On one hand we want to minimize the upper bound of negative log likelihood of x 1 when feeding to the decoder inputs of the form (z 1 , f s (x 1 )) and (z 1 , f s (x 1 )), where z 1 are samples form the approximate posterior q(z|x 1 ).

in Figure 6 we present results for interpolation and swapping.


Perturbation size specifies how well parameters of the individual class densities can be estimated from finite data.

the study of usefulness of unlabeled data under this assumption was undertaken by Castelli and Cover ( [5]) and Ratsaby and Venkatesh ( [11]).


However, this may not produce sufficient parallelism when drawing the φ k , because the number of topics is usually small compared to the number of cores.

to make this practical it is important to generate high performance inference code.


Applying the same reasoning to the loss function in the regularized risk (1) we obtain the following loss l(x i , x i+1 , y i , y i+1 , x i , x i+1 , f ) as a stochastic estimate of the objective function defined in (5).

see Figure 1 for illustrations of this idea.


In this section, we consider the following linear system in which the goal is to minimize the expected return over 20 steps.

figure 4 shows that when the Fisher information matrix is estimated using MC (BPG-MC), the BPG algorithm still performs better than MCPG, and outperforms the BPG algorithm in which the Fisher information matrix is estimated using ML (BPG-ML).


For instance, suppose P were uniform over all subtrees of T 0 , then log(1/(P (T )) = Ω(n), yielding a vacuous excess risk.

for any classifier ĥ learned over a sample {X i , Y i } i , we are interested in the excess-risk E( ĥ) .


A common setting where B&B is ubiquitously applied is MILP.

both prior methods handle a relatively simple setting where the model only predicts information about the current state, so that they can simply train by standard supervised learning.


This is a natural setting in practice because each representative is supposed to represent equal number of voters.

a mathematical characterization of optimal representative democracies would also highlight the subcases where direct democracy is best.


3(a) for an example of a voxel v as shown in Fig. . For computing the diffusion predictions, we use a discrete grid in the sphere by uniformly sampling the spherical coordinates using L points in azimuth and elevation coordinates (Fig.

we note that matrix M ∈ R N θ Nv×N f (Fig.


We now turn to a setting where the arm set is finite but very large.

in this section, we propose an improved approximate inner product method called L1 sampling which we claim is more accurate than the sampling proposed by Jain et al.


The following trends emerge: in the mid to long run, DN-p-LMS is never beaten by p-LMS by more than a fraction of percent.

bregman divergences play a central role in the design and analysis of a range of machine learning (ML) algorithms.


We study this questions by considering the sparsity structure on the parameter ✓.

in this problem, the samples from the unknown distribution are distributed among m different machines.


The key idea in this section is to use spatially co-occurring points of a point to improve the similarity values given by the kernel function.

this failure is due to introduction of a large number of points in the scarf themselves.


The task to label next is chosen separately from the labeler.

this will highlight the viability of our overall scheme presented in Section 5 that ties data collection together with data curation and learning.


As [14] show for PCA, one can start with a random matrix that is only slightly larger than the true rank k of the correlation matrix, and with extremely high likelihood converge in a few iterations to within a small distance of the true principal components.

because of the Zipfian distribution of words, many words are rare or even unique, and hence one is not in the asymptotic limit.


In 'o1' setting, policies depend on the local state s m t and the single count observation n t (s m t ).

to overcome the slow convergence of the vanilla actor-critic method we developed multiple techniques based on value function factorization and training the critic using individual value function of agents.


High sparsity is one of the key factors for the compression of DNNs [5,21].

given a probabilistic model p(y | x, ✓) we want to tune parameters ✓ of the model using training dataset D = {(x i , y i )} N i=1 .


Let u(x, t) be the synaptic input at time t to the neurons whose preferred stimulus is x.

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


As long as we can show that the values we obtain for α are upper bounds, then we can show that the objective function will decrease after the forward-backward routine, as the existing sequence of states is also a valid path (with no new incurred penalties).

(Note: there are no burn-in iterations and all samplers are initialized with a randomly initialized 20-state labeling.)


where z is the logits or unnormalised log probability outputted by the network θ.

we used the SGD with Nesterov momentum and set the momentum to 0.9.


For prediction, both iMedLDA and gMedLDA are slightly slower than fMedLDA.

for those data with non-zero Lagrange multipliers (i.e., the data are around the decision boundary or misclassified), the second term will bias the model towards a new posterior distribution that favors more discriminative representations on these "hard" data points.


5 (right) shows, even with such a clearly flawed environment model, I2A performs similarly well.

in general we found diminishing returns with using I2A with longer rollouts.


The update w i,t → w i,t+1 is based on the gradients ∇ i,t of a loss function L(•) satisfying L (∆) = −g(∆).

comparing to OBR stresses the effectiveness of the exploration/exploitation rule above and beyond the details of underlying generalized linear predictor.


Starting from a representation robust to a limited range of variations in the appearance of humans in images, we derive a generative probabilistic model which allows for automatic discovery of pose information.

we show the results for: • Linear SVM classifier: Trained as described, using the SVMLight software package.


Figure 4b shows that the mean level of asymmetry is indeed highly correlated with the mean scores of the morphs (Pearson correlation of -0.91, P-value < 10 -19 ).

combining the distances-vector and the slopes-vector yields a vector representation of 6,972 geometric features for each image.


The transpose operator is here denoted as (•) T . In this work, we assume that a value function is given for the Multiagent POMDP.

when multiple agents interact and cooperate in the same environment, the optimal decision-making problem is particularly challenging.


Similarly, there has been recent interest in making parametric assumptions on the dynamics and rewards directly, as in the recent work on factored MDPs.

a precise characterization of such constraints seems elusive.


to evaluate the blocks, we used 4,722 curated gene sets from the molecular signature database [24] and computed a p-value to measure the significance of the overlap between each block and each gene set.


[22] provide methods and code for computing derivatives for Cholesky factorization, QR decomposition, and symmetric eigenvalue decomposition when seen as matrix operators.

in practice, however, it is primarily targeted at scalar valued functions.


GD with 1-norm regularization behaves like GD for small k and like EG for large k. The GD algorithm keeps all the small weight around and the weight of the first component only grows linearly.

one way to closely approximate the above version space algorithm is to run the Exponentiated Gradient (EG) algorithm [KW97b] with a large learning rate.


Recall from Section 3 that in the absence of budget constraints, we were able to treat the bandit instance created for a query phrase independent of the other bandit instances.

let POL i decide which of the remaining arms of B i to activate.


Figure 2 plots the error rate as a function of the number of missing features.

our method considers instances as sets of (feature,value) pairs which naturally handle the missing value case.


This is obtained in much the same way as we obtain an adaptive regret bound for the fixed-share forecaster in the next result.

for instance, for a given horizon T , the discounts β t,T may be larger as t is closer to T . in a game-theoretic setting, the earlier losses may matter more then the more recent ones (because of interest rates), in which case β t,T would be smaller as t gets closer to T . We mostly consider below monotonic sequences of discounts (both non-decreasing and non-increasing).


2 shows the bias and variance estimates from each method at locations (5,5,0,• .

this example has q = 10 measurements and 11 classes.


When 1 = 2 , the coverage diagram can be used as a similarity measure for two manifolds.

in this paper, we introduce the concept of coverage risk which is a generalization of the mean integrated expected error from function estimation.


A language model evaluates the probability distribution of sequences of words.

nonparametric models perform significantly worse than fully trained deep models [12].


That is, the MLE is equivalent to solving the variational problem: min θ,q(Z) L(θ, q(Z); X).

in the MLP case, we concatenate the activations of 2 layers as the features used in the supervised tasks.


When α true is higher than the α fixed by the statistical test, the test underestimates Type I error, which means we should not rely on its decision regarding the superiority of one model over the other.

figure 2 shows the obtained results for the Power of the test estimates.


The corresponding constrained relaxation to the maximum-likelihood problem has the form Using this model instead of ones we saw previously, we sacrifice less on the front of the approximation to the true likelihood, at the expense of increased computational effort.

based on this expression , we have, for every k: where we have used the fact that , for every symmetric matrix R, we have Using again the Lipschitz continuity properties of the weighted log-sum-exp function, we obtain that for every Q, the absolute error between Z(Q) and Z card (Q) is bounded as follows: a measure of quality is D st (Q), the distance, in l 1 -norm, between the model and the class of standard Ising models.


The algorithm exploits properties of singular value decomposition and works well with translation, shearing and scaling deformations.

. . , x N ) T (expressed as a N × D matrix) and D is the dimension of the points.


By Theorem 1 and 2, f 1 B and f 2 B do not satisfy as many desired normative properties as the Kemeny rule for winners.

a Condorcet winner is the alternative that beats every other alternative in pair-wise elections.


[29] assume that an appropriate choice of weights on visual feature vectors for a given question vector sufficiently captures the joint representation for answering.

the effects of other various options, Skip-Thought Vectors [12] for parameter initialization, Bayesian Dropout [5] for regularization, image captioning model [10] for postprocessing, and the usage of shortcut connections, are explored in Appendix A.1.


For example, in non-homogeneous Poisson processes λ * (t) is a function of time that does not depend on the history.

alternatively, we can use observational data, where we have example actions A, outcomes Y , and features X, but do not know how actions were chosen.


2 Reusing the flow from the previous step gives an additional speedup.

. . ≥ γ M . equations ( 12) constitute the parametric submodular minimization problem as defined above, which reduces to the monotonic parametric max-flow problem for pairwise E. Let • denote the largest integer not exceeding an argument of the operation.


Since we are omitting many other branches, these names should not be understood as referring to actual historical proto-languages, but, at best, to collapsed points representing several centuries of evolution.

the log-linear model groups rules with features of the appropriate degree of generality.


Efficient algorithms only exist for restricted classes of systems in the domain of AVs, and they are fundamentally difficult to scale.

weather conditions and driving policies of other agents).


We observe significant speed-ups brought by our algorithm, which is almost 50 times faster than the convex ones.

due to the nuclear norm penalty, these convex optimization algorithms need to do full singular value decomposition (SVD) to solve the proximal mapping of nuclear norm at each iteration, which results in an extremely high time complexity of O(d 3 ).


( 8) Now, we use dynamic programming approach that has been used to solve 0-1 Knapsack problems including MCKP given in (7) [28].

we define the maximum payoff one can collect with budget b among goods {1, ..., n} when the bid value x k is restricted to the set D t for each good k as Then, the following recursion can be used to solve for V K (B) which gives the optimal solution to (8): (9) This is the Bellman equation where V n (b) is the maximum total payoff one can collect using remaining budget b and remaining n goods.


The problem of inferring a distribution over partial derivations from observed words can be approximated using particle filters as outlined in Section 2.

the sophisticated dynamic programming algorithms typically used for incremental parsing implicitly represent all possible continuations of a sentence, and are thus able to recover the correct interpretation in a single pass.


The gradient perturbation approach can overcome all the issues and thus is preferred in practice.

we referred to it as objective perturbation approach.


However, the differences between model parameters, which can have a high sample complexity when there are few of them, are often pointed out only in passing [4,6,14].

by obtaining a debiased lasso estimate for each node in the graph [34] notes this leads to a sparse unbiased precision matrix estimate with a known asymptotic distribution.


The previous section provided an algorithm to solve the inference part of our energy disaggregation problem.

the performance of our algorithm is compared to the structured variational inference (SVI) method of Ghahramani and Jordan [1997], the method of Kolter and Jaakkola [2012] and that of Zhong et al.


¡ ¦ , which holds because ¡ ¦ is a transfer function, we get: Furthermore we assume orthogonality (see also below) given by: and get accordingly: We now apply PLANCHEREL'S theorem [5] in order to transfer the integral into the timedomain and prove that it is negative.

we want to express © ¥¤ by the environmental transferfunctions ¨¢ 7 3¨¦ and ¨¢ `¦ .


Let Λ 1 , Λ 2 be the non-negative measures to give φ 1 and φ 2 , respectively, in Eq.

in Section 2 we provide review of characteristic kernels on (R n , +) from this viewpoint.


This implies that the neuronal gain functions -the firing rate of the post-synaptic neurons as a function of the average • http) / culture.neurobio.ucla.edu/ "'pel firing rate of the pre-synaptic neurons -must be sigmoidal: small at low firing rate to provide stability, high at intermediate firing rate to provide a threshold (at an unstable equilibrium), and low again at high firing rate to provide saturation and a stable attractor.

in such networks, activity among excitatory cells results in inhibitory feedback.


DropConnect is slightly different from dropout, in that the dropout mask is independently sampled for each weight instead of each activation.

our analysis is based on a simple assumption that, in order to reduce the interference of noise, the training process will try to maximize the signal-to-noise ratio (SNR) of representations.


This generative model for transformed images has a number of attractive properties.

lastly, the partial derivatives of the objective function have a simple form that may be computed efficiently.


Alternative computational models from dynamical systems theory [4] argue that fading memory properties of neural circuits are essential for real-time processing of quickly varying visual stimuli.

in all cases, the performance reached its maximum shortl y before or during the presentation of the second letter.


For each range image in our database, a low-resolution (but still full-sized) range image, z low , was generated by setting to zero the top two steerable filter pyramid layers.

average size of these textures was 172,669 pixels per image.


Learning and anticipation are central features of cerebellar computation and function (Bastian, 2006): the cerebellum learns from experience and is able to anticipate events, thereby complementing a reactive feedback control by an anticipatory feed-forward one (Hofstoetter et al., 2002;Herreros and Verschure, 2013).

after having established the gradient descent algorithm, we can implement the same rule in an on-line manner, dropping the repetitiveness assumption inherent to trial-by-trial learning and performing all computations locally in time.


These MUDs have good convergence properties and do not need a training sequence to decode the received bits, but they need large training sequences before their probability of error is low.

most of last generation digital communication systems such as Global Positioning System (GPS), wireless 802.11b, Universal Mobile Telecommunication System (UMTS), etc, may take advantage of any improvement on this topic.


We saw in Section 2 that the solution to the Lasso can be easily computed once the active set and signs of the coefficients are known.

hence, our algorithm is well suited for compressive sensing with sequential and noisy measurements.


(3.2)) and sampling on the right (where we plot cj , the output of our Langevin sampler; see Eq.

the other focuses on the present odors, and requires a comparison between the posterior probability inferred by an animal and neural activity.


We first give a generalization of the concept of Shannon entropy to general (both adaptive and nonadaptive) policies.

we can apply a known result for optimizing adaptive monotone submodular function [2] to obtain Theorem 4.


In general, there may be many different graphs which match any subset of all pairs effective resistances, and hence many minimizers to our optimization problem.

in general, the problem is non-convex and does not admit an obvious polynomial time solution.


Our model could be extended in a number of ways.

the dynamics of objects moving in continuous trajectories through the world over short epochs will be encoded in the population activity of the phase variables φ i .


In this paper, we consider the inverse of the above problem.

this means that we should rescale each column: for some α ∈ R Y , such that B1 = 1.


These models are shown to be extremely efficient when training and test data are drawn from the same distribution.


To this end, we define a pseudo-LDS, which pairs a subspace-restricted linear model of the impulse response with an autoregressive model: Definition 2.

in the next section, we survey local search algorithms that either only converge to local optima or require an exponential number of iterations in the worst case.


Therefore, we can set the values of K • u much larger than the theoretical values without compromising the quality of approximation.

as we can see, in this case RDP converges quickly on high-quality results and exhibits the desired diminishing returns property of anytime algorithms-the quality gain is large initially and it diminishes as we continue to refine the discretization.


. . , x sK ) for some covariance function κ : R K × R K → R. We propose to combine these two different explanations of the data into one coherent model.

non-iid observations due to hidden confounding variables may hinder accurate recovery of the true network structure.


The goal of training is then to adjust the parameters Θ = {θ l } L l=1 in order to minimize a given loss over the training set of inputs.

these connnections are trained to approximately invert the computation of the feedforward connections in order to be able to compute target activities for each layer by successively inverting the desired output target.


Placing a weight d i on each sample, we could optimize the sum F (d) = m i=1 d i Fi and obtain a tractable optimization problem.

although left for future work, we suspect that the same techniques we present here can also be extending to these other cases, potentially providing a wide range of analogous results that still apply under off-policy sampling.


Optimal scale estimation procedures is particularly important when the variance of an estimator is so large that convergence is unlikely.

experimental Setup Because we follow the experimental setup of Burda et al.


Like the region term, the object term is defined by a logistic function that maps object features φ o : P o , v hz , I → R n to probability of each object class.

in this phase, the algorithm behaves exactly as in [7] by iteratively proposing re-assignments of pixels to regions (variables R) and recomputes the optimal assignment to the remaining variables (S and v hz ).


4 can improve significantly (in terms of the constants) depending on the regularity of the loss function: smoother loss functions will result in "simpler" learning problems and vice-versa.

the main technical aspect is to show that regularity provided by Asm.


The simulations were performed on graphs with p = 100 nodes, expected neighborhood size of s = 10, sample size n = 300, and (1) , (2) ∼ N (0, 1 p ).

in the finite sample regime we conjecture Assumptions 4.1 and 4.2 to be weaker than the faithfulness assumption: violations of faithfulness as well as of Assumptions 4.1 and 4.2 correspond to points that are close to conditional independence hypersurfaces [39].


To be complete, understanding of sensory plasticity must come at two different levels.

we used a PFA-based simulation to verify that the distributional importance-weighted sampling procedure described here is indeed able to learn the correct model given sensory and reinforcement-value data.


We revisit from a statistical learning perspective the classical decision-theoretic problem of weighted expert voting.

the inability of Hoeffding's inequality to guarantee consistency even in such a felicitous setting is an instance of its generally poor applicability to highly heterogeneous sums, a phenomenon explored in some depth in [23].


Another way to view this is to think of a pair of opposite -polarity "basis vectors" sharing the same coefficient α t . The most closely related potential function technique to ours is that of SVMs [9], where the classification margin (and thus the bound on generalization) is maximized by a simultaneous optimization with respect to all of the training points.

in contrast to SVMs, however, we offer an on-line and incremental learning machine for building kernel discriminants whose complexity (number of kernel evaluations) can be directly controlled (traded off for accuracy).


We first consider the basic proximal-gradient method in the convex case: Proposition 1 (Basic proximal-gradient method -Convexity) Assume (H) and that we iterate recursion (3) with y k = x k . Then, for all k 1, we have with The proof may be found in [29].

for example, we can establish that inexact proximalgradient methods converge under some closedness assumptions on the mapping induced by the approximate proximity operator, and the assumption that the algorithm used to compute the inexact proximity operator achieves sufficient descent on problem (2) compared to the previous iteration x k−1 [16].


The variance parameter for the critic output distribution can be absorbed into the learning rate parameter for vanilla Gauss-Newton.

but to avoid instability in training, it is often beneficial to use an architecture where the two networks share lower-layer representations but have distinct output layers [17,27].


First, participants in 2 l moons U h did not learn the manifold while those in 4 l moons U h did, even though the two conditions have the same ǫNN highlighting.

(single-h) a single horizontal linear boundary.


Very recently, [14] compressed the word embeddings computed by the word2vec algorithm and applied to similarity/analogy task and Question Answering.

for experiments using BLEU scores as performance measure, we report results when the BLEU scores achieved after compression is within 3 percent difference from original score.


Recently, a growing number of researchers have argued for a probabilistic approach to vision, in which the functioning of the visual system is interpreted as performing Bayesian inference in latent variable models, see e.g.

olshausen and Field suggested [12] that the firing rates of the neurons correspond to the maximum a posteriori (MAP) estimate of the latent variables, given the image input: An important problem with this kind of a MAP representation is that it attempts to represent a complex posterior distribution using only a single point (at the maximum).


Let T n denote the family of all multi-class decision trees with n internal nodes in dimension d. In Appendix J, we derive the following upper bound on the Rademacher complexity of T n : All of the experiments in this section use T n as the family of base hypothesis sets (parametrized by n).

assume that Φ is twice differentiable and that Φ (u) > 0 for all u ∈ R. Then, the projected coordinate descent algorithm applied to F converges to the solution α * of the optimization max α≥0 F (α) for F = F sum , F = F maxsum , or F = F compsum .


Here we explain how they can be appropriately chosen from data samples.

since KMM can only estimate the values of the importance at training input points, it can not be directly applied in the CV framework; an out-of-sample extension is needed, but this seems to be an open research issue currently.


None of the methods we have proposed will work well for high-dimensional, approximately factorial distributions that have exponentially many modes formed by the cross-product of multiple lower-dimensional distributions.

as a result, the relative energies of data points in different modes can be completely wrong without affecting the learning signal given by equation 3.


For the same reason, there might be no (conditional) dependence between W and a possible unmeasured common parent of X and Y .

[16] derives analytical bounds under (3) given a fixed, numerical value of w . We know of no previous analytical bounds as an algebraic function of w . In the Supplementary Material, we provide a series of algebraic bounds as a function of our free parameters.


We call these critical state-action pairs, Crit(P ) := {(i, a) : a / ∈ O(i; P, A) ∧ (∀ > 0, MakeOpt(i, a; P, ) = ∅)} .

if we keep exploring and never exploit the knowledge accumulated, we will not behave optimally.


The running times are discussed in Appendix G.2.

by the law of total covariance, the covariance in ( 6) has the form where the last equality follows by the multilinearity property of cumulants (see Appendix C.1).


This paper addresses a single shortcoming that (with the exception of stereo) is shared by most active range acquisition devices: Namely that range is captured at much lower resolution than images.

the details of the CG algorithm are omitted for brevity, but can be found in contemporary texts.


In fact, if f ✓ is a bijection between samples in high probability regions, then f 1 ✓ is automatically also such a bijection.

intuitively, if (x, v) lies in a high probability region, then both f ✓ and f 1 ✓ should propose a state in another high probability region.


Following [13] (see also [30] and references therein), Lemma 1 can be improved under very mild assumptions on the strategies.

we want the sample complexity E µ [τ ] to be small.


By exploiting convex duality of the sub-problems and eigenvector properties, a solvable convex formulation of the problem can be derived that preserves solution equivalence to the original.

for the bundle method we developed, whenever the size of B is larger than a given constant b, we will keep the active points of B that correspond to the first b largest α values, and drop the remaining ones.


This term can offset the L 1 term by co-activating voxels that are spatially nearby.

the model displayed good performance in predicting the scored ratings for the three subjects in test data sets, and a variant of this model was the third place entrant to the 2006 PBAIC.


To the best of our knowledge, this is the first algorithm in machine learning that directly constructs a convex relaxation for a bi-level optimization based on the inner optimality conditions.

we next detail the solution to the former, relegating the latter to Appendix D. Given M , we optimize over (π, θ, γ, v) by projected LBFGS [33].


This bound is very similar to bound obtained in Theorem 1, and says that the function f is robust, as long as the eigengap between the second and third eigenvalues is sufficiently large for G(X) and G − (x), and the second eigenvalue does not change significantly if we slightly perturb the distance threshold used to determine whether an edge exists in the graph in question.

is there a way to construct a graph such that the neighborhood structure of the graph captures the neighborhood of datapoints with respect to the metric in question?


This dynamic programming algorithm can be viewed an application of the Viterbi algorithm.

when the functions f i are convex, Theorem 3.6.


Definition 4.1 (Normal scores rank correlation coefficient).

when X and Y are jointly multivariate Gaussian distributed, this problem becomes analytically tractable.


Let ∂ K L(α, •) denote the gradient w.r.t.

suppose now we are only given an indefinite kernel matrix K 0 ∈ S n . Luss and d'Aspremont [15] proposed the following max-min approach to simultaneously learn a proxy PSD kernel matrix K for the indefinite matrix K 0 and the SVM classification: Let For simplicity, we refer to the following function defined by f (α) = min as the objective function.


In addition, p 2 = 1 − p and µ 2 = β 4 w 2 = ( 1−pα 2 1−p ) 2 p 2 α 4 η 2 ≤ p 2 α 2 σ 2 4(1−p) 2 .

let φ : R d → R * + be a strictly positive weight function such that E[φ(X)] = 1.


The analysis of AIDE is equivalent to that of Grosse et al.

a meta-inference algorithm is considered accurate for a given x if r(u; x) ≈ q(u|x) for all u.


. . , x n , represented as vectors in X = R d , and the binary similarities S(x i , x j ) between the points, with +1 corresponding to x i and x j being neighbors and -1 otherwise.

we are given the entire similarity mapping S, e.g.


The separation isn't perfect as W becomes negative where the common input correlation is positive and U becomes negative where the direct input correlation is positive.

the system of equations is well-posed because the W j p1 W  q2 appear in the same combination for each of the three equations at a given delay.


Hence, the work in [14] most closely resembles our work, but has the major drawback of requiring paired training data.

we explore two regularizers to address these requirements.


2 In this case, we use a simple estimate for the base station position, that is the average of the 3 calibration points x i with maximum signal strength y i .

2.1, which clearly does not fit the propagation law of radio signals.


In the wake of the success of TS in these online learning problems, a natural question is whether and how TS can be applied to dueling bandits to further improve the performance.

in addition, for a Copeland winner i * ∈ C, let L C = K j=1 1(p ji * > 1/2) be the number of arms that beat arm i * .


Each S ∈ S in objective ( 13) must be S = {j} for some j ∈ V. The objective then becomes f (u) = ∑ j∈V w {j} u j + const, a form of standard VC.

we seek a labeling l where l i ∈ L ∪ ⊘ identifies the line (and vanishing point) that edge i belongs to, or assigns outlier label ⊘.


We now wish to generalize the results to the population of the United States (U.S.), but we find the distribution P (x, y, z) in LA to be different from the one in the U.S. (call the latter P * (x, y, z)).

we also consider issues relative to the variance of the estimand aiming for improving sample efficiency and increasing statistical power.


This model assumes that only pairwise (or second-order) correlations exist between the representations of different items.

the minimal color change condition taps the conditional probability of the memory for the target given the memories for the distracters, p(ŝ t |ŝ −t = s −t ) where −t represents the indices of the distracter items, because the actual dis- tracters s −t are shown during test.


Shifting regret is a more general notion of regret, where the learner is compared to a sequence of comparators u 1 , u 2 , .

at the largest scales, Naïve Bayes approaches offer a simple, easily distributed single-pass algorithm.


As expected, with increasing α the model complexity drops significantly while the model performance also deteriorate gradually.

for an m-layer network, the time complexity of collecting the best action combination is O( ∏ m 1 n i ), which is NP-hard and unacceptable for very deep architectures such as VGG and ResNet.


2 Below, we describe a method which makes heavy use of this information.

. . , v r } lies in the span of the data points, i.e., P = is the kernel matrix and r ≤ m is the number of nonzero eigenvalues.


Sparse embeddings have three key advantages: a) they reduce prediction time, b) reduce the size of the model, and c) avoid overfitting.

increasing the number of clusters beyond a certain limit might decrease accuracy as the error incurred during the cluster assignment phase itself might nullify the gain in accuracy due to better embeddings.


So a generative mechanism would keep sampling the functions and deliver them when the conditions hold true.

it has a 1/poly(γ (1) ) dependence which could be bad if γ (1) is too small: intuitively, if γ (1) is too small then you will wait for a long time in step 2 of Algorithm 1 for β t−1 to decrease without proceeding to f (2) , incurring large regret (f + B) in the process.


We have seen that GE operators can strengthen deep residual network architectures.

for this experiment, we train both a baseline ResNet-50 and a GE-θ model (with global extent ratio) from scratch on ImageNet using a fixed 100 epoch schedule.


The general algorithmic goal is to find a subset of points that maximize diversity, while obeying a cardinality (or more generally, matroid) constraint.


To show the linear time and space complexity, recall that the differentiation w.r.t.w k,j can be efficiently computed by back-propagation in a top-down pass of S once we have computed τ S t=1 c t u t in a bottom-up pass of S. Remark.

this is not the case for SPNs, where the effective number of mixture components is τ S = Ω(2 H(S) ), which also depends on the input network S. To simplify the notation, for each t ∈ [τ S ], we define c t n i=1 p t (x i ) 1 and u t w p 0 (w) (k,j)∈T tE w k,j dw.


Note that the standard graph-Laplacian formulation sets d = m. (e) Y : μi = |Y T v i | if i ≤ d; 0 otherwise.

we consider a feature transformation of the form ψ(x) = S 1/2 ψ(x), where S is an appropriate positive semi-definite operator on H. The following result establishes an equivalent feature space formulation of the semi-supervised learning method in Figure 1.


For an operator to be orthogonal, it must preserve the L 2 norm of its inputs.

the same operation with walk cycles of pedestrians is not defined.


The second remark is about the rates of convergence.

we establish tight risk bounds for the SFDS, which are nearly as strong as those proved for the Lasso and the Dantzig selector in the case of known σ * .


If x is already 'contained' in the tree T , i.e., if x 2 B x j for some leaf j 2 leaves(T), then the prediction is taken to be G leaf(x) .

update extent of node j 12: if j / 2 leaves(T) then .


Furthermore single-linkage algorithms are known to provably recover a ground truth clustering if the similarity function has some stability properties [6].

let G i,j be a subgraph of G with vertex set V i ∪ U j containing any edge (v, u) ∈ E(G) where v ∈ V i and u ∈ U j .


The observed aggregate signal is assumed to be the sum of the component signals so that Y t = I i=1 X it + t where t ∼ N (0, σ 2 ).

given p S (S), the map f naturally introduces another prior for τ , which is an induced prior denoted by p * τ (τ ).


The decentralized sensing problem argued in this paper was first addressed by Berger and his collaborators.

in Section 2, we introduce a system model for the sensor network.


our complete model is thus where µ and K are the GP mean and covariance kernel, λ * is a positive scale parameter, and σ(x) = (1 + exp(−x)) −1 .


They capture the semantic similarities of the words, and they also serve as the input into the amortization networks.

we develop two sharing strategies: hierarchical modeling and amortization.


When α = 0, we obtain (1), while when α → ∞, we essentially solve a structured classification problem based on the expert's data [13].

the optimization is formulated in a way that permits mistakes in the demonstrations provided by the expert, and also accommodates variable availability of demonstrations (i.e., just an initial batch or continued demonstrations).


In Figure 3(right), we again observed divergence of the gradient off-policy update on state-action values in the primal, and the convergence of all the dual algorithms (see Figure 3).

for the same reason as before, we chose the bases for the algorithms randomly.


For I i ∈ I i we denote by A(I i ) the set A(h) and by P (I i ) the player P (h) for any h ∈ I i . I i is the information partition of player i; a set I i ∈ I i is an information set of player i.

at each information set, we sample an action uniformly randomly with probability and according to the player's current strategy σ t . Through experimentation we found that = 0.6 worked well across all games; this is interesting because the regret bound suggests δ should be as large as possible.


Another paradigm that appears to share many features of the 2AFC task is the Go/NoGo (GNG) task [6], (see Luce [5] for a review), where one stimulus category is associated with an overt Go response that has to be executed before a response dead-line, and the other stimulus (NoGo) requires withholding response until the response deadline has elapsed.

various versions of augmented DDM have been used to fit GNG behavioral data, with one variant in particular suggesting that the decision threshold in GNG ought to be higher than 2AFC [2], in an apparent contradiction to our model's predictions (Figure 4).


Both tests suggest the competitive nature of the proposed O(n) procedure, while clearly showing the benefit of using function estimation (as e.g.

when asserting this for a number n v ∈ N of samples X ∼ P X with n v → ∞, a misprediction would occur less than δn v times.


The lower panels demonstrate the robustness of the methods on highly noisy (large σ) data, in which case the estimated errorbars become significant, but the performance degrades only slightly.

biophysically accurate models of single cells are typically formulated compartmentally -a set of first-order coupled differential equations that form a spatially discrete approximation to the cable equations.


An ordering on the variables is called causal if it is consistent with the ground truth causal DAG.

since that work considers a non-parametric approach, it is restricted to general independence tests among distributions, which may not have high efficiency.


The idea of using Q-values for multiple goal arbitration was independently introduced in [10] and [11].

since the Q-tables were trained under the assumption of perfect state information, they will be somewhat inaccurate under conditions of partial observability.


In the case of Figure 3 (c), the convolution is still a skewed one, but the scale of this skewness is less than the original ones.

figure 5 (b) shows the theoretical and empirical probability of underestimation Pr( V π + (s 1 ) < E V π + (s 1 )).


Future work can possibly overcome this limitation by backpropagating the error through the network modules.

the modular networks use conventional natural language parser [21] to obtain a network layout for composing the network architecture [11].


[12] propose an interpretable neural network architecture whose predictions are based on the similarity of the input to a small set of prototypes, which are learnt during training.

r n the decoder associated with h, and x := h dec (h(x)) the reconstruction of x, we use an additional penalty L h (x, x) on the objective, yielding the loss: ) Achieving (iii), i.e., the grounding of h(x), is more subjective.


Except in highly contrived situations, this type of correlation will always exist.

beamformers and sLORETA are basically linear methods with no issue of global or local minima.


6 shows that we do not need to be limited to exactly 11 reference contexts, either fewer or more than 11 can be used.

the inverse dynamics problem for a robotic manipulator is to compute the torques τ needed at the joints to drive it along a given trajectory, i.e.


We also observe that our method helps an agent ignore known small (deceptive) rewards, and discover alternative ways to obtain the optimal reward.

its search range covers only a small proportion of the state space.


This upper bound can in turn be bounded by a quantity that is feasible to calculate: max x f(x)-(B* f) (x) = maxxmin a f(x)-(Ba f) (x) :S min a max x f(x)-(B a f)(x).

in the spirit of [7,8,6]  The main benefit of this factored representation is that it allows large MDPs to be encoded concisely: if the functions Ra,r(xa,r) and P(X~IXa,i) depend on a small number of variables, they can be represented by small tables and efficiently combined to determine R(x, a) and P(x'lx, a).


We used the IBM Almaden association and sequential patterns generator to create this dataset [17].

2a and the "probabilistic object model" (POM), explained in the previous section.


If the functions f t (x), t ∈ D, are convex, then D e f t (x) dt is convex.

an identical derivation yields the optimal q(ξ|y) ∝ exp log p(x, ξ|y) x ∝ p(ξ) exp log p(x|ξ) x when q(x|y) is fixed.


To account for this, states are defined over time intervals, i.e.

a histogram is first computed for each image in the sequence and the distance between successive histograms is used as a measure of local activity.


Very recently, optoelectronic reservoir computers have been demonstrated by different research teams [10,9], conjugating good computational performances with the promise of very high operating speeds.

in addition an input mask m i is applied to the input u(n), to enrich the reservoir dynamics.


The noise processes are i.i.d Gaussian: for any ¡ .

the distributions are very peaked and we are simply tracking the mode.


This line of research is sometimes referred to as learning to rank [11].

consistency is a desirable property for GMMs.


In this work we show that the convergence rate of the SVRG algorithm can be preserved even under an inexact approximation to the full gradient.

the first component is maintaining the list of non-support vectors at x s . we maintain a list of examples i where f i (x s ) = 0.


In the supplementary material, we discuss an example of continuous influence maximization [26] that uses continuous and infinite action space while the number of base arms is still finite.

in both studies, the regret bounds contain an undesirable factor of 1/p * , where p * is the minimum positive probability that any arm can be triggered by any action, 1 and this factor could be exponentially large for both influence maximization and cascading bandits.


As rate increases, the local manifold structure is revealed, and the slope yields its intrinsic dimension.

3(b) and (c), which show training and test dimensionality estimates for r = 2 and r = ∞, respectively.


The covariate model (2) was proposed by Johnstone and Lu [JL04] and has been extensively studied in statistics and random matrix theory.

maximizing the second process leads (after decoupling the term x, v 0 y, u 0 ) to two separate problems, one for the vector x, and the other for y.


Secondly, we define the entropy over the entire batch Module collapse would correspond to a low H b .

our algorithm learns to use a variety of modules without such a modification and we show that training is less noisy compared to baselines.


(The MSE results did not stay the same because the image completions happened over different subsets of the pixels.)

two sub-region nodes (whose scopes form the partition) are then added as children to the partition node.


Two core problems in the learning framework, matching of image patches and finding salient parts, are formulated as two instances of the problem of finding maximal cliques with hard constraints.

we aim at solving the discrete subgraph selection problem by employing the recently proposed extension of particle filter inference to problems with state permeations [20].


The proof of Lemma 1, given in Section A.3, primarily involves establishing a uniform deviation result; if we let P denote the feasible set for (1), then we wish to show that | Ã − B, M | ≤ 1 2 αβkn for all M ∈ P. This would imply that the objectives of (1) and ( 6) are essentially identical, and so optimizing one also optimizes the other.

the optimization problem (1) therefore chooses a set of βm items in each row to maximize the corresponding values in Ã, while constraining the item sets to have low rank (where low rank is relaxed to low nuclear norm to obtain a convex problem).


Unfortunately this requirement is not met in our scheme as if we only receive the reward for the selected arm -a partial reward feedback scenario.

each function has an optimum f * c = max ∀x∈X f c (x).


Various modifications of RLS are made to improve its performance either from the viewpoint of manifold [1] or in a more generalized form [7,11].

( 4) is a constant, then there is a new Representer Theorem; (2) The same conditions become a sufficient condition under which constant functions should not be penalized; and (3) under the same conditions, a function belongs to the null space if and only if the function should not be penalized.


For input bits In principle, this allows to relax the effective resolution of the ADC.

digital-to-analog conversion at the input interface is inherent in the bit-serial implementation, and row-parallel analog-to-digital converters (ADCs) are used at the output interface to quantize .


Neural Fictitious Self-Play (NFSP) is an implementation of fictitious play, where approximate best responses are used in place of full best response [32].

the main limitation with these classical works was scalability: there was no direct way to use function approximation, and empirical analyses focused almost exclusively on one-shot games.


Furthermore, the selection properties are comparable to the Lasso [8].

this framework is not limited to marginal screening and can be applied to a wide a class of model selection procedures including greedy algorithms such as orthogonal matching pursuit.


( 1), right] in the essentially same way as the standard BP deals with block-angular sparsity of J [see Eq.

since mlu − dn = dF (CA + nB) − d(F CA + nB) = d(F − 1)nB, Pearlmutter's method can be up to F times faster than Algorithm 2.


We denote with K n = Φ T n Φ n the empirical kernel matrix with entries [K n ] i,j = k i,j .

in the 1/ √ n risk rate setting Gaussian projections would require ν = 1/ √ n resulting in m ≥ n log(n) random features, which would not bring any improvement over computing K n . Moreover when D is infinite, as it is usually the case in the non-parametric setting, the JL projection is not explicitly computable in general and Biau et al.


For mammals, the bulk of visual processing for motion is thought to occur in the cortex, and the motion energy model is one of the dominant models [2] [3].

given the possibility of combining the position and phase tuning mechanisms, an interesting question is how these two mechanisms might be exploited when constructing populations of motion energy neurons.


The joint probability of preferences can thus be represented as a completely disconnected CDN with logistic functions in which all pairwise object preferences are treated as being independent.

one possible concern here is that we may require a fully connected CDN topology over all possible pairwise preferences between all nodes in order to capture all of these dependencies, leading to a model which is cumbersome to learn.


Given the same k, the model with a larger s performs better.

., which eventually converges to 3 2 as n → ∞.


the proof is deferred to the full version.


For Ŷ = max( Ŵ ⊺ X, 0) being the retrained layer response, Ŷ − Y F ≤ .

finally, in Section 6, we report some retraining experiments using the Net-Trim and conclude the paper by presenting some general remarks.


The knowledge tracing problem is inherently difficult as human learning is grounded in the complexity of both the human brain and human knowledge.

the main contributions of this work are: 1.


We can interpret LMT as an interpolation between the original function, which is highly expressive but extremely non-smooth, and constant functions, which are robust and smooth.

carlini and Wagner [6] showed that we can create adversarial perturbations that deceive networks trained with defensive distillation.


We interpret k to be a latent variable that signals the hidden cause of the underlying input distribution, with distribution P k . Critically, we assume that the hidden variable k changes slowly compared to the inter-spike period of the neuron.

biophysically synaptic efficiency in the brain is more closely modeled by spike timing dependent plasticity (STDP).


While the proposed formulation reduces the computational complexity of enforcing order constraints, it is entirely independent of the regularizer that is minimized (under these constraints) while learning the optimal ranking function.

as illustrated in Figure 1, the formulation is more general and does not require a total ordering of the sets of training samples A j , i.e.


Nowadays the concept of tomography has gained wider meanings and the idea applies, in different forms, to many kinds of communication and transportation networks [11,12,13].

the corresponding probability distribution may depend on the length of the path, i.e.


For such a model with large m, the number of tetrads involved in our testing methodology is so large that even after taking the supremum norm one shouldn't expect (3.5) to hold; for example, when m = 50, the dimension of Θ is 2• 50 4 = 460600, and one should be skeptical about the validity of (3.5) when we only have the sample size n = 250.

while we have defined X as a set of nodes, it will be convenient to abuse notation slightly and let X also denote a random vector (X 1 , .


We provide some insights on this by constructing model misspecification artificially.

compared to the two-stage estimator, the joint estimator estimates the workers' parameters based on both the control items and the target items, even though their true labels are unknown.


the robot randomly samples a poke direction (θ) and length (l).

this is not a general way of learning task relevant features and it is unclear whether features adept at object recognition are also optimal for object manipulation.


This interpretation makes it easy to formulate a cost: given any x ∼ P G (x), we want P G (c|x) to have a small entropy.

the goal is to learn a generator distribution P G (x) that matches the real data distribution P data (x).


We assume the noise in the observations is zero mean and normally distributed, i.e.

the Kalman filter reconstructions of hand trajectories in off-line experiments are more accurate than previously reported results and the model provides insights into the nature of the neural coding of movement.


From the data, the distribution families (µ 1 , Σ 1 ) and (µ 2 , Σ 2 ) can be estimated.

due to uncertainty, any attempt to behave "optimally" in the world must take into account plausible alternative models.


Our main convergence results are also readily generalized to stochastic target policies by replacing the sub-sampling process described in Section 2 with a sample-weighting process.

., which we can break into causally related 4-tuples, (s 1 , a 1 , r 1 , s 1 ), (s 2 , a 2 , r 2 , s 2 ), .


This policy is explicitly not safe to use throughout the state space X \ S x 0 .

we extend control-theoretic results on Lyapunov stability verification and show how to use statistical models of the dynamics to obtain high-performance control policies with provable stability certificates.


Since every subset of a permitted set is permitted, that means there are no forbidden sets and the network is monostable.

theorem 3 For nonoverlapping groups, the top c groups with the largest group input could end up the winner depending on the initial conditions of the dynamics, where c is determined by the equation BC 2' : Proof sketch: Suppose the ath group is the winner.


edu/sceneunderstanding/ In conclusion, we have proposed and evaluated the first model and learning algorithm for scene understanding that exploits rich relational information from the full-scene 3D point cloud.

∀i, j, l, k : Note that the products y l iy k j have been replaced by auxiliary variables z lk ij .


An extension of the classical CM sketch that works well in practice is conservative updates [11]; in our setting, we observe one token at a time, and so the conservative update is equivalent to simply incrementing the minimum counter(s).

for all finite, measurable partitions A 1 , .


To measure the convergence of representations through training time, we computed the projection weighted mean CCA value for each layer's representation throughout training to its final representation.

as in [22], a neuron activation vector denotes the outputs a single neuron z has on X.


Among a large set of hyperparameters and across 7 different GAN objectives, we notice a conspicuous increase in FID score as GILBO moves away from ∼ 11 nats to either side.

they require a tractable posterior, preventing their use with most GANs.


6) is maximized when f * = µ * and f = f map .

5), which provided a very slight improvement in prediction accuracy.


kernel (2) such that the Gaussians in the kernel expansion (3) are highly localized.


They derive asymptotic (as the time horizon grows large) instance-specific regret lower bounds and propose algorithms achieving this minimal regret.

our problem includes classical, linear, unimodal, dueling, and Lipschitz bandit problems as particular examples, see Section 3 for details.


The state decoder is applied to both encoded state codes (for auxiliary encoding loss) and predicted state codes (for prediction loss).

we still do not have a system for physical reasoning that can approach the abilities of even a young child.


Here, D is the amplitude of Gaussian noise.

the relation between the propagation speed and network structure is not well understood.


Other prior work learned monotonic functions on small datasets and very low-dimensional problems; see [2] for a survey.

flexible monotonic functions are computationally challenging to learn beyond a few features.


Furthermore, MoM algorithms only make a single pass over the training data, are highly parallelizable, and always terminate in polynomial time.

this approach, outlined in Algorithm 1, is an alternative to the ones presented in the literature up to now (even though in the noiseless, realizable setting, it will provide the same Algorithm 1 SIDIWO: Simultaneous Diagonalization based on Whitening and Optimization Require: M 1 , M 2 , M 3 , the number of latent states l 1: Compute a SVD of M 2 truncated at the l-th singular vector: results).


none of the above give results that are truly sparse in time; and all of the above have to go to some lengths to obtain reasonable cell segmentations: [13,4] recur to heuristic post-processing, while [3] invokes structured sparsity inducing norms and [15] use an additional clustering step as initialization.


Suppose the initialization point is uniformly sampled from [−1, 1] d . There exists a function f defined on R d that is B-bounded, �-gradient Lipschitz and ρ-Hessian Lipschitz with parameters B, �, ρ at most poly(d) such that: 1. with probability one, gradient descent with step size η ≤ 1/� will be Ω(1) distance away from any local minima for any T ≤ e Ω(d) .

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


This phenomenon also occurs for a special class of DAGs, which we call single-overlap graphs.

the first or second order method can be applied to directed graphical models as long as the number of parents is reasonably small.


We introduce a mathematical model for studying representative democracy, in particular understanding the parameters of a representative democracy that gives maximum decision making capability.

for a voter-competence distribution F , the representative democracy with group competence function µ is consistent if and only if there exists K * ∈ N such that µ(K * ) > 0.5.


Unfortunately, this is generally a #P-hard problem, which was shown to be the case even for Ising models by Jerrum and Sinclair [17].

more formally, F is submodular if, for any S ⊆ T ⊆ V , and any v ∈ V \ T , it holds that F (v|T ) ≤ F (v|S).


Then the permutations are generated randomly as follows: choose one of the n objects to be ranked 1 at random, where object i is chosen to be ranked 1 with probability w i /( n j=1 w j ).

given the nature of the topic, there are a lot of exciting lines of research done over the past century and we shall not be able to provide comprehensive coverage due to a space limitation.


While causal power and I:!.P were each capable of capturing certain trends in the data, causal support was the only model capable of predicting all the trends.

it is important to note that the responses of the human subjects in columns 8-10 (contingencies {l.00 , 0.50} , {0 .80 , 0.40} , {0 .40, O.OO}) are not quite consistent with the predictions of flP : they show a slight V-shaped non-linearity, with P( C -+E) judged to be smaller for 0.80 , 0.40 than for either of the extreme cases.


The term compares the current firing rate g(u i (t k )) with its average firing rate 2 ḡi (t k ), and simultaneously the running average ḡi (t k ) with the constant target rate g. The argument indicates that this term also depends on the optimization parameter γ.

we rewrite L 12 as a sum over the contributions of the individual time bins, The weight change ∆ wk 1j is then proportional to the gradient of this expression with respect to the weights w 1j , i.e., ∆ wk 1j = α(∂∆L k 12 /∂w 1j ), with some learning rate α > 0.


The last term (modulated by η) is not strictly necessary for consensus but introduces additional regularization.

this now leads to the final distributed consensus learning formulation, similar to [10]: where we marginalized on X.


(See the supplementary material for comparisons to some other recent methods).

note that since the normalization is global, it does not compensate for variations due to shading.


It then learns their true distance, and aims to minimize its squared loss.

after it observes the contexts x t i at round t, it uses these to derive upper confidence bounds on the expected rewards, corresponding to each context -represented as a vector rt .


Under the assumptions [A1],[A2], for a smooth test function φ, the MSE of SVRG-LD (in Algorithm 2) at time K = hT is bounded, for some C > 0 independent of (T, h) in the following manner: The result in Theorem 3 is qualitatively equivalent to that in Theorem 2 when m = N/n .

h t is set in such a fashion that This provides an approximation to a first order Langevin diffusion, with dynamics where U is the unnormalized negative log posterior.


Table 1 shows the RMSE over the test set of the different matrix completion methods.

in many cases one cannot measure all pair-wise distances between objects, resulting in an incomplete Euclidean distance matrix and hence an incomplete kernel matrix.


In fact, under DBM, ε-greedy and KG have close performance in the overall model agreement.

our results indicate that all decision policies considered here capture human data much better under the dynamic belief model than the fixed belief model.


It simulates particle movement along the contour lines of a dynamical system constructed from the target density.

the stationary distribution of the chain remains correct, given that we take care when adapting the surrogate.


We compare the efficiency of the three screening rules on the same prostate cancer data set in Table 2.

sAFE takes much longer time even than the solver.


A new image is formed in which each pixel is the mean of an m by m block of the original image.

at the same time, we suggest that statistical methods still have much to learn from constraint-based methods.


Thus we start by calculating these eigenvectors, and cycle through them one at a time.

following [1,2], we fitted lines to the plots, modeling the variance as var ¡ ¤£ ¦¥ mean § .


Notice that, in sharp contrast to the nearest neighbors-based methods, which first fix the number of neighbors or the neighborhood radius and then compute the weights between points in each neighborhood, we do the two steps at the same time.

first, we consider the problem of clustering and embedding of face images of two different subjects from the Extended Yale B database [22].


This framework is based on a free energy (negative log marginal likelihood) and can be seen as a generalization of adaptive TAP [1, 2, 3] and expectation propagation (EP) [4,5].

we cannot expect that message-passing algorithms similar to loopy belief propagation or expectation propagation (EP) [4] which sequentially update moments and Lagrange parameters are guaranteed to converge.


As shown, it appears that the fan-in to node f i will be ℓ and thus will grow without bound.

the columns M1 and M-HMM correspond to the model that is used to initialize the model in the corresponding row.


For this reason, we resort to Chebyshev-like inequalities and we propose the following concentration bound derived from Cantelli's inequality and customized for the IS estimator.

preventing uncontrolled updates in the space of policy parameters is at the core of the natural gradient approaches [1] applied effectively both on PG methods [18,33,63] and on PGPE methods [26].


However, one important aspect of human visual perception is that it is not space invariant: the fovea processes visual information with high spatial detail while regions away from the central fovea have access to lower spatial detail.

all video clips were rendered at 1024 × 760 pixels (22.5 deg ×16.7 deg) and a frame rate of 24fps.


This means that compared to GD, SGD can filter out global minima with large non-uniformity.

for very small batch size, say B = 4, the non-uniformities for both datasets are significantly lower than the predicted upper bound.


Here, π(j) ⊆ {1, ..., j − 1}, and w j is the set of parameters defining conditional distribution j.

any convex relaxation of (1) that uses a distribution q y over missing values and does not make arbitrary distinctions can never do anything but produce a uniform distribution over the hidden variable values.


A natural representation on these unknown weights is via Dirichlet distributions, since Dirichlet distribution is the conjugate prior of a general discrete probability distribution.

if the algorithm is guaranteed to converge in the limit (as explained in Section 3.5, this holds for our DNG-MCTS algorithm), it is convenient and reasonable to approximate X s,π as a Normal distribution.


We say that γ low is a lower bound on the local convergence rate if γ high ≥ γ low holds for all upper bounds γ high .

we consider a specific utility model (exponential utility), but our bias and convergence analysis immediately carry over if we assume that each trader is optimizing a risk measure (rather than an exponential utility function) similar to the setup of Frongillo and Reid [9].


This demonstrates the potential of CIGAN to learn meaningful state abstractions without requiring a distance function in observation space.

the probability of the next state s is finally given by: We emphasize that there is not necessarily any correspondence between the action vector a and the real actions that generated the observation pairs in the data.


Also, it converges faster than MCMC because its update rule is deterministic and leverages the gradient of the target distribution.

1, we show the mean squared error (MSE) performance on the test tasks.


In fact, when we split the face dataset randomly, we found that the EM algorithm did help.

first, the value of β is typically very large, which results in a small stepsize σ.


A similar approach has been taken for tuning the single parameter in ridge regression where cross validation can be obtained in closed form [16].

( 15) is computationally expensive and almost impossible in practice even for medium size datasets.


With our approach, the average SNR improvement other the 10 test signals was 6.6 dB.

lRTFS can accommodate multiple t-f bases in the following way.


Our bounds have an asymptotic interpretation in the number n of datapoints, which allows us to study EP's convergence with respect to the true posterior.

our extension to the Brascamp-Lieb inequality is as follows.


may or may not correspond to the objective function the clustering algorithm attempts to optimize, and may involve a global quality measure rather than some average over individual instances.

we have proven their fulfillment rigorously only for a certain stability measure and clustering setting.


Moreover, pruning techniques cannot be applied directly to the resulting hypersurfaces, and even second order measures do not exhibit standard quadratic forms to apply quadratic programming.

[Proof in [17, Appendix]] Knowing that the approximation of ρ is bounded for a wide family of functions, the techniques described in Sec.


We also defined Xl n = X n+l , and the time index in the summation Xl n B kl extends only over lags l from 0 to L − 1.

clearly, for this SNR the templates have been recovered accurately and their occurrences within the waveform have been found with only a few missing events.


Alternatively, we might turn to more efficient conditional gradient algorithms [28], which require instead, the much cheaper linear minimization oracles.

we do similar updates for The overall performance clearly depends on the efficiency of this LMO, which can be solved efficiently in our case as illustrated in Algorithm 3.


This is shown by the blue bars which illustrate of selecting the EYE action at each subsequent choice with respect to after the first choice (d ⇡r ).

at each time t 2 T i subject i observes state s i t 2 S as an input, calculates and then executes action a i t (e.g., presses a button on a computer keyboard; a i t 2 A and A is a set of actions) and receives a reward r i t (e.g., a monetary reward; r i t 2 <).


For example, we could use gradient descent.

we can compute the model reward function ( § 2 easily from the reconstructed beliefs.


We have , and hence we have ṽτ ṽ τ t s=1

putting these two inequalities together, we get that using the expression for A t ∆x t from (5) we have Assume that g (v t • x) ∈ [−a, 0] for all x ∈ K and all t. The other case is handled similarly.


When we choose ŷ in this way i,j W i,j |ŷ i − ŷj | ≤ i,j W i,j |y i − y j | and the lemma follows from Theorem 1.

most previous work on label selection methods for learning on graphs has considered active (i.e.


An efficient estimator is one whose variance attains the Cramer-Rao lower bound asymptotically.

the dotted line represents the true value, κ = 4.


For fully detailed visualization results in high resolution and corresponding analysis, please refer to supplementary material Sec.

the generator needs to play against a real-fake discriminator as well as an identity discriminator simultaneously to generate high-quality faces that are really useful for unconstrained face recognition.


Intuitively, larger δ and smaller ε indicate more severe mode collapse.

either real or generated), we can consider these packed samples as a single sample that is drawn from the product distribution: P m for real and Q m for generated.


We collect the spike counts from all q simultaneouslyrecorded physical neurons into a vector y t ∈ IR q×1 , whose ith element is y i t . The choice of the link functions g and h is discussed in Section 3.

if the latent system were inadequate to describe the activity, we should expect to see dynamical features in the empirical firing that could not be captured by the imputed firing rates.


In fact, it is common to let f, h be the identity [He et al., 2016b], in which case each unit takes the form y = x + g Φ (x) .

we study a more standard residual unit, and make minimal or no assumptions on the network, data distribution, and loss used.


Following the partition lemma, each assignment arises at most once.

to the best of our knowledge, there has been no equivalent solution when building a junction tree is infeasible.


Simply using a nonlinear neuron combined with Oja's learning rule allows one to compute higher moments of the distributions which yields ICA if the signals have been preprocessed (whitening) at an earlier stage [1].

5), where three signals generated by Ornstein-Uhlenbeck processes have the same spatial distribution but different time constants of the autocorrelation.


The basic idea is to simulate individual softplus neurons with groups of hardplus neurons that compute what amounts to a piece-wise linear approximation of the smooth region of a softplus function.

rBMs of this size cannot generate any distribution where the two "classes" implied by f are separated in log probability by more than 2δ.


The angle predictions for all the patches are passed through a sigmoid activation at the end to obtain grasp success probability for a specific patch at a specific angle.

the key lies in moving data collection efforts from a lab setting to real-world homes of people.


Given a feature vector s, the goal of the SVM is to find an f (s) that minimizes the objective function γ ) is a regularization term that controls the complexity of f (s), and γ is a tuning parameter controlling the trade-off between error penalization and the complexity of the classification function.

we generate the first word y = tanh(Cs n ).


In Figure 2 we plot the average value of the objective function over 50 instances of the problem for C n = P n , n = 100.

assume that v 0 , v 0 > 0 and power iteration has risk within a constant from the maximum likelihood estimator, provided an initialization is available whose scalar product with v 0 is bounded away from zero.


By focusing only on the 99th percentile of |d ⇡ur |, we hoped to limit our analysis to the circuitry known to be involved in decision-making.

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


It consists of the following: • A finite planning horizon H. • The number of agents M . An agent m can be in one of the states in the state space S. The joint state space is × M m=1 S. We denote a single state as i ∈ S. • A set of action A for each agent m. We denote an individual action as j ∈ A. )

in the original loss function ( 13), the focus is on minimizing the global loss, rather than adjusting each individual critic factor f w (•) towards the corresponding empirical return.


Then, to reduce computational cost, principle component analysis (PCA) is performed to reduce the dimensionality to 16.

our setting represents each image as a distribution over these codewords.


Suppose that we define the first order transition probabilities of a PARW by Then, we see that state i is an absorbing state (either partially or fully) when λ i > 0, and is a transient state when λ i = 0.

before presenting theoretical analysis, let us discuss the intuition behind it from both flow (Fig.


The sequential-LSTM consists of five sequentially connected LSTM cells of 500 units each.

we evaluate the FS-RNN on two standard character level language modeling data sets, namely Penn Treebank and Hutter Prize Wikipedia.


Notice that the focus on the head of the zebra is distinctively the strongest in the fourth representer point (last column) when the training image manifests clearer facial features compared to other training points.

when f t is close to f i with a large negative weight α ij , the prediction score for class j is then decreased.


As pointed out in [32], increasing the size of substructures will largely decrease the probability that two graphs contain similar substructures, which usually results in the "diagonal dominance issue" [14].

our return probability based kernels are significantly different from the above ones.


In contrast, ABO captures the linear increasing trend of the true function and produces a credible interval which successfully captures the function's behavior.

our first set of experiments are test functions commonly used as benchmarks for optimization [20].


In fact, the K = 3 eigenmodel performs better than the other two models for any value of K considered.

to represent this structure well, we would need two latent classes per hub, one for the hub itself and one for the nodes connecting to the hub.


The duality comes with the convenient mapping from dual to primal variables w(α) := Aα as given by the optimality conditions [13].

our convergence rate as shown in Theorem 2 only degrades with the much smaller number of worker machines K, which in practical applications is often several orders of magnitudes smaller than the mini-batch size b.


Definition 2.1 allows two types of errors: C i s are not required to form a partition i.e., some nodes can be left out, and a small fraction of estimation errors is allowed in each C i , e.g., if x j = 0.9 but x j = 0.2, then the j-th "row" in D (i) is incorrect.

because the corrupted nodes are removed, the whole path is around C. Also, by the uniform density assumption, walking on the shortest path in G is equivalent to walking on C with "uniform speed", i.e., each edge on the path will map to an approximately fixed distance on C. the shortest path distance scales with the latent distance, i.e., (d − 1) c , which implies Theorem 2.2 (cf.


We note that as in prior work [19], SafetyNets amortizes the prover and verifier costs over batches of inputs.

this assertion is in turn checked using the protocol described in Section 3.1.


The first property is ensured by simply removing particles that are not resampled from the ancestry tree.

we have presented a SLAM algorithm which is the culmination of our efforts to make multiple hypothesis mapping practical for densely populated maps.


The outputs of these discriminant saliency detectors are next compared with either human performance, or the state-of-the-art in computer vision for each application.

in fact, (1) can be applied to any type of stimuli, and any type of features, as long as it is possible to estimate the required probability distributions from the center and surround neighborhoods.


Restricting the number of harmonics to relatively small integers, we evaluated numerically the optimal values of the coefficients for large systems.

the saturation size y E " ( ' increases rapidly with ( .


Note that the representation is not unique [5].

the proposed method interprets each weight vector as a point on the manifold only when the weight update is performed.


Estimating bias, variance and noise Group-specific variance V a may be estimated through sample splitting or bootstrapping (Efron, 1992).

the discrimination level Γ FNR for false negatives decreases by a striking 40% when increasing the training set size from 1000 to 10,000.


The guarantee of differential privacy under continuous observation assures us that even if all later users collude in an effort to learn user t's context or preference, they still have very limited advantage over a random guess.

here, we assume user t provides a context c t which actually determines the mapping of the arms into feature vectors: φ(c t , a) ∈ R d . The sequence of choice thus made by the learner is a 1 , .


SURE-T methods yielded a slightly better denoising performance than SURE-based methods (approximately 0.02 -0.06 dB and 0.04 -0.12 dB for BSD68 and Set12 datasets, respectively) with considerably increased the overall inference time.

[28] proposed a Monte-Carlo-based SURE (MC-SURE) method to determine near-optimal denoising parameters based on the brute-force search of the parameter space.


Given that our goal is to compare RBM training approaches rather than achieving the best possible training across all free parameters, neither momentum nor adaptive learning rates were included in any of the implementations tested.

interestingly, for the Caltech 101 Silhouettes dataset, it seems that the persistent algorithms tested have difficulties in ascending the pseudo-likelihood in the first epochs of training.


The m th fidelity (an approximation) expends λ (m) < λ (M )  and returns a biased estimate of the highest fidelity.


In the model-based setting, a recent line of research has imported ideas from the bandit literature-including the use of upper confidence bounds (UCB) and improved design of exploration bonuses-and has obtained asymptotically optimal sample efficiency [1,5,10,12].

in the model-free setting, Strehl et al.


We prove that the probability of F is high conditioned on any setting of these variables.

an algorithm M is natural if, when given a sample X = (X 1 , .


The sigmoid loss is, in turn, upper bounded by the exponential loss (which is used, for example, in Adaboost [9]).

the PAC-Bayes theorem is currently not able to recognize the predictive power of the majority vote in these circumstances.


As baseline we used a fairly straightforward means of document matching via its length.

a biased empirical estimate of the above is obtained by replacing sums by empirical averages.


To do so, we require the mappings f and g to map adjacent heterogeneous vertices in the known bipartite graph onto nearby positions in a unified Euclidian space R d , in order to ensure that the known bipartite graph can be recovered to some extent by the nearest neighbor approach.

there is therefore a strong incentive to develop new useful prediction methods based on protein sequences, chemical compound structures, and the available known compound-protein interaction information simultaneously.


The nature of the GSM generative model (linear combination of features with multiplicative gain modulation) makes it an unusual choice for a classification task.

current models do not explicitly take into account such gain variations, and often eliminate them using an ad hoc preprocessing step that normalizes inputs [8,9,13].


BO adopts a Bayesian perspective and assumes that there is a prior on the function; typically, we use a Gaussian process (GP) prior.

with our approach of setting the prior and posterior parameters, BO outperforms all other methods in the task and motion planning benchmark problems.


Curiously enough, the motivation for the updates in both cases seems completely different.

the SILK algorithm maintains a buffer of size ω.


In this section, we compare Acc-Prox-SVRG with Prox-SVRG and APG on L 1 multiclass logistic regression with the regularization parameter λ.

for k ≥ 1, V k ≤ W k . For k ≥ 2, we have Since 0 < √ µη(1 − p) < 1, the above inequality leads to From the strong convexity of g (and f ), we can see for k ≥ 2, we have and that is exactly (24).


The proof of the main theorem follows in Section 4.2.

however the algorithm never relies on the estimated dimensions and views them rather as guesses d i .


We treat the offset corresponding to curve Y i as an additional real-valued latent variable in the model.

they are not designed to handle finer sub-grid alignments.


We lay out the simulation results in this section and demonstrate the accuracy of the contrastive estimator Θ stated in Theorem 4.4.

(ii) We show that our contrastive estimator is consistent and achieves the nearly optimal statistical rate of convergence.


Several recent works have established the same local error bound conditions for several interesting problems in machine learning [7,32,33].

by definitions, the only stage with i = S 1 is the posttermination stage, namely, stage s = S. In this case, C(x, x, i, j, s) = 0 since stage S performs no computation.


Here, we take an alternative approach using an attractive feature of the Parzen estimator -it only requires the view similarity between any two images, not the actual views.

[17] suggest a method to find a single most representative image (canonical image) for a category relying on similarities between images based on local invariant features.


Therefore, to retrieve the attention for a specific word, we convolve the matrix along the visual dimension using a 1 × 1 dimensional kernel.

acknowledgments: This research was supported in part by The Israel Science Foundation (grant No.


In probability and statistics, the Jacobi metric has been mentioned in the rejoinder of [7] as an area of research promise.

one exception is Hamiltonian Monte Carlo (HMC).


Our goal here is to explore the problem of where to label image regions for obtaining a good matte.

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


By continuity, there must be a value of Ui in its allowed interval for which V is indifferent to playing 0 or 1, so w E W e. This completes the proof of Lemma 5.

since we identify players with vertices in G, it will be easier to treat vertices symbolically (such as U, V and W) rather than by integer indices.


It has been shown [7] that the added sophistication of modeling others as rational agents results in a higher value function compared to one obtained from treating others as noise, which implies the modeling superiority of I-POMDPs over other approaches.

the belief update for a particular level-0 model sample, θ j = 0.5, 0.67, 0.5, 0.85, 0.5, -1, -100, 10 , is solved using Algorithm 2.


Fortunately, a simple power method [10] can be used to efficiently compute a maximum eigenvector solution to the inner problem by only performing matrix-vector multiplications on the individual factors of the two low rank matrices making up T (α), meaning the inner problem can be solved without ever forming a large n × n matrix T (α).

before proceeding it is important to realize that there are many alternative conceptions of "robustness" in the literature that do not correspond to the notion we are investigating.


Thus the duality gap at the k-th iteration is given by: We define the relative duality gap as: Rel.gap := Dgap/(1 + |pobj| + |dobj|), where pobj and dobj are respectively the objective function values of the primal problem (12) at point X k , and the dual problem (2 )}, we measure the relative changes of objective function value F (X) and the iterates X and Y as follows: We terminate ALM when either Note that in (19), computing log det(X k ) is easy since the spectral decomposition of X k is already available (see ( 14) and ( 15)), but computing log det( Σ − Λ k ) requires another expensive spectral decomposition.

[16] applied Nesterov's optimal first-order method to solve the primal problem (1) after smoothing the nonsmooth ℓ 1 term, obtaining an iteration complexity bound of O(1/ϵ) for an ϵ-optimal solution, but the implementation in [16] was very slow and did not produce good results.


But for more complex and natural scenarios such as detecting a tiger in the jungle or looking for a face in a crowd, finding the optimum amount of top-down enhancement to be applied to each low-level feature dimension encoded by the early visual system is non-trivial.

search array A has a fixed choice of target and distractor parameters.


Since timeline trees' primary strength is ignoring sections of history to focus on a few key events, they would not be expected to model this problem well.

in terms of control performance, the "No Timestamps" variant performs nearly identically to the full timeline tree.


Enforcing AND is a necessary domain truncation for a valid UG which alters the mode.

we describe new initialization and edge-marginal updating methods for nondecomposable GGMs, and also introduce a highly effective hybrid NF/SLS method.


Precise conditions can be specified which guarantee convergence in probability.


It is therefore common practice to obtain an approximate solution using convex relaxations.

theorem 4: SOCP relaxations (and the equivalent QP relaxations) which define constraints only using graphs G k = (V k , E k ) which form (arbitrarily large) trees are dominated by the LP-S relaxation.


Neural networks are increasingly deployed in real-world safety-critical domains such as autonomous driving, aircraft collision avoidance, and malware detection.

note that concurrent work of Weng et al.


In practice, these approaches exhibit prohibitive computational complexity in high dimensions, and the Gaussian assumption may fail to accommodate the burstiness often inherent to real-world count data [9].

we assume that the time-step factors and transition weights for component k are tied to its component weight ν k . we define the following structure: where π k = (π 1k , .


Goal predicates are named by prepending a 'g' to the corresponding world predicate.

our learner (see Section 3) uses a bias that focuses on states where large improvement appears possible.


We compare our N 3 Net against VDSR and MemNet as well as two non-local models: SelfEx [16] and the recent WSD-SR [8].

a reduction at this stage would mean a very early fusion of features.


The results are reported in Figure 2    In both the uncertain cost and the uncertain transition probability setups, the distributionally robust approach outperforms the other two approach over virtually the whole range of parameters.

we can partition S according to the stage each state belongs to, and let S t be the set of states belong to t th stage.


While determining the exact magnitude of maximum SNR may be impractical, choosing a distribution with uniformly distributed direction and a constant magnitude close to this optimal value, performance can be improved.

we applied learning to a system used to sudy the dynamics of flapping flight via a wing submerged in water (see Figure 4 for a description of the system (Vandenberghe et al., 2004)).


In Markov Decision Processes (MDPs, Puterman (1994)), when the performance is measured by (1) the sample complexity (Kearns and Singh, 2002;Kakade, 2003;Strehl and Littman, 2008;Szita and Szepesvári, 2010) or (2) the regret (Bartlett and Tewari, 2009;Jaksch, 2010;Ortner, 2012), algorithms have been developed that achieve provably near-optimal performance.

trying to capture the properties of f via the distribution-free ||f || ∞ bound is not satisfactory.


While there is no direct formal correspondence, the basic ideas behind Gaussian process regression with a radial basis kernel and similarity-based models such as ALM are closely related.

the data reported for each set of studies are ordered by increasing MAD (corresponding to increasing difficulty).


Given a set of images {I j } K j=1 , we first extract their features {v j } K j=1 with a pretrained CNN, and then average {v j } K j=1 to obtain v. The image encoder converts v into a context vector h v ∈ R D which is used as the visual input for all subsequent modules.

the post-processing we use is that we first select 4 most commonly predicted key words with normal descriptions by other baselines, then for each key word, if the generated report does not describe any abnormality nor normality of these key words, we add the a corresponding sentence of these key words that describe their normal cases respectively.


The lemma highlights the role of Q in judging the difference between P 0 and P, and leads immediately to the following corollary (see Appendix C).

we report results in terms of {0, 1}-valued classification error: `(w, (x, y)) = 0 if and only if y is the largest coordinate of p(w, x).


We compared this value to the one we would obtain if we had a training and a test set with 250 observations each such that we could fit the model on the training set for various values of λ, and see which one gives the smallest prediction error on the test set.

if θ 0 has a sparse representation with k non-zero coefficients, it has been shown in the noiseless case that it is sufficient to use n ∝ k log m such measurements.


the MCD learning rule decides the learning direction.

5 shows the measured output of a noisy neuron (upper trace) with {s i } sweeping between 1.5 and 3.5V, {w i }=4V, V aj =1.8V, and v ni generated by LFSR (Linear Feedback Shift Register) [9] with an amplitude of 0.4V.


In our current problem setting, the goal is to train a prediction model f c : x → y for each cluster c of similar treatment sequences, where x denotes the input features and y denotes the label.

we also thank Levi Valgaerts for the constructive suggestions.


To avoid this, we introduce an additional binary unit u for each node u in a layer, which will record whether node u was influenced in previous time steps.

for this, we use the closed-form interpretation of the IC function as an expectation of an indicator term over a randomly drawn subset of edges from the network (see [2]).


We propose a new search paradigm of active information retrieval in which the user initiates only one query, and the subsequent iterative process is led by the engine/system.

with these changes, we obtain: (2) bs J(Y i 8. ll) = -+ log(as) -w(as + 1) We can optimize the choice of S with a simple greedy method that successively finds the next best cluster index i to include in the information set.


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

the whole protocol can be summarized as follows: where We note that if g is an unbiased estimate of the gradient, then Q(g) is also an unbiased estimate of the gradient since In distributed machine learning, each worker calculates gradient g and transmits it to the master node or the parameter server for an update.


and regular, the optimum auction is a Vickrey auction with a reserve price that equals the monopoly price of the distribution.

the information structure plays a crucial role in the argument of bidders' incentives.


Toy dynamics This experiment is a twist of that used in [5].

we thank all the anonymous reviewers for valuable suggestions.


As we have already shown in Figure 1, the reaching period data are strongly under-dispersed, even absent conditioning on the latent dynamics (implying further under-dispersion in the observation noise).

with θ controlling the (log) rate of the distribution and g(•) controlling the "shape" of the distribution, the GC family provides a rich model class for capturing the spiking statistics of neural data.


One might object that the previous learning rule is not biologically plausible because it involves currents present separately in the pre-and post-synaptic neurons.

it remains unclear how such supervised learning is implemented in biological neural networks.


Since we are minimizing f (i) 1 , the objective encourages the normalized features, f (i) , to be sparse and mostly close to zero.

notice that the sparseness of the features (in the 1 sense) is maximized when the examples are on the axes.


2(left) shows the reconstruction obtained in several single images coming from three different artificial sequences.

once learning is accomplished, each specialized function maps (with different levels of accuracy) the input space.


The regularization parameter is set by cross-validation on the training set.


[LYY13] provides an upper bound of estimation error by assuming the design matrix X is a Gaussian random matrix.


In order to assess the capability to account for inputs of preceeding time steps, it is sensible to define another measure, the memory capacity MC (cf.

this causes input information either to disappear quickly (the simplest case would be an identity map from input to output) or stay forever in the network respectively.


On the AwA dataset, SVM+ can take advantage of privileged information -be it deep belief DeCAF features or semantic attributes -and shows significant performance improvement over SVM.

experimentally, however, we observe in the section on experiments the scenario described.


For this reason, it is natural to introduce an assumption that is slightly stronger than (1).

these results are interesting since they are the first for extreme bandits, but their parametric assumption is unlikely to hold in practice and the asymptotic nature of their bounds limits their impact.


We compute the MSE exactly for the geometric mean estimator (for 0.344α < 2).

the geometric mean estimator, however, can still be improved for certain α, especially for large samples (e.g., as k → ∞).


A significant difference between our previous work [9] and this paper is that scalability is achieved in our earlier work by restricting the approach to "egocentric" modeling, in which counting processes are placed only on nodes.

in this case, estimating time-varying coefficients improves predictive performance, which makes sense because we have seen in Figure 3 that METAFILTER's coefficients tend to vary more over time.


Denoising and dereverberation of speech in this condition has proven to be a very difficult problem [4].


To organize goal-oriented behavior we assume that, in parallel to the activation dynamics (1), there exists a second dynamic process which can be motivated from classical approaches to Reinforcement Learning [11,12].

we chose a modulation of the following kind: To every existing connection (ji) we associate a codebook vector a ji onto the motor layer which is compared to the current motor activity a via a Gaussian kernel function k a .


Based on the assumption, we propose a UNIT framework that are based on generative adversarial networks (GANs) and variational autoencoders (VAEs).

the proposed shared-latent space assumption implies the cycle-consistency assumption (but not vice versa).


If we assume the line segment is infinitely long, or in other words is indicating only a general motion direction l , equation ( 1) is independent of the position Pk of the sprite and only depends on the sample that is currently shown.

video textures reorder the original video samples into a new sequence.


[16] demonstrated how these properties can be used to learn winner-take-all competition between groups of neurons in an LT network with lateral inhibition.

in most applications the equations ( 7) or (9) will be incompatible and can only be satisfied approximately.


Most consumer-level 360 • cameras only record mono audio, and syncing an external spatial audio microphone can be expensive and technically challenging.

baselines Since spatial audio generation is a novel task, no established methods exist for comparison purposes.


Conditional distributions are derived in Appendix B.

here a convenient model of p(X, Θ) is mixture of Gaussian.


In combination, these arguments suggest that working with mechanistic steps may facilitate the application of statistical machine learning approaches, and take advantage of their capability to generalize.

the sole example is a paper from 1990 on inductively extracting overall transformation patterns from reaction databases [12], a method which was never actually incorporated into a full reaction prediction system.


Because of the crucial importance of the ordering of the features in a decision list, these sets do not provide enough information by themselves to be able to reconstruct the hypothesis.

we can thus think of our learning algorithm as compressing the training set into a small subset of examples that we call the compression set.


We cannot find a closed-form solution for the maximization.

then we change q(α) back to q s ( α) using the inverse mapping α = sα.


The details are somewhat technical and we give a more detailed discussion in Appendix C.3.

as mentioned earlier, 1D and 2D histograms have been studied extensively in several areas such as databases [8,14] and density estimation.


We see, first, that CMICOT with t ≥ |F int | significantly outperforms all baselines, except the idealistic CMI method whose results are similar to CMICOT.

we refer to this FS method as CMICOT (Conditional Mutual Information with Complementary and Opposing Teams) and present its pseudo-code in Algorithm 1, which has a form of a SFS strategy with a specific algorithm to calculate the score (lines [10][11][12][13][14][15][16][17][18][19].


In order to induce RIL to change actions, worker i must let RIL learn a wrong Q-function.

sc t i (j) denotes worker i's score on task j, which will be computed by the Bayesian inference algorithm.


Starting with the Multidimensional Scaling (MDS) strain cost function [25,26] we derived an algorithm which maps onto a neuronal circuit with local learning rules.

in addition, [36] computed similarities among visual stimuli by matching them with the similarity among corresponding retinal activity patterns (using an information theoretic metric).


In order to use analytical tools for solving this problem, we have to turn the regularization term k into a continuous function of assignments.

a variant of EM algorithm finds the globally optimal solution.


Therefore, we have made the full-information game as difficult as the bandit game.

second, in the full-information setting, we show that predicting against a switching costs adversary is strictly easier than predicting against an arbitrary adversary with a bounded memory.