new type of cover is polynomial in the number of edges, yielding significant improvements in the bound.

we can then select the label arg max y P (y | x).


Their complexity bound is of the order of (1/ε) 2+log κ/(log(1/γ))+o (1) , where κ ∈ [0, KN ] is a problem-dependent quantity.


Instead of requiring relevance labels, we use the pseudoinverse estimator to convert page-level reward into per-slot reward components-the estimates of φ x (j, a)-and these become targets for regression.

both PI-OPT and SUP train gradient boosted regression trees (with 1000 trees, each with up to 70 leaves).


Making the story even more complicated, this taste-dependent rewarding value of food is demonstrated to be modulated by not only the approximated nutritional content of the food, but also the internal physiological state of the animal [16].

"Reinforcement learning" and "negative-feedback models of homeostatic regulation" are two control theory-based computational frameworks that have had major contributions in learning and motivation literatures in behavioral psychology, respectively.


Second, we provide a tighter upper bound of the Gibbs decoder distortion by randomizing the search space of the optimization problem.

moreover, prior generalization bounds have not focused on latent variables.


This control is provided by the following lemma.

we have yet to take full advantage of the superior mathematical structure afforded by the SD algorithm.


The updates described before using GMM, the Kullback-Leibler divergence or the variance, all fit within the framework of empirical risk minimization, given by (6), which rewritten at the sample scale gives The proof follows from a standard approach from M -estimation theory [31, Theorem 5.7] but a particular attention shall be payed to the uniform law of large numbers because of the missing i.i.d.

the importance sampling estimate of ϕ based on the sampling policy q, is given by where (x 1 , .


little is known about the convergence rate of this procedure.


In many cases where we found that SBL was not locally minimized, we initialized the SBL algorithm in this location and observed whether or not it converged to the optimal solution.

it is in this respect that SBL approximates the minimization of the alternative objective posed by (14).


The only difference is that the statistics required for this M-step is computed approximately rather than exactly.

we randomly generated properly normalized transition and observation matrices and evidence given those matrices.


Together, the cross-amplitude and cross-phase spectra form the cross-spectrum, defined as the Fourier transform of the cross-covariance between the pair of channels.

the SM-LMC kernel encodes the cross-amplitude spectrum (square root of the cross power spectral density) between every pair of channels, but provides no crossphase information.


Suppose there is an oracle that can answer pair-wise queries of the form, "do u and v belong to the same cluster?".

we design novel algorithms that closely match this query complexity lower bound, even when the number of clusters is unknown.


This is ideal: our method is capable of near perfect recovery of the underlying social network over which a relatively small number of contagions diffused.

we consider a diffusion process where a contagion (e.g., disease, information, product adoption) spreads over the edges of the network, and all that we observe are the infection times of nodes, but not who infected whom i.e.


Knox and Stone [7,13] tried eight different strategies for combining feedback with an environmental reward signal and they found that  The parameters to each method were manually tuned before the experiments to maximize learning performance.

the reward function acts as a single source of information that tells an agent what is the best policy for this MDP.


Unfortunately, closing these gaps of Async-MSGD for highly complicated nonconvex problems (e.g., training large recommendation systems and deep neural networks) is generally infeasible due to current technical limit.

this suggests a clear tradeoff between the asynchrony and momentum.


On the other hand, if and ˜ are dependent, the expected value of on the boundaries of ˜ are not necessarily different.

as stated earlier, according to PIC, 2 C|; = 2 C is independent form ( E|C , 2 E|C ) = (a, 2 E ), while as we can see from the expressions in (2), such independence does not hold in general in the reverse direction.


However, marginalization of nuisance variables is potentially expensive and can mar the very sparsity of the graphical model that permitted efficient inference.

proposition 7 can be used at runtime to determine what percentage δ R ( Ā, R) of the optimal objective is guaranteed, for any focused selector, despite the lack of conditional independence of S conditioned on R. In order to compute the bound, a greedy heuristic running on a separate, surrogate problem with R as the relevant set is required.


To recover F (α) , we need to apply the power α/γ operation.

instead, they proposed to measure the entropy from a number of locations across the network, i.e., by examining the entropy of every OD flow in the network.


Our model builds upon the existing TCM model proposed by [5] where the EM algorithm is applied to learn a motif on a single target set.

other motif-finding algorithms such as MEME could not return the noncanonical motif enriched in a very small set of sequences.


In this area, most past work focuses on using exact (combinatorial) solvers to verify the robustness properties of networks, either via Satisfiability Modulo Theories (SMT) solvers [Huang et al., 2017, Ehlers, 2017, Carlini and Wagner, 2017 or integer programming approaches [Lomuscio and Maganti, 2017, Tjeng and Tedrake, 2017, Cheng et al., 2017.

due to the skip connections, the indicator functions are not independent, so we cannot directly conjugate each individual indicator function.


Minimality is natural with respect to our motivating applications-it is reasonable to assume that the measured nodes are non-redundant, in the sense that omitting a node from C would cause at least one edge to be lost from the measured communication pattern.

propositions 1 and 2 show that even if the planted cover is not minimal, we can still recover its nodes with such unions of minimal vertex covers.


The operation ∆F (x) + x is performed by a shortcut connection and an element-wise addition, while the residual function is parameterized by residual layers within each residual block.

these methods require target labeled data to learn the perturbation function, which cannot be applied to unsupervised domain adaptation where target domain has no labeled data.


It is in fact the same adaptiveness that leads to low regret that also leads to the strong revenue loss guarantees for adaptive learning algorithms.

advertiser 1 can increase its own utility by bidding some b 1 smaller than v 1 but still large enough to ensure that b 1 ρ 1 (b 1 ) still be ranked the highest at the end of the learning stage.


For example, it can happen that while projecting onto Gaussians negative covariance matrices appear.

also here it is not yet clear how to integrate IPF with convergent belief propagation without ending up with a triple-loop algorithm.


The Lasso algorithm [12] is commonly used to achieve L 1 regularization for linear regression.

if T is known in advance, one can select a constant η accordingly so the regret vanishes as T → ∞.


Our experiments illustrate the capability of our approach to recover a spread of policies in the spectrum from risk neutral to minmax requiring a running time that was on average about ten times the running of value iteration.

figure 3 shows the resulting policies and corresponding cost (travel time) histograms for one such randomly chosen route.


2 shows results for four representative conditions (see Appendix F for all results), while the middle and bottom rows aggregate across conditions.

the magnitude of each term of the outer summation is only O( m), whereas the IPS terms are m Ω( ) .


The images reconstructed by Bayesian CCA captured the essential features of the presented images (Figure 3 (a), 2nd row).

previous works have shown that image bases similar to receptive fields of simple cells are learned from natural scenes by the sparse coding algorithm [4,9].


By decomposing the model parameter of each task into a product of two components: the across-task feature indicator and task-specific parameters, and applying different regularizers to the two components, we can select features for individual tasks and also search for the shared features among tasks.

when many or all features are relevant to the given tasks, it may prefer the 2 norm penalty on c. only a limited number of features are shared between tasks, i.e., the features used by individual tasks are sparse with respect to the features selected as useful across tasks by c. We can impose the 1 norm penalty on β.


To examine if learning rate can be used to explain different types of learning behavior, we have simulated three types of behavior (No Learning, Expert and WSLS, Fig 1b ) in a low volatility condition.

to examine the underlying computational principles that guide different learning behavior in an uncertain environment, we compared an R-W model and a Bayesian approach in a visual search task with different volatility levels.


The discussion so far has been related to the characteristic property of k that makes γ k a metric on P. We have seen that this characteristic property is of prime importance both in distribution testing, and to ensure classifiability of dissimilar distributions in the RKHS.

if constant functions are included in H, then it is easy to show that the characteristic property of k is also sufficient to achieve the Bayes risk.


From [Berg et al., 1984] (Theorem 3.2.2, p.74), the Persistence Fisher kernel is positive definite.

tL acknowledges the support of JSPS KAKENHI Grant number 17K12745.


With mixed proportion φ , successes of arm 1 and failures of arm 2 are attributed to successes on the shared "hidden" arm 3, whereas failures of arm 1 and successes of arm 2 are attributed to failures of arm 3.

an agent learning a coupling parameter while sampling arms can manifest a range of exploratory behaviors that depend critically on both the recent reward history and the current state of the belief about c, illustrated in figure 3.


For example, a patient suffers from runny nose may also suffer from sore throat or headache.

here, we focus on the hierarchical model proposed in [3], which is the best prior work.


To derive an efficient algorithm making use of the structure incorporated in the constraints we follow [22] and change to the dual domain.

note that our approach can be run in parallel to achieve even faster convergence.


( 2) to impose additional low rank regularizations to exploit these task correlations.

besides imposing structured sparsity via tensor ℓ 2,1 -norm regularization for imaging marker selection, our new method also imposes two trace norm regularizations to capture the interrelationships among different cognitive measures over the temporal dimension.


Figure 1 (bottom) shows that only MC 3 can reproduce the distributional property of flight distance as a Lévy flight with estimated power-law exponent μ = 1.14.

there is as of yet no consensus on the exact nature of the algorithm used to sample from human mental representations.


Here, we wish to capture information about small objects or image regions that are identified by segmentation.

the result sc(S * ) is smaller than zero if S * scores worse than the average random summary and larger than one if it scores better than the average human summary.


Clearly, structured prediction failed to recover the underlying tree structure.

we encourage θ i• and θ •i to agree with their mean u i• , by introducing an additional term to the Lagrangian L where u i• is updated as an independent parameter.


We us the same training, validation and testing split as in [35].

for example, by constraining y 1 to {0, . . . , y 1,max /2} and {y 1,max /2 + 1, . . . , y 1,max } for Ŷ1 and Ŷ2 respectively, while keeping all the other intervals unchanged.


In this section, we show that the uncertainty set that we constructed is consistent.

the distributionally robust counterpart of ( 8) is of the form of ADRO (6).


In this literature, we have presented the divergences in the context of spike trains generated by neurons.

similar to (7), we find an upper bound and show that the bound uniformly converges to zero.


In past work, we modeled forced-choice tasks using a response pathway with only the alternatives under consideration.

of critical interest is the finding that a nonword prime formed by recombining two pleasant targets (e.g., HULIP from HUMOR and TULIP) or unpleasant targets (e.g., BIUT from BILE and SMUT) also served to bias the targets.


that characterize the set of selected relevant documents, and use these features in formulating a new query (e.g., [5,6]) .

to capture the ranking implied by the user selections, we define weights (distribution) {Bx}, L: XEX Bx = lover the underlying documents.


These images exhibit vulnerabilities at test time, whereas data poisoning is a vulnerability at training time.

we first two image datasets: MNIST-1-7, and Dogfish dataset used by Koh and Liang (2017).


The analysis is based on the assumption that the low frequency spectrum of voiced speech can be modeled as a sum of (noisy) sinusoids occurring at integer multiples of the fundamental frequency, f 0 .

the output of the filterbank will consist of a sinusoid at f 0 and three other signals that are random or periodic, but definitely not sinusoidal.


In this section we show the experimental results obtained when we applied the tools described in previous sections to the beef meat data base [8].

additionally, to gain insight into consumer preferences, we used feature subset selection tools.


In order to assess the encoding accuracy of a neural population, the stochasticity of the neural response is taken into account.

first we study the symmetrical case k = 1/2 the receptive fields of which are given in Fig.


The length and thickness of these shapes vary with the speed of the vehicle (see figure 1 for examples of these shapes).

ground truth matrices were provided for New College and City Centre.


Because of the harder noise model, they necessarily require multiple noisy copies per clean example and the unbiased estimation schemes also become fairly complicated.

the results for higher noise rates are impressive as observed from Figures 2(d) and 2(e).


One consequence of the lower bound (19) is the existence of extremely badly conditioned instances, say with  = (100d) 2 and K = 3/2, such that in the first d 1 iterations it is impossible to decrease the initial error by more than a factor of 2 (the initial error may be chosen arbitrarily large as well).

k. This means the "norm error" vanishes, while the "convex error" cannot increase too much, as A min z t ⇡ A min u min = 0.


This paper considers the problem of MV-set estimation using a training sample drawn from P , which in most practical settings is the only information one has about P . The specifications to the estimation process are the significance level α, the reference measure µ, and a collection of candidate sets G. All proofs, as well as additional results and discussion, may be found in [6] .

the sample size will grow no faster than a polynomial in 1/ and 1/δ, paralleling results for classification.


We measure the proximity of a covariate vector x i ∈ R V +1 to β k using the softplus function of their inner product as ln(1 + e β k xi ), which is a smoothed version of ReLU(β k x i ) = max(0, β k x i ) that is widely used in deep neural networks [14][15][16][17].

as x i moves away from hyperplane k, that proximity measure monotonically increases on one side of the hyperplane while decreasing on the other.


For each of the 1000 classes, we train a linear SVM using all examples of that class available in the ILSVRC2010 training set (this number varies from a minimum of 619 to a maximum of 3047, depending on the class) and 4995 negative examples obtained by sampling five images from each of the other classes.

as this procedure is performed identically for every image we consider, we will drop the dependence on I and simply refer to the "image" x.


The agent then observes its new state and chooses a new action.

alternatively, coarse-to-fine pruning [21], classifier-based pruning [23], [22] beam-width prediction [3], etc can result in even faster inference if a small amount of search error can be tolerated.


YKN acknowledges support from NRF/MSIT-2017R1E1A1A03070945, BK21Plus in Korea, MS from KAK-ENHI 17H01760 in Japan, KEK from IITP/MSIT 2017-0-01778 in Korea, FCP from BK21Plus, MITIP-10048320 in Korea, and DDL from the NSF, ONR, ARL, AFOSR, DOT, DARPA in US.

lLR asymptotically produces the bias of Eq.


The second assumption is that each document is represented solely by an unordered "bag of words".

the DCNT is a hierarchical, Bayesian nonparametric generalization of LDA.


To address the above-mentioned issue, we extend the Rademacher random variables to the complex domain and consider all roots of z m = 1, that is, Ω = {ω j } m−1 j=0 where ω j = e i 2πj m . Suppose σ(i) is a Rademacher random variable with Pr[σ(i) = ω i ] = 1/m.

for an n × n × n tensor T and a vector u ∈ R n , we define two forms of tensor products (contractions) as follows: Note that T(u, u, u) ∈ R and T(I, u, u) ∈ R n . For two complex tensors A, B of the same order and dimension, its inner product is defined as A, B := l A l B l , where l ranges over all tuples that index the tensors.


The auxiliary function is a useful concept because of the following lemma, which is also graphically illustrated in Fig.

rewritten in matrix form, this is equivalent to the update rule in Eq.


The authors also argued that the sharpness can be arbitrarily changed by reparametrization of the weights.

even though we show a very promising connection between large batch and robust training, but we emphasize that this is an analysis paper to understand the original problem.


On each round t, perform update:  where  0 is chosen so that w t is a valid probability distribution.

we propose a new bandit algorithm based on log-barrier regularization with importance sampling that guarantees fast convergence of O(d log T /✏) where d is the number of actions.


The choice between Primal and Dual ALM depends on the type of sparsity present in the LP.

the resulting algorithm is sketched in Algorithm 1.


The performance measures of choice in these situations are those that evaluate algorithms over the entire dataset in a holistic manner.

this can be advantageous in scenarios with a time budget in the training phase.


We have proposed a "rational process" model of perceptual multistability based on the idea that humans approximate the posterior distribution over the hidden causes of their visual input with a set of samples.

the visual system might be able to evaluate only relative probabilities of two similar hypotheses (as in Metropolis-Hastings), or to compute local conditional posteriors of one scene variable conditioned on its neighbors (as in Gibbs sampling).


Pseudo code for the algorithms (and for max-product) is given in Fig.

the updates in the algorithm and the analysis differ.


We can combine all the heads into a single ensemble policy, for example by choosing the action with the most votes across heads.

this is strange and we discuss this phenomenon in Appendix D. in light of this empirical observation for Atari, we chose p=1 to save on minibatch passes.


A Hilbert space F of functions from G x to G y is called a reproducing kernel Hilbert space if there is a positive definite , where * denotes the adjoint operator, ii.

an example of inputoutput signals are depicted in Figure 1.


In such a case, overall clustering algorithm can be formulated in two steps: (i) performing principal component analysis (PCA) (Pearson, 1901) on the covariance matrix and (ii) recovering cluster membership matrix using the k eigenvectors that correspond to the k largest eigenvalues.

the blockdiagonal structure of the Hessian matrix in (OPT8) can be exploited to solve this problem much more efficiently.


This demonstrates our secondary contribution, that the ability to plan in PGRD significantly improves performance over standard OLPOMDP (PGRD with d = 0).

note that if φ is a vector of binary indicator features, this representation allows for arbitrary reward functions and thus the representation is completely general.


In domains where there are a large number of variables within each slice dynamic programming based exact inference cannot be used.

in [9], it was pointed out that MEMMs suffer from the label-bias problem to which as a solution CRFs were invented.


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

lou/SP Gerstner/CP is/N chairman/N of/N IBM/SC" would include features such as !


Then, there exists a constant C V ∈ R such that ∀ε > 0, Note that, while we require no assumptions on the densities here, in certain specific applications, such us for some Rényi-α quantities, where f = log, assumptions such as lower bounds on the density may be needed to ensure f is Lipschitz on its domain.

in our framework, we assume that the underlying distributions are not given explicitly.


On NORB, the model size used by Salakhutdinov and Hinton [18] is already as large as we are able to fit on most of our graphics cards, so we were not able to do the same for this dataset.

we are able to classify nearly as well using a single large DBM and a generic inference procedure, rather than using a DBM followed by an entirely separate MLP model specialized for classification.


Figure (4) shows two images of roads in rural scenes and two fields.

we demonstrate results for : (I) indoor and outdoor scenes (as reported in [2]), (II) rural English road scenes, (III) rural English fields, (IV) a painting of the French countryside, (V) a field of broccoli in the American mid-west, (VI) the Ames room, and (VII) ruins of the Parthenon (in Athens).


ROI Mapping reduces noise by averaging voxel activations, whereas the Talairach transformation effectively introduces new noise due to imperfections in the morphing transformation.

we use k Nearest Neighbor with a Euclidean distance metric, considering values of 1, 3, and 5 for k (see, for instance, [5]).


These computations, appearing as T a→b c (α b,i,k , α c,k+1,j ), T b→c a (1,2) (β b,k,j , α c,k,i−1 ) and T b→a c (1,3) (β b,i,k , α c,j+1,k ) output a vector of length m, where computation of each element in the vector is O(m 2 ).

this multiplicative factor can be prohibitive for a large number of hidden states; various heuristics are used in practice to avoid this problem [16].


This however does not provide a satisfactory solution mainly because it does not take into account how the ranking is performed.

second, the methods were compared as multi-label systems using the Hamming Loss.


Most of these works aim to slim down filters in different ways, e.g.

their output channels are 20 and 21, respectively, since a spatial versatile filter with size 5 × 5 can produce three channels outputs simultaneously.


note that this is a closed-loop approach, in comparison to GLASSES [5] which is an open-loop approach.


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

we have introduced a simple approximated formulation of compact generalized non-local operation, and have validated it on the task of fine-grained classification and action recognition from RGB images.


The DWI measurements for a single voxel in the brain are y 1 , .

the problem of fitting a mixture model and the problem of fitting an ensemble of weak learners have several important differences.


For the third case, let λ 1 = T α and λ t = 0 for 1 < t ≤ T . Note that The original online gradient descent (OGD) algorithm as analyzed by Zinkevich [2] used the Euclidean distance of the current point from the optimum as a potential function.

it is natural to ask if this is essential: is there an algorithm that can adapt to the convexity of the loss functions and achieve the same regret rates in both cases-O(log T ) for uniformly convex functions and O( √ T ) for arbitrary convex functions?


Written under partial support by the Austrian Science Fund FWF, project # S9102-N04, project # IST2002-506778 (PASCAL) and project # FP6-015879 (FACETS) of the European Union.

whereas previous models for discrete or continuous attractors in recurrent neural circuits required that the whole dynamics of such circuit was entrained by the attractor, our new model predicts that persistent firing states can co-exist with other high-dimensional attractors and with responses to time-varying afferent inputs within the same circuit.


The probability of generating a document is defined as Our initial approach was to learn hidden topics using LDA directly on the words surrounding the images.

this is important in order for the first step of our method to be able to improve the precision of training data used in the second step.


Simulations show that our method can in theory provide a substantial speedup over standard training methods.

we then use the inferred learning rule to compute an optimal sequence of stimuli, selected adaptively on a trial-by-trial basis, that will drive the animal's internal model toward a desired state.


We found empirically that the Monte-Carlo procedure is more accurate as the simulated PIP losses concentrate tightly around their means across different runs.

given an embedding matrix E ∈ R n×d , define its associated Pairwise Inner Product (PIP) matrix to be PIP It can be seen that the (i, j)-th entry of the PIP matrix corresponds to the inner product between the embeddings for word i and word j, i.e.


( 9)] associated with the four weights [p j , p k , v 0,j , v 0,k ] T ; they may be expressed in a compact form as where the entries are given below with B ≡ Notice here that the subscript d implies datum d (d = 1, ..., m); hence, h d is the hidden-node output on datum d (but not the dth hidden-node output) common to both nodes j and k due to Theorem 1: When e = 0, the n-by-n Hessian ∇ 2 E and its block H in Eq.

singularities have been well discussed in the nonlinear least squares literature also: For instance, Jennrich & Sampson (pp.65-66 [5]) described an overlap-singularity situation involving a redundant model; specifically, a classical (linear-output) model of exponentials with h i ≡ φ(v i x) and no thresholds in Eq.


The privacy and accuracy guarantees are stated below.

their local algorithm exhibits optimal communication but a rather high time complexity: Server running time is Õ(n 5/2 ) and, crucially, user running time is Õ(n 3/2 ) -complexity that severely hampers the practicality of this algorithm.


As a result, even if the values of ρ which provide β U,ρ > β L are small, there is still the potential of perfect clustering.


For our goals, the matrix C essentially contains a subset of r features from the data matrix X.

let X ∈ R n×d and Y ∈ R n×ω be the input matrices in a multiple regression problem.


A small k will be very sensitive to noise and necessarily lead to many classes receiving a probability of zero, which is undesirable for our application.

we define three distributions based on the prior probabilities, P (y), of the acoustic phonetic classes.


ρ X represents the output of the sensor-neurons and stretch receptors that contact this motor-neuron (e.g., ρ ES , ρ AL , ρ GL , etc.)

sometimes dynamic biped walking can be achieved without considering any stability criterion such as the ZMP.


This voltage across C pot decays with time from its peak value due to a leakage current set by V bpot .

when the postsynaptic neuron fires immediately before the presynaptic neuron the strength of the synapse diminishes.


They share with Support Vector machines and Regularization Networks the concept of regularization via Reproducing Kernel Hilbert spaces [3], that is, they allow the direct specification of the smoothness properties of the class of functions under consideration.

for a given P E IR ffl xn let us analyze the computational cost involved in the estimation procedures.


. . , x n ) of data, not for data x in isolation.


Kingman's coalescent is a standard model from population genetics for the genealogy of a set of individuals.

taking n → ∞, there is a distribution over genealogies of a countably infinite population for which the marginal distribution of the genealogy of any n individuals gives the n-coalescent.


This property makes them useful, for instance, in actually distorting the optimal policy in Markov decision problems to ensure that exploration is plmmed and executed in favor of exploitation.

if the expectation is confirmed, then there will be continued activity representing the difference between the value of the reward and the expected value given the ambiguous stimulus.


This condition allows for a new efficient algorithm which we call the alternating blockwise leapfrog algorithm.

in practice we find it very beneficial to use multiple steps in each blockwise leapfrog update in ABLA; this can cause SSHMC to require more time than HMC.


In this evaluation, partially observed training data are the data records whose leaf nodes are labeled and inner nodes are hidden.

the recently proposed Maximum Entropy Discrimination Markov Networks (MaxEnDNet) [20,19] represent a key advance in this direction.


Let Ô Ø ´Üµ be the Gaussian density with mean ¼ ¾ and standard deviation ¼ , which is assumed to be known here.

it turns out that the weakened condition is still restrictive in practice.


The results are shown in Figure 3 and Table 1.

assuming perfect transitions, if θ(β) and the Fisher information matrix G θ (β) = cov x∼p θ (∇ θ log p θ (x)) are continuous and piecewise smooth, then as K → ∞ the bias δ behaves as follows: where θ(β) represents the derivative of θ with respect to β.


[32], because the ones they used were much smaller, resulting in an expensive cross-validation procedure involving a separate hyperparameter search for each fold.

straightforward recurrent autoregressive models would update a hidden state sequentially for every variable, requiring D sequential computations to compute the probability p(x) of a D-dimensional vector, which is not well-suited for computation on parallel architectures such as GPUs.


Note that in this step synchronization thread 0 on all servers use level-0 links only while thread 1 on all servers use level-1 links only.

the experiment demonstrates that BML has particular advantage in this scenario.


The intracellular recording in Figure 4(a) shows the known neuron is active for only a brief section of the recorded signal, and is then inactive for the rest of the signal.

for the accuracy analysis, we determine one cluster that corresponds to the known neuron.


Computing the Shannon entropy in massive data have important applications in neural computation [17], graph estimation [5], query logs analysis in Web search [14], network anomaly detection [21], etc.

our second key component is a new estimator of T α using a moment estimator which does not have (or barely has) finite variance.


The worst-case expected regret of any full-information algorithm is Ω( 3 √ ΛV T + V ), while that of any bandit algorithm is Ω( Proof.

we would like to understand the interplay among the parameters Γ, V, Λ, and T , defined in (1).


We further show that the learned informative knowledge can be generalized across different matting algorithms.

the proposed informative regions are general across different matting algorithms.


To reduce the storage of the m k ( )'s, Barnard et al [1] store the color distribution only for illuminants of a fixed brightness.

denote this reflectance by x = (x r , x g , x b ), with each channel ranging from zero to one.


Assume the observations z are always bounded.

[16] can only guarantee that the solution converges to a stationary point of the optimization problem.


The Spectral approach performs even worse sometimes.

our method Low Rank uses the same latent structure, but achieved much more robust results.


This bound can be expressed on a scale that is independent of the temperature parameter γ; intuitively, ∆ max corresponds to a utility difference so slight that the user identifies the best item only with probability 0.56 under R L with temperature γ.

a number of these focus directly on (myopically or heuristically) reducing uncertainty regarding utility parameters as quickly as possible, including max-margin [10], volumetric [12], polyhedral [22] and entropy-based [1] methods.


One can add other parameters such as the average humidity, frequency of switching between policies, average energy consumption and so on.

by playing a strategy which is optimal in Γ(u i ) results in a play which is almost optimal in Γ(u).


For each document j, document-specific topic frequencies are drawn π j ∼ DP(αβ).

approximations based on truncations of the stick-breaking topic frequency prior [2,4] are not nested, and their artifactual placement of extra mass on the final topic K is less suitable for our split-merge online variational inference.


Given the reference set and the comparison set, we are able to compute the rank scores indicating the relative ranks for the complete sentences.

this can be treated as G and R play a minimax game with the objective function L: where θ and φ are the variable parameters in G and R, respectively.


These questions are the main focus of this paper.

in the proof of the convergence of LTSA, it is assumed that the errors in the local step converge to 0.


we hypothesize that only n = kernels preserve sufficient information about the magnitude of their inputs to work e composition with other kernels.


While the worst-case performance of such approximate policies can be significantly bad as compared to the optimal dynamic solution, the empirical performance, especially of affine policies, has been observed to be near-optimal in a broad range of computational experiments.


Here, we see that the quality of the TAP approximation becomes less good.

(The predicted posterior variance of the internal field is (β∆λ c (i)) −1 and goes to zero as β → ∞ indicating the transition to a deterministic model.)


We show that one can efficiently maximize the joint posterior probability of all the node labels by a simple greedy algorithm.

this significantly increases the number of "meta-labels", making it unsuitable for large hierarchies.


Computing the optimal twisting functions boils down to performing exact inference in the model, which is assumed to be intractable.

here n t is the number of neighbors of x t , τ = 0.1 is a scaling parameter, and d = 1 is a regularization parameter ensuring a positive definite precision matrix.


's adversarial training objective [8] (referred to as "Adv.

we penalize the norm of adversarial perturbations, by encouraging relatively large values for the correctly classified samples and possibly small values for those misclassified ones.


A number of algorithms have been proposed to solve such systems of linear inequalities for feasible points d. In our sampling algorithm we implement the relaxation method introduced by Agmon [11] and Motzkin and Schoenberg [12] due to its simplicity.

the Z-test scores on the 4 differently sized splits are reported in Table 2 b) and allow us to reject the null hypothesis with very high confidence.


The tradeoff is controlled by varying the level of discretization.

the coin-flipping process captures the live-edge characterization of the Independent Cascade model [7], in which the presence of edge (u, v) in G allows influence (e.g., behavior, disease, or some other spreading phenomenon) to propagate from u to v. Influence maximization seeks a seed set S of at most k nodes to maximize the expected number of nodes reachable from S, which is easily modeled within our model by assigning appropriate rewards and actions.


This is surprising, considering the fact the POO was simultaneously running 100 different HOOs.

for a standard partitioning, there is no semi-metric of the form (x, y) = ||x − y|| α for which the near-optimality dimension is d = 0, as shown by Valko et al.


We assume that all edges have a minimum influence strength, and that even when all neighbors of a node u are influenced in a time step, there is a small probability of u not being influenced in the next step; we consider a specific seed distribution, where each node has a non-zero probability of (not) being a seed node.

we stress that a node is influenced at time t if it changes its opinion from 0 to 1 exactly at t. Also, in both the LT and IC models, no node gets influenced more than once and hence an influence cascade can last for at most n time steps.


Our second approach for the NNQH problem relies on a Euclidean embedding for the hyperplane and points.

to hash a database point x we use h u,v (x, x), whereas to hash a query hyperplane w, we use h u,v (w, −w).


As observed in Figure 4, we see that the PG sampler applied to the iHMM and sticky iHMM, converges far more quickly from both "small" and "large" initialization of K = 3 and K = 30 "active" states to the true value of K = 10 hidden states, as well as converging in JLL more quickly.

we can compute p(y t |s n t−1 ) = K+1 k=1 π(k | s n t−1 )f (y t | φ k ) for each particle s n t where n ∈ 1, ..., N − 1.


Data We used the three datasets used in [11]: IMDB, Elec, and RCV1, as summarized in Table 1.

a convolution layer embodies an embedding of text regions, which produces an m-dim vector for each text region.


Since there are exponentially many constraints, we follow [10] in adopting a constraint generation strategy, which starts by solving the problem with no constraints and iteratively adding the most violated constraint for the current solution of the optimisation problem.

we can partition the optimisation problem into k optimisation problems conditioned on the sets Y k := {y : |y| = k}: where A [k],n denotes the particular matrix A n that we obtain when |y| = k. However the inner maximization above, i.e., the problem of maximising a supermodular function (or minimising a submodular function) subject to a cardinality constraint, is itself NP-hard [19].


Prominent among these are the FINST model of Pylyshyn [29], and the object file model of Kahnemman et al [18].

[37], have been proposed, there have been no attempts to demonstrate their applicability to real video scenes.


The learned policy is the result of minimum-cost planning using these cost functions.

the algorithm in its most basic form is given by the update rule w t+1 ← w t − γ t g t , where {γ t } ∞ t=1 is a prespecified stepsize sequence and g t is a subgradient at the current timestep t. Note that computing the subgradient requires solving the problem µ * = arg min µ∈Gi (w T F i − l T i )µ for each MDP.


Then, for Since distances can be written as a sum of three inner products (Eq.

our estimators are more similar to orthogonal series density estimators, which are computationally attractive because they require no pairwise operations between samples.


Optimization thus has to independently tune features throughout the image without knowing the global structure.

we train 3 different DNNs following CaffeNet architecture to discriminate 2000 classes.


This conditional probability is related to the concept that the margin is an indicator of confidence which is recurrent in semi-supervised self-learning algorithms [3,6,10,11,12].

theorem 1 Suppose that B Q is as in (1).


They propose a latent structural SVM framework to learn the semantic relevance relations from text to image sequences.

we compare with four baselines; we choose (MLBL-B) among the three variants of [12], and (CNN+LSTM) among mRNN-based methods.


We estimate the probability distribution obtained by applying matrix P repeated starting from any initial condition.


. . , d M ) where each d m ∈ n . We wish to impose that any x ∈ n may be represented approximately as x = Dα, where α ∈ M is sparse, and our objective is to also minimize the 2 error x − x 2 .

the DP still assumes that the members of {x i } i=1,N B are exchangeable.


To guarantee support recovery, our proof critically exploits a novel observation (Lemma B.4 in Appendix B.2) that if at any iteration of OMP, full support recovery has not happened, then OMP decreases function value by a fixed, but small, additive constant.

none of these works give strong results for this problem.


Let us note that, even if we obtain a good weight vector w with small (w), we cannot always compute w x t from limited observation of x t and, hence, in our setting the prediction error might not be as small as (w).

for example, the algorithms proposed by Cesa-Bianchi et al.


In this section we formally introduce the Random Recursive SVM model, and discuss the motivation and justification behind it.

linear SVMs often fail to solve complex problems however, and with non-linear kernels, SVMs usually suffer from speed and memory issues when faced with very large-scale data, although techniques such as non-convex optimization [6] or spline approximations [19] exist for speed-ups.


In step w (w ∈ [0, k − 1]), thread t sends N n (w+1) gradient pieces to, and receives the same number of gradient pieces from, each of its 1-hop neighboring servers.

one way is to partition the machines into two clusters, one for parameter servers and the other for workers.


This work was supported in part by the European Commission under Grant MIRG-268398, ERC Future Proof, SNF 200021-132548, ARO MURI W911NF0910383, and DARPA KeCoM program #11-DARPA-1055.

further assumptions on the multivariate functions beyond smoothness are needed for the tractability of successful learning [13,14,16,19].


When it fails, we deem that y k may not be a good extrapolation.

there is no literature showing that there exists an accelerated gradient method satisfying the conditions in their framework.


To test the effect of size, we first randomly sampled 10,000 frames for which we have object bounding boxes (as detected by YOLO) for the attended object.

our study was reviewed and approved by the IRB at our institution.


[2] proved that there always exists η (k) = β r k > 0 satisfying (13), and every limit point of {A (k) } ∞ k=0 is a stationary point of (9).

note that we use superscripts for time indices and subscripts for data indices.


We assume that the observed tensor T ∈ R I1×I2•••×IN can be decomposed as a true tensor D with rank-(r 1 , r 2 , .

aDMM decomposes a large problem into a series of smaller subproblems, and coordinates the solutions of subproblems to compute the optimal solution.


In the literature, we identified two sets of quantitative data that give us a good starting point for making measurements to determine whether our algorithms may be computing similar functions as area V2.

one V2 study by [22] reported that the receptive fields in this area were similar to those in the neighboring areas V1 and V4.


Kearns [11] extended Valiant's model and introduced the statistical query oracle STAT(c, D).

the intuition that given I V x = h, the strings with x h+1 ∈ U +1 have higher probability of positivity than that of the strings with x h+1 ∈ U +1 is still true under product distributions.


We also note that under the relatively minor assumption of the existence of an oracle for offline optimization, the algorithm of Kalai and Vempala [2005] is an efficient algorithm for this setting.

there is only one (non-trivial) special case [Gyorgy et al., 2007] in the literature where an O * (poly(n) √ T ) regret has been established, and this case assumes significantly more feedback than in the partial information case -their result is for Path Planning (where D is the set of paths on a graph and n is the number of edges) and the feedback model assumes that learner receives the weight along each edge that is traversed (significantly more information than the just the scalar loss).


For diversity-driven DDPG, we use the actions stored in Z, and modify Eq.

for example, in HalfCheetah of MuJoCo [4], the agent quickly learns to flip on its back and then "wiggles" its way forward, which is a sub-optimal policy [5].


We will take advantage of this fact to develop an efficient stochastic inference algorithm within the framework of G-flow.

based on its hypothesis about pose history, each expert has an opinion about the current pose of the object, U t , and the texture maps of the object and background, V t and B t . Each expert also has a credibility, a scalar that measures how well the expert's opinion matches the observed image y t . (5) can be interpreted as follows: The filtering distribution at time t is obtained by integrating over the entire ensemble of experts the opinion of each expert weighted by that expert's credibility.


The algorithm starts with some U 0 and V 0 , and given a new observation (M) ij , SGD updates the i th -row and the j th -row of the current iterates U t and V t respectively by t , and, where η is an appropriately chosen stepsize, and U (i) denote the i th row of matrix U.

σ min (X U) not too small requires both σ min (U U) and σ min (X W) are not too small, where W is top-k eigenspace of UU .


Finally, we have yet to account for neurophysiological data within this framework, and constraints at the neural implementation level.

[4][5][6][7][8] Our model accounts correctly for both attraction and repulsion, determined by the smoothness prior and the geometry of the scene.


In addition, the macro-actions only return the observation it makes at the point when the macro-action terminates, reducing the complexity of the problem, possibly at a cost of some sub-optimality.

the performance of MCVI degrades, as the planning horizon increases.


. . , σ K , λ), which has K(D + 2) + D parameters.

errors 0.1 can be considered negligible; higher precision is unnecessary.


In the case of a sparse use of trajectories to cover a space, the cost of the approach is dominated by the E © costs of updating second derivative matrices, and thus the cost of the trajectory-based approach increases quadratically as the dimensionality increases.

this is a model of a robot that walks along the trusses of a large structure such as a bridge, much as a monkey brachiates with its arms.


For each model, we generate K = 50 data sets to calculate the std.

large eigenvalues are overestimated and small eigenvalues underestimated, the condition number is large and the matrix difficult to invert [MP67,ER05,BS10].


Note that this joint distribution is for a general Lévy measure ρ, density f ρ and it is conditioned on the valued of the random variable T . We can recover the well known Stick breaking representations for the Dirichlet and Pitman-Yor processes, for a specific choice of ρ and if we integrate out T , see the supplementary material for further details about the latter.

draw with a simple rejection sampler [2] where the rejection constant is bv and the proposal is U p0, vq.


The above does not have a closed form solution.

it takes as input an n × n matrix of non-negative distances D where D i,j denotes the target distance between entity i and entity j.


The nodes change their cluster in a random manner.

namely, with probability 1/n each node is reassigned; when this happens it is moved to the ith community C i (which we also call a cluster C i ) with probability α i , where {α i } k i=1 form a probability distribution.


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

3(c)) varies more richly with network width.


We compared the proposed model with probabilistic canonical correlation analysis (PCCA), horizontal anomaly detection (HOAD) [13], consensus clustering based anomaly detection (CC) [16], and one-class support vector machine (OCSVM) [18].

because the proposed model simultaneously estimates the parameters and infers anomalies, the estimated parameters are not contaminated by the anomalies.


To do so, we will first rewrite the runtime in Corollary 5.1 as: In order to compare the runtimes, we must consider the relative magnitudes of the dimensionality d and the norm B.

recall that using a norm-regularized approach, such as SVM, makes sense only when d B 2 .


Our modifications incorporate three features that model processing in the barn owl's auditory system.

experiments performed in multiple source environments by Takahashi et al.


It is computed by taking the expectation over output values H(X|R) = E r − p(x|r) ln p(x|r)dx .

although this is large relative to the variance of a pixel, as a result of strong spatial correlations in the input, some projections of the data (low frequency components) had SNR over 40dB.


Finally, the IL penalties are τ j (z j + |s j /σ| 2 ) 1/2 , enforcing sparsity more strongly for smaller z j .

while this suboptimal behaviour of our optimization will be analyzed more closely in future work, it is our experience so far that the gain in using greedy sequential Bayesian design optimization over simpler choices is generally largest below 1/2 Nyquist.


However, most efforts focus on the supervised learning scenario where a closed world assumption is made at training time about both the domain of interest and the tasks to be learned.

any generalization ability of these models is only an observed byproduct.


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

it must store the entire sequence in memory before it constructs the output hypothesis, and its memory footprint grows linearly with training set size.


When hallucinations are formed they evoke corresponding representations in all hidden layers, even the lower ones that by themselves cannot support stable shape representations (Figure 2b).

this is a result of recurrent interaction with the higher layers, likely contributing to the stability of the overall internal state.


For each node i, we denote P i , S i respectively as the set of direct predecessors and successors of node i.

m i = |P i |, n i = |S i | imply the in-degree and out-degree of the node i. Matrix A denotes the corresponding adjacency matrix where each entry a ij ∈ [0, ∞) is the weight of link (i, j).


Traditional finite mixture models often suffer from overfitting or underfitting of data due to possible mismatch between the model complexity and amount of data.

model selection or model averaging is required to find the correct number of clusters or the model with the appropriate complexity.


If we approximate the true posterior p(Θ|y, O, m) by the estimated variational posteriors q(Θ|y, O, m), p(x t |y, O, m) can be calculated by p(x t |y, O, m) ≈ p(x t |y, Θ, m)q(Θ|y, O, m)dΘ.

the optimal class y can be obtained by In the calculation of ( 8), the integral over Gaussian means and covariances for a frame can be solved analytically to be Student distributions.


Therefore, algorithmic stability is sufficient for uniform generalization.

the converse is proved by showing that for any δ > 0, there exists a bounded parametric loss and a distribution P δ (z) such that algorithmic stability is also necessary for uniform generalization.


Note that a crude upper bound on Var t X t is b 2 .

σ ≤ b √ T . We choose a discretization 0 = α −1 < α 0 < .


Starting at t = 1, since the initial distribution is π 1 ∈ CRP(S, µ, 0), the conditional cluster assignment of the sequence i in π 1 is given by the CRP probabilities from (1): To find the conditional distribution of b t given a t , we use the definition of the fragmentation operation as independent CRP partitions of each cluster in π t . If a t = ∅, then the sequence i is in a cluster by itself in π t and so it will remain in a cluster by itself after fragmenting.


The same relation holds for the average value of α computed based on the probability distribution function (2) with σ = σ*.

<α i > computed from the neurometric data with a = a* and b = b* is equal to <α> based on (2) with σ = σ*.


Only expanding the optimistic leaf would not be enough to make ASOP consistent; this is shown in the appendix.

a second leaf (the safe one), defined as the shallowest leaf in the current tree, is also expanded in each iteration.


( 5) and its empirical estimate: θ µ,x := E µ [r1 s | x], and θi := r i 1 si .

our regression estimator ( 5) is simply φx = Γ † µ,x θ µ,x .


Stochastic Gradient Descent (SGD) uses the gradient of a single sample as the search direction at each iteration.

the computation for each iteration is very fast, which leads to fast convergence at the beginning.


We obtain the integrals by observing that, in the passive design, the state variable I s = −I mem /sτ 1 .

here, I sf and I sb represent the outputs of the first LPF in the upstream and downstream BM segments, respectively; τ 1f and τ 1b represent their respective time constants.


Is is not hard to see that for every φ : [d + 1] → {±1}, the approximation error of the class of halfspaces with respect to D φ is zero.

in order to ensure a large approximation error for every distribution, the number of classes must be at least linear in the dimension, so in this sense, the lemma is tight.


This phenomenon can be seen in Figure 1, where it is impossible to accurately resolve the clusters in the space based on the 2 principal components, through either K-means or GMM.

by jointly learning the suitable feature space and clustering, we are able to separate the unknown and known neurons clusters more accurately.


each class in the partition is exactly the set of leaves descending from some node in the tree.

a t-c partition can be uniquely encoded as the set of these nodes whose leaf descendants comprise the classes (Figure 1a,b).


Given a feature φ, our set of classifiers H φ consists of all one-vs-one classifiers, all one-vs-all classifiers, and all node classifiers from a tree-based method [13], where a node classifier can be trained to distinguish two arbitrary clusters of classes.

for a K-class problem, the number of classifiers given a single feature is |H φ | = (K−1)K 2 + K + N φ,tree , where N φ,tree is the number of nodes in the tree model.


Our major goal with these experiments is to test our algorithm SPN-CG for high-dimensional real world settings and show the efficacy of learning SPNs by increasing their expressiveness iteratively.

we directly adapt the experiments as presented in [26].


We show that if the distribution of Y differs across categories, then so does the distribution of the distance of Y from almost every point z.

any univariate consistent two-sample test on the distances from z results in a consistent test of the equality of the multivariate distributions F 1 and F 2 , for almost every z.


Using the expression (9) of V , we have V, V = η 2 (t)∆ T (t)Σ(X, t)∆(t), where ∆(t) = ∇ψ * (Z(t)/s(t)) − ∇ψ * (z ).

since the mirror map has values in X and X is assumed compact, the diameter D = sup x,x ∈X x − x is finite, and ∆(t) ≤ D for all t. dβ(t) ≤ D 2 η(t) 2 σ 2 * (t)dt, and integrating, Since β(t) is a non-decreasing process, two cases are possible: if lim t→∞ β(t) is finite, then lim sup t→∞ |V(t)| is a.s. finite and the result follows immediately.


For any set cover instance, we will put all elements to be the input of our multi-input-probabilistic-AND gate, and connect the output with a large number of additional nodes.

if k sets can cover all elements, all of those addition nodes will be activated, on contrast, if at least one of the elements cannot be covered, almost all of the additional nodes will remain inactive.


There are several tricks that enable successful training: • Changing the activation function: The threshold activation function, σ(a) = 1 a>0 , has zero derivative almost everywhere.

we cannot apply gradient-based methods with this activation function.


Since the latent variables are not directly connected, the complexity of inferring the posterior distribution of H is the same as in EFH when all the input data are observed, as reflected in the factorized form of p(h|x, z).

multi-view latent space MNs do not increase the complexity on testing if our task depends solely on the latent representation (i.e., expectation of H), such as information retrieval [26], classification, clustering etc.


Structure learning must now estimate a W to minimize the hinge loss as in [29] 1 At the minimum, the slack variables ξ i happen at the equality of the constraints.

we can move the constraints to the objective function, which is: Notice that this function is convex, but not differentiable.


Although this worst case formulation (15) might appear to be conservative compared to working with a known distribution on R and using (2), when additional information about the distribution is available, such as symmetry or unimodality, (15) can be brought very close to using a Gaussian distribution, as shown in Figure 1.

given reasonable constraints, the minimax approach does not have to be overly conservative, while providing robustness and tractability.


A key factor in understanding this algorithm is the observance that a strategy a receives higher reward than a strategy b if and only if the gradient at a is in the direction of b (i.e., r t • (b − a) > 0).

the step (3) adjustment is in the direction of the gradient if and only if z t received higher reward than x t . Notice also that, as long as x t is not near the boundary, the change due to step (3) is of lower magnitude than the change due to step (1).


Our approach extends Tenenbaum and Freeman's work on bilinear models for learning content and style [12] by casting the problem within probabilistic sparse coding framework.

whereas prior work on bilinear models used global decomposition methods such as SVD, the approach presented here emphasizes the extraction of local features by removing higher-order redundancies through sparseness constraints.


Since the rewards are independent of whether we choose to explore, one sees that E[μ i (t " i (k))] = µ i .

we can decompose E[max j μj (t " i (k)) μi (t " i (k))] as follows: The second term in (2) is bounded by i = µ 1 µ i . Summing over all these steps and all arms, we obtain the first term in our bound (1).


It can be shown that with high probability, we always have |✓ i (t) μi (t)|  r i (t), where r i (t) = q 2 log t Ni(t) is defined in Algorithm 1.

we can focus on the case that |✓ i (t) μi (t)|  r i (t) for any i and t. Note that we do not need to pay compensation in empirical steps.


Generally speaking, however, SSDA can remove only the noise patterns it has seen in the training data.

sSDA would only be suitable in circumstances where the scope of denoising tasks is narrow, such as reconstructing images corrupted by a certain procedure.


Furthermore, we have K g (x, z) = k(x, •)g(x, x) dx, k(z, •)g(z, z) dz H . Thus, it is clear that the feature map of x depends not only on the kernel k, but also on the density g(x, x).

by virtue of Lemma 4, the kernel K g allows the SVM to place different kernels at each data point.


Therefore, if A i,j = d(p i , q j ) is large, then since d(p i , q j ) ≤ d(p i , q 1 ) + d(q 1 , p 1 ) + d(p 1 , q j ), at least one of d(p i , q 1 ), d(q 1 , p 1 ), d(p 1 , q j ) is large, and further, all these distances can be found by reading the first row and column of A.

large entries cannot hide in the matrix.


Now, suppose w * t is the optimum of Eq.

( 9) at iteration t, the item r t (w) we added can be shown to be the delta over w * t , that is, r t (w) = I(w = w * t ); in addition, we have q t (w) = 1 t t s=1 I(w = w * s ) when the step size is taken to be β t = 1 t . this Frank-Wolfe update can be naturally interpreted as greedily inserting a hidden unit into the current model p(v | q t , ϑ t ).


α3 α 1 q rs1 = α 4 q rs1 , where α 4 = α2α1 α3 .


The same reasoning applies simultaneously to every pair of arms.

if the confidence intervals of each pair of arms j i and j i+1 overlap for each i ∈ [k], the algorithm is forced to play all arms j with equal probability.


This monotonicity simplifies the problem.

we exploit this fact to complete the variable reduction.


for a nonzero row (w ⋆ ) k , some entries may be zero, due to the ℓ 1 -norm imposed on each row of W . under the formulation in Eq.


But in many cases, the residue vector is not so small due to the distortion in hand-written patterns.

it is almost impossible to judge which is the case only from the magnitude of the residue vector.


Finally, our algorithm was successful in identifying the following types of "adversaries": (1) uniform workers who always label 1 or 1 (in temp, task2, stage2), (2) malicious workers who mostly label incorrectly (in bluebird, stage2) and (3) random workers who label each task independent of its true label (such workers were identified as "spammers" in [13]).

our algorithm is able to identify a broad set of adversary strategies in addition to those detected by existing techniques.


However, for the example just described, a sublinear policy regret can be similarly achieved.

this notion of regret is also not the pertinent one for the study of our scenario.


However, through the combinatorial power of language, these phonological sequences can represent a huge number of distinct combinations of concepts.

this basic maintenance mechanism can be leveraged in many different circumstances to bind information needed for immediate use (e.g., in working memory tasks).


Therefore, for a pre-specified accuracy ✏, we need at most T = Moreover, Corollary 4.8 implies where the last inequality comes from (4.6).

we need at most Then combining (4.7) and (4.8), we obtain where the last inequality is from kV ).


For example, in bigLSTM model that achieved start-of-the-art performance on OBW, more than 90% of memory is used to store two (input and output) word-embedding matrices.

for deep neural net models alike, the main challenge to serve them on-device is to store tremendous memory usage of word embedding matrices.


The learning gradient is given by The dropout gradient is a random variable and we can take its expectation.

a short calculation yields remarkably, in this case the expectation of the gradient with dropout is the gradient of the regularized ensemble error The regularization term is the usual weight decay or Gaussian prior term based on the square of the weights to prevent overfitting.


In general, voiced segments in an utterance have approximate periodicity in each local time region while the period gradually changes.

when a long reverberation is added to a speech signal, signals in different time regions with different periods are mixed, thus degrading the periodicity of the signals in local time regions.


7 and the definitions of the intervals I K and I A .

i A constitutes a confidence interval for the AUC value of C at the confidence level In practice, the confidence interval E is often determined as a result of the assumption that C follows a binomial law.


The alternating minimization procedure of the previous section has a simple closed form in this case, consisting of the iterative update rule .

we can reasonably ask how the lines found under this exponential assumption differ from those found under a Gaussian assumption (that is, those found by regular PCA), provided all data is nonnegative.


Formally, let G = (V, E) be the random graph over n nodes obtained from an independent cascade process over the graph generated by the stochastic block model.

similarly as for the stochastic block model, edge probabilities for the independent cascade model may vary between different communities and are identical within a single community C, where all edges have weights q ic C . an edge e between two nodes in a community C is in E with probability p C := q ic C • q sb C , independently for every edge, where q ic C and q sb C are the edge probabilities in the independent cascade model and the stochastic block model respectively.


There is a close analogy between the marginal likelihood and the log-partition function or free energy from statistical physics [5].

many concepts and algorithms originating in statistical physics have been applied to problems arising in probabilistic inference.


However, the notion of a version space is more complex when the problem is inseparable.

it is reasonable to adapt a greedy approach which selects the point that will cause the larger change in the value of the objective function.


4 clearly show some connectivity difference between AD, MCI, and NC, it is highly desirable to test if the observed difference is statistically significant.

we further perform a hypothesis testing and the results are summarized in Table 2.


As can be seen, there is good agreement between theory and simulation, with the largest discrepancy occurring for small values of the scale factor.

when confronted with a changepoint, the network no longer approximates a Kalman filter and instead maintains two competing hypotheses in a way that is qualitatively similar to that of the run-length distribution in [1].


Since the no policy regret algorithms we work with do not directly induce distributions over the functional space F but rather only distributions over the action space A, we would like to state all of our utility inequalities in terms of distributions over A.

we would like to check if there is a stationary distribution a of M a such that a, b)].


The number of columns to be computed in one sweep is then given by p + z =q |B(S z , S q )|.

we would like to find a partition {S 1 , .


On optimizing A: By fixing β, the optimization problem ( 17) is reduced to where The problem ( 18) is a trace ratio problem, i.e., min A trace(A ⊤ S β W A)/trace(A ⊤ S β W ′ A).

a closedform solution can be obtained by transforming (18) into the corresponding ratio trace problem, i.e., min the columns of the optimal A * = [α 1 α 2 • • • α P ] are the eigenvectors corresponding to the first P smallest eigenvalues in On optimizing β: By fixing A, the optimization problem (17) becomes min where The additional constraints β ≥ 0 cause that the optimization to (22) can no longer be formulated as a generalized eigenvalue problem.


The spectral distribution of light reflected off a surface is a function of an intrinsic material property of the surface-its reflectance-and also of the spectral distribution of the light illuminating the surface.

the observed color of the same surface under different illuminants in different images will be different.


For estimating F (α) , the geometric mean estimator [10] is close to be statistically optimal (efficiency ≈ 80%) at α ≈ 1.

it was our first attempt to test the following estimator of the Tsallis entropy: , where where G() is defined in (8).


For N large we can replace L with L = {x p(x) > λ} with small loss in accuracy, where p is an estimate of p using the unlabeled data; see Rigollet (2006) for details.

let k j = n i=1 I (X i ∈ C j ) and for x ∈ C j define m(x) simply averages the labels of the data that fall in the set to which x belongs.


Together these results demonstrate that the median model uses recurrent computations to perform object recognition and that particular motifs in its recurrent architecture, found through hyperparameter optimization, are required for its improved accuracy.

given well-selected forms of local recurrence and long-range feedback, a ConvRNN can do the same challenging visual task as a deeper feedforward CNN.


For almost all of the 25 models, all three algorithms were not able to successfully find the top solutions.

we added regions of triplets (two for every grid face) to tighten the LP relaxation (for STRIPES and Nilsson) and to perform GBP instead of BP (for BMMF).


Namely, a (k+1) = w (k) and Recall that the LOG and EXP penalties are differentiable and strictly concave in |b| on [0, ∞).

the above algorithm enjoys the same convergence property of the LLA was studied by Zou and Li [23] (see Theorem 1 and Proposition 1 therein).


For example, for any To make E 1 (P i ) → 0+, we need to make about k 2 points in P i go to +∞.

we have g E (nk) ≈ n 2 • k 2 and β = 1 4 .


All of these observations validate the effectiveness and efficiency of our proposed technique.

we believe that our approximation machine is a promising technique for building scalable online kernel learning algorithms for large-scale classification tasks.


However, we know that each sample is assigned to only one class.

the network's prediction is expected to be the same despite transformations and disturbances.


This is especially important in hierarchical Bayesian models where, typically, the size of the model used is proportional to the number of observations.

with SAGA-LD, we can achieve better performance with very few samples.


This algorithm, straightforward as it is, provides (asymptotically) optimal regret guarantees (see Section B in the appendix for a brief review) and is arguably one of the most well-studied and widely-used algorithms in online learning theory and applications [24,39,57].

several natural questions arise in multi-agent online learning : if each agent adopts OGD to minimize regret, what is the resulting evolution of the joint action?


if each V t computed in blockFW is a ( 1 2 , ε 8 )approximate solution to (3.1), then for every t, the error h it takes O(κ log h1 ε ) iterations to achieve the target error h t ≤ ε.


Since K K is the closure of the space span {K x y : (x, y) ∈ X × R p }, any f ∈ K K has all its components equal.

the quantile estimators h j = f j + b j are parallel (and non-crossing) curves.


In particular, implicit regularization has been shown to play a crucial role in training deep models [14,13,18,11]: deep models often generalize well even when trained purely by minimizing the training error without any explicit regularization, and when there are more parameters than samples and the optimization problem is underdetermined.

there are many zero training error solutions, all global minima of the training objective, many of which generalize badly.


However, observing target i at track j will zero out p everywhere outside the coset µ j S n−k µ −1 i , which is difficult for the Fourier approach to handle.

in fact, by analogy with (7), denoting the operator that projects to the space of functions supported on this coset by P i j , the new distribution will just be P i j p. if we set ν 0 = ξ, after any single observation, our distribution will lie in V 1 of the corresponding Bi-CMRA.


There is an edge (the body) connecting root r to the vertex c 1 on the head.

this graph has diameter D = max(p + 2, 2p) and there are + mp + 1 vertices in total; an octopus O m,p is balanced if = mp + 1.


However, by making novel use of the Sherman-Morrison-Woodbury formula , a much smaller matrix of the order of the original input space is inverted at each step.

a problem with a 32-dimensional input space and 7 million points required inverting positive definite symmetric matrices of size 33 x 33 with a total running time of 96 minutes on a 400 MHz Pentium II.


Reliabl v inference from the observed number of spikes about the underlying firing rate of a neuronal response, however, requires a sufficiently long time interval, while integration times of neurons in vivo [3] as well as reaction times of humans or animals when performing classification tasks [4,5] are known to be rather short.

it is important to understand, how neural rate coding is affected by a limited time window available for decoding.


NFs have demonstrated success in various domains [2,16], but the flows do not explicitly use information about the target posterior.

it is unclear whether the improved performance is caused by an accurate posterior approximation or simply a result of overparametrization.


For naturalness, we show that both speaker adaptation and speaker encoding can achieve an MOS similar to the baseline multi-speaker generative model.

the proposed techniques can potentially be improved with better multi-speaker models in the future (such as replacing Griffin-Lim with WaveNet vocoder).


This requires one last property: for the Gamma process, the RPM G(•) is independent of the total mass ⇤.

the clustering of spikes (determined by G(•)) is independent of the rate ⇤ at which they are produced.


Note that the ppd relies on the number of parameters (through the number of integrals and the likelihood), the model equation (through the likelihood), and the parameter range (through Ω).

as GC, the PPC is sensitive to all these aspects.


By equation ( 16), the number of mistakes will be upper bounded by 10p + 5 because there is a cut of size 1 and the diameter is 2p.

for balanced octopi O m,p with p ≥ 3, as m grows the number of mistakes of the kernel perceptron will be bounded by a fixed constant.


Recall that w(a, b) specifies the strength of the pairwise relationship between two neighbouring variables v a and v b .

for our example SOC constraint, the vertices of this graph are given in Fig.


Finally, MF-based techniques have been demonstrated to be effective for word-sense disambiguation using a set of manually-specified MFs [13]; this work was later extended to automatically derive MFs from resources like Wordnet [10].

mFs have been used implicitly in a broad range of textual classification tasks.


Interestingly, using INFORMATIVEFIX we can fully recover the hidden matrix of the NOLA dataset by just querying 30% of entries.

the values of entry-wise PDFs can be used to guide adaptive exploration of the hidden datasets.


We already inductively know that all of its prolongations will solve all tasks up to .

given tasks X E¤ X § we first initialize 7 ¡ £¢ ¦¤ ; then for b h2 4 ¦ ¡ invoke OOPS db !


Let X § mf % g0 d k (1 be the number of times that a reduced joint action Young showed that AP in a weakly acyclic game converges to a strict Nash equilibrium w.p.1.

aP on the VG for the game in Table 1 leads to an equilibrium with payoff 1 which is actually an optimal Nash equilibrium for the original game.


For 50 word clusters, one cluster contained almost half of the words, while the other clusters were typically much smaller.

since the algorithm also tries to maximize I(Tw; D), the words merged into the big cluster are usually the less informative words about D. a word must be highly informative to stay out of this cluster.


In contrast, with discretized 3D shapes, the probe functions are generally defined on heterogeneous shape graphs/meshes, whose nodes are points on each individual shape and edges link adjacent points.

the functional spaces on different 3D shapes are independent and not naturally aligned, making joint analysis over the probe functions non-trivial.


This restriction implies that a Poisson graphical model distribution only models negative dependencies, or so called "competitive" relationships among variables.

such a Poisson graphical model would have limited practical applicability in modeling more general multivariate count data [20,21], with both positive and negative dependencies among the variables.


Consider a setting with binary relevance judgement labels, so that Y = {0, 1} r with n = 2 r . The prediction space is T = S r (group of permutations on r objects) with k = r!.

for y ∈ {0, 1} r and σ ∈ S r , where σ(i) denotes the position of document i under σ, the Precision@q loss for any integer q ∈ [r] can be written as follows: by Theorem 3, for the r-dimensional surrogate ψ * P@q : {0, 1} r × R r → R+ and pred * P@q : R r →S r defined as we have that (ψ * P@q , pred * P@q ) is � P@q -calibrated.


We compute the embedding for each example and then the centroid c T i of each class in the embedding space.

we can compute the similarity vector for each labeled example, where the i th element is the similarity between this labeled example and the centroid of each class: [v t (x t )] i = ψ(x t , c T i ).


If (a) the weight functions w n and the sampling densities q n are pointwise strictly positive and such that w n (x)q n (x) converges in the L ∞ -norm, and (b) E qn(x) w 2 n (x) is bounded , then θn − θ n converges to zero in probability and we have where From Proposition 1, it is worth noting that in general θ n will not converge to the population maximum likelihood estimate θ 0 , i.e., using a different sampling distribution than p 0 (x) may introduce a non asymptotically vanishing bias in estimating θ 0 .

active learning requires to ensure that (a) our estimators have a low bias and variance in estimating θ n , and (b) that θ n does actually converge to θ 0 .


During training, the network function f θ evolves along the (negative) kernel gradient with respect to the neural tangent kernel (NTK) However, in contrast to F lin , the realization function F (L) of ANNs is not linear.

the derivatives ∂ θp F (L) (θ) and the neural tangent kernel depend on the parameters θ.


In [12, Lemma 1], it is shown that setting the elements outside the active set for block j to zero satisfies the optimality condition of that step.

in our algorithm we only need to update the elements in Active Ij (A).


Though with these relaxations, we build connections between the constrained embedding framework as discussed in this section with the one proposed in Section 2.

we can view our proposed method as embedding both object nodes and group nodes into a hyperlane so that object nodes are close to the group nodes they link to.


More precisely, the rate can only change if the stimulus changes or a spike leaves or enters one of these windows.

we obtain a sequence of changepoints In the GLM neuron model setting the instantanious firing rate of neuron i is obtained by a linear filter of the feature map: where λ is the nonlinear transfer function.


We also replace the original Gaussian Process-based model with a Bayesian Neural Network, enabling more scalable inference.

we expand the scope of the HiP-MDP to applications with higher dimensions and more complex dynamics.


These computations, appearing as T a→b c (α b,i,k , α c,k+1,j ), T b→c a (1,2) (β b,k,j , α c,k,i−1 ) and T b→a c (1,3) (β b,i,k , α c,j+1,k ) output a vector of length m, where computation of each element in the vector is O(m 2 ).

the inside-outside has a multiplicative O(m 3 ) factor in its computational complexity, which we aim to reduce.


This update has the form of the joint distribution of an ERDM using separate duration and count variables [4].

we can employ similar forward-backward recursions.


There are, however, more flexible probabilistic models, such as Markov random fields or dynamic Bayesian networks, that can better represent statistical properties in the target variables.

we would like to incorporate such models into LTP learning to further improve the performance.


Finally, a Dirichlet prior with parameter ) is placed on the topics & 0' (¨¦ .

the generative process is given by ¥ ©¦ ¨ 21 43 65 07 & 8' (¨¦ 91 43 65 ) @7 A 1 B¥ ¦ ©¨ " 8 1 C& #' (¨D FE HG Given the observed words I CP " Q ¡ , the task of Bayesian inference is to compute the posterior distribution over the latent topic indices R BP ¡ , the mixing proportions ¥ !¦ ©¨ , and the topics & #' (¨¦ .


First, activity of non-monitored presynaptic neurons may significantly distort reconstruction results.

successful reconstruction would require monitoring all active pre-synaptic neurons, which is rather challenging.


On these inputs, the transferred weights from the segmentation network become less meaningful since these examples can be drastically different from the training set.

we utilize joint optimization to update the agent by minimizing L seg alongside the policy and value function in an online fashion.


Moreover, to ensure fairness of comparison, we also allow each baseline method to access and include all training datasets of all training multitask problems, besides the training datasets in a test multitask problem at hand.

we report the better performance of each baseline method when it learns on the test multitask problem only and on all the training and test multitask problems, respectively.


Moreover, the on-policy operator is a contraction with respect to • z,r .

proof: once again by the contraction map fixed point theorem there exists a fixed point of O among row normalized matrices H, and repeated applications of O will converge to a matrix H Π such that OH Π = H Π ; that is, H Π satisfies the policy based Bellman equation for dual representations.


p (A|Z = z) is equal to 1 for a s * and 0 for the rest of the actions.


Note that Sobolev spaces are large: In fact, Sobolev spaces are more flexible than Hölder spaces (a generalization of Lipschitz spaces to higher order smoothness) in that in these spaces the norm measures the average smoothness of the functions as opposed to measuring their worst-case smoothness.

functions that are smooth most over the place except for some parts that have a small measure will have small Sobolev-space norms, i.e., they will be looked as "simple", while they would be viewed as "complex" functions in Hölder spaces.


For a good generative model, we expect that x 0 = g ✓ (z 0 , y source ) is diverse for randomly sampled z 0 and o(x 0 ) = y source holds with high probability.

by reducing the distance between z and z 0 , L 1 has the effect of generating more diverse adversarial examples from class y source .


Persistence diagram Dg can be considered as a discrete measure µ Dg = u∈Dg δ u where δ u is the Dirac unit mass on u.


In addition, for every γ ∈ (0, 1) define the auxiliary measure where Q S γ is constructed according to (15) with Applying Lemma 2 with φ(u) = u log u, we can write Next we apply Lemma 3.

defining η = 1+h 2 and using the easily proved fact that combining Eqs.


VAML takes a robust approach: It considers the worst-case choice of V in the value function space F that is used by Planner.

it minimizes c 2 2,ν ( P, P * ) = dν(x, a) sup As argued by Farahmand et al.


A new machine is presented whenever all machines on the screen have been tried.

the exploratory drive is always maintained with one unexplored slot machine.


While this SDP can be solved by standard online packages, general-purpose solvers tend to scale poorly in the number of constraints.

for our work, we implemented our own special-purpose solver, exploiting the fact that most of the slack variables {ξ ij } never attain positive values 1 .


That is, we would like to learn a mapping f : X → {±1} k over an infinite domain X using only a finite training set of objects, and then apply the mapping to obtain binary codes f (x) for future objects to be encountered, such that S(x, x ) ≈ sign( f (x), f (x ) − θ).

the mapping f : X → {±1} k is usually limited to some constrained parametric class, both so we could represent and evaluate it efficiently on new objects, and to ensure good generalization.


Similar "divisive normalization" mechanisms have been successfully used to account for many nonlinear behaviors of neurons in both visual and auditory neurons [26,27].

it seems that mammalian visual systems are equipped with the basic computational building blocks that can be used to process local phase coherence.


Our choice is motivated by the fact that the F+Tree does not make use of stale samples.

we can perform multinomial sampling with a O(log(K)) cost.


We define the variational estimator θ vb by the variational parameter θ that attains the minimum value of the stochastic complexity F (X n ).

then, putting (15) into (12), we obtain our aim is to evaluate the minimum value of (20) as a function of the variational parameter θ.