The piecewise model performs better, but because the observation covariance is not conditioned on o t , the Kalman filter learns to use a very large observation covariance, which forces it to rely almost entirely on the dynamics model for predictions.

since the BKF learns to output the observation covariances conditioned on o t that optimize the performance of the filter, it is able to find a compromise between the observations and the dynamics model.


Because FBM (correctly) assumes the reward structure to remain fixed during a game, it updates the posterior mean by weighing new observations with decreasing coefficients, as the variance of the posterior distribution decreases over time.

by assuming the reward rates to have a (small) fixed probability of being redrawn from a prior distribution on each trial, DBM continuously updates the posterior reward rate distribution by exponentially forgetting past observations, and injecting a fixed prior bias [5,9].


It is well known that belief propagation computes exact variances in tree-structured GMRFs [36].

in graphs with cycles its loopy version typically underestimates the marginal variances since it overcounts the evidence, even when it converges to the correct means [13,33].


According to the statistical typicality account, attractiveness ratings would look like Figure 5b, having a shape similar to the population distribution (Figure 5a).

the disfluency account would qualitatively predict the difficulty of categorization to be the greatest and thus processing fluency and attractiveness to be lowest near the categorization boundary.


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

for periodic tasks the approach of growing trajectories backwards from the goal cannot be used, as there is no goal point or set.


Boltzmann machines (BMs) are appealing candidates for powerful priors in variational autoencoders (VAEs), as they are capable of capturing nontrivial and multimodal distributions over discrete variables.

non-differentiability of the discrete units prohibits using the reparameterization trick, essential for low-noise back propagation.


. . , x n . Independently, each variable has a very strong prior of being true.

variable x i is never true unless x i−1 is also true.


First, notice that when U a is unknown, we do not have an explicit definition of the first constraint.

implicitly we can determine whether t has a better payoff than t by observing the attacker's best-response to s. Second, the above LP has exponentially many variables, one for each pure strategy.


Our general form of the asymptotic free energy also allowed us to elucidate the behavior of the VB free energy when L and/or M diverges with the same order as N . This attempt successfully revealed the sparsity of the solution for the case when M diverges while L ∼ O(1).

when L diverges, we found that the leading term of the free energy does not contain interesting insight into the sparsity of the solution.


Although the above algorithm provides a characterization of the manifold, it does not directly provide an embedding nor a density function.

once the tangent plane function is trained, there are ways to use it to obtain all of the above.


Since the Frobenius-norm penalty does not automatically produce a low-rank solution, it should be combined with an explicit low-rank constraint, which is non-convex.

the trace-norm penalty tends to produce sparse solutions, so a low-rank solution can be obtained without explicit rank constraints.


We will now deal separately with f 1 and with f 2 .

from the inequality (4) above, we observe that from the inequality (2), we see that if e i is a basis element present in the basis expansion of f 1 , Since ∆ acts by rescaling basis elements, we have Therefore by Proposition 4.3 for t sufficiently small and some constant Hence we see that Consider now the second summand f 2 .


A Mixture Elimination algorithm is proposed and shown to achieve O( √ T ) regret.

the benchmark for the definition of regret in [17] is restricted to within a finite policy set.


Thus it is natural to encode the program as an external memory module.

in contrast to traditional memory networks [19,20], where the memory slots are organized as a linear array, the information contained in a program has rich structure.


When the size of the behaviour data is small, the clustering performances of both DPM-BIRL and EM-MLIRL were not good enough due to the sparsity of data, hence their EVD results were similar to that of the baseline algorithm that independently runs BIRL on each trajectory.

as we increased the size of the data, both DPM-BIRL and EM-MLIRL achieved better EVD results than the baseline since they could utilize more information by grouping the trajectories to infer the reward functions.


This might seem a strange goal, since one could surely just listen to the input spikes.

in order for the output spikes to track the hidden variable, the dynamics of the interactions between the neurons must explicitly capture the dynamics of the process X(T ).


This question reflects one fundamental aspect of "bounded rationality," a term coined by Herbert Simon [1].

bounded rationality has proven to be a slippery concept to formalize (prior work has focused largely on finite automata playing simple repeated games such as prisoner's dilemma, e.g.


When a given IFAT cell's RF falls on a region of visual space with uniform brightness, all of the OR pixels projecting to that cell will have the same mean firing rate, so the excitatory and inhibitory inputs will cancel.

if a cell's excitatory inputs are exposed to high light intensity and its inhibitory inputs are exposed to low light intensity, the cell will receive more excitatory inputs than inhibitory inputs and will generate an output spike train with spike frequency proportional to the contrast.


[1,4,19]) can be seen as a non i.i.d setup as the rewards chosen by the adversary might depend on the agent's past actions.

even if the algorithms developed for this framework can be used in our setting, they might perform very poorly as they are not designed to take advantage of any mixing structure.


Clearly, after almost every trade, the market price is quite far from the equilibrium/stationary point, and hence the classical supply and demand analysis of this market yields a poor description of the actual behavior, and in particular, of the predictive quality of the price at any given time.

the mean price is consistently close to the mean belief of the traders, which in turn is quite close to the true parameter q.


They propose a randomized bandit algorithm that is robust to adversarial attacks on the stochastic rewards.

our work shows that the existing stochastic algorithms are vulnerable to adversarial attacks.


Turning back to our bounds, both the latent trace norm and its scaled version can perform as well as knowing the mode with the lowest rank (the first mode) (see also [21]) when d = P = Q.

when the dimensions are heterogeneous, similarly to the matrix completion case above, the plain latent trace norm fails to recognize the lowrank-ness of the first mode and Table 2: Sample complexities of the overlapped trace norm, latent trace norm, and the scaled latent trace norm in various settings.


Nevertheless, even this approach for computing the Jacobian matrices still requires the solution of multiple linear systems, which scales poorly when the number of hyperparameters k is large.

l "observed features" j ∈ {1, . . . , R} "noise features" j ∈ {R + 1, . . . , 40} we can do much better by reorganizing the computations in such a way that the Jacobian matrix J d is never explicitly required.


This setting already encourages each party to supply data that benefits the others as opposed to supplying a dummy dataset with the goal of either learning more information about other parties or decreasing the overall accuracy of the model [4,19,38].

it is not clear if this is sufficient to prevent other malicious behavior.


In general, any PNFA where the nondeterministic transitions can only be visited once can be expressed as a mixture of PDFAs.

if we replace transitions to q 3 with transitions to q 0 , as in 2(b), there is no longer any equivalent finite mixture of PDFAs, since the nondeterministic branch from q 0 can be visited an arbitrary number of times.


Bayesian sequential updating or belief propagation, implemented in the form of particle filtering, has recently been used in estimating the hand trajectories of monkeys based on M1 neuron's responses [4] and the location of a rat based on the responses of the place cells in the hippocampus [3].

linear methods have been shown to be quite adequate for decoding LGN, motor cortical, or hippocampal place cells' signals using population vectors or the optimal linear decoder [10,5,8].


PMP also retains the bilinear property of uniform convolution, meaning that where H = j w j P j and D = The disadvantage of PMP is that it typically leads to inefficient algorithms because the evaluation of the matrix-vector product Hx = Dw requires generating many expensive intermediate transformed images.

eFF can be combined with the PMP model by introducing a set of basis images efficiently generated by transforming a grid of delta peak images [9].


The regret of ESCB in the general possibly correlated case is unknown and the regret bound for CombUCB1 is not improved in the independent case.

oLS-UCB is adaptive in the sense that its performance gets better when more information is available on the independence of the arms.


These methods contain maximum likelihood Expectation-Maximization (EM) based imputation, KNN based imputation and Matrix Factorization based imputation.

all of these methods rarely take into account the temporal relations between two observations.


The approximated CTBN structure score still satisfies structural modularity, if not broken by the structure prior P (G).

an implementation of a k-learn structure learning strategy as originally proposed in [14] is prohibited, as the latent state estimation depends on the entire network.


1 necessarily has to be a plug-in statistic.

both terms involved in Bias TBIC comprise the same general statistic.


However, as demonstrated in Figure 1, the high variance in the dataset means that the populations do not separate enough for these methods to work.

as we demonstrate in Figure 1, when the data points are mapped to the learned representations of the network, such a separation does occur.


Linear functionals on finite dimensional normed space are bounded.

in most nonparametric statistics problems that are of interest, the RKHS is infinite dimensional.


The phenomenon studied here could hold in any EDA, because for any type of model, the probability is high of generating a population which reinforces the move just made.

more complex models have many more parameters, and also have more sources of variability, so the issue may be less important.


This is superior to the scaling in our result (10).

the two methods rely on slightly different underlying assumptions, and the current form of the neighborhood-based approach requires solving a total of p Lasso programs, as opposed to a single log-determinant problem.


A key difference is that in PITC it is not obvious which variables should be grouped together when making the conditional independence assumption, here it is clear from the structure of the model that each of the outputs should be grouped separately.

the similarities are such that we find it convenient to follow the terminology of [10] and also refer to our approximation as a PITC approximation.


Early MoE work used linear experts [3,4,11,12] and some of them were neatly trained via variational methods [4,11,12].

these methods cannot model nonlinear data sets well.


Since both voicing streams will be nearly identical, the mutual information should peak when the two participants are either involved in a conversation or are overhearing a conversation from a nearby group.

we have the added complication that the streams are only roughly aligned in time.


Our approach via compression schemes also ultimately reduces the problem to learning with respect to finite classes.

our compression technique leads to a more refined bound.


Both the existing CNN filters and the expensive training data that produced them are "flat", i.e., the product of perspective projection to a plane.

a 360°image is projected onto the unit sphere surrounding the camera's optical center.


Of course, the main constraint is the availability of only a finite data set to learn from.

many current problems in machine learning can be characterized as learning with additional information constraints, arising from the manner in which the learner may interact with the data.


As is well known in information theory, the expected number of bits required to compress data X generated according to a known distribution P is the distribution's entropy, H(P ) = E P log 1/P (X), and is achieved by encoding X using roughly log 1/P (X) bits.

in many applications P is unknown, except that it belongs to a known collection P of distributions, for example the collection of all i.i.d., or all Markov distributions.


As a learning principle, sparsity is essential to understanding the statistics of natural images [2].

it remains unclear to what extent sparsity and subspace pooling [3,4] could produce invariance exhibited in higher levels of visual systems.


In chunky EM, all mixture components share the same data partition.

for a particular block of data, the variation in membership probabilities differs across components, resulting in varying differences from the equality constrained variational probabilities.


The KCs serve merely as a readout stage and are not interconnected.

2 there is also a crucial disagreement of the full dual dynamics with biology: the requirement for feedback from the KCs to the PNs.


Note we implement PILCO with a linear mean function 1 , φ a x, where φ a are additional hyperparameters trained by optimising the marginal likelihood [11,Section 2.7].

the covariance function k is squared exponential, with length scales Λ a = diag([l 2 a,1 , ..., l 2 a,D+F ]), and signal variance s 2 a : The original PILCO algorithm ignored sensor noise when training each GP by assuming each observation z t to be the latent state x t . this approximation breaks down under significant noise.


If the marginal distributions are assumed to be Gaussian, a closed-form solution exists in the frequency domain and FFTs can be used to recover the image very quickly.

real-world images typically have marginals that are non-Gaussian, as shown in Fig.


This approach has been used to identify neural activity trajectories that are informative about stimuli and behaviour and yield insights into neural computations [7,8,9,10,11,12,13].

these methods are designed for analyzing one population measurement at a time and are typically applied to population recordings of a few dozens of neurons, yielding a statistical description of the dynamics of a small sample of neurons within a brain area.


Highly complex dynamics may therefore be postulated for the hidden space transitions, and also for the hidden to the visible transitions.

unlike traditional neural networks the models remain probabilistic (generative models), and hence the full machinery of Bayesian inference is applicable to this class of models.


Regression with subset selection finds for each k ∈ {1, 2, . . . , m} the feature subset of size k that gives the smallest residual sum of squares.

it is a combinatorial optimization and is known to be NP-hard [14].


Note that if we fix q = h and z = 1, interval rounding becomes equivalent to complete rounding.

the analyses in [5,10] shows that other values of q provide better approximation factors for various special cases.


Note that, given an optimal solution N , B and D to (20), an approximate solution to the original problem (2) can be recovered heuristically by first rounding N to obtain , then recovering W and V , as shown in Lemmas 1 and 2.

since our primary objective is to determine whether any convex relaxation of a two-layer model can even compete with one-layer or locally trained two-layer models (rather than evaluate heuristic rounding schemes), we consider a transductive evaluation that does not require any further modification of N , B and D. In such a set-up, training data is divided into a labeled and unlabeled portion, where the method receives X = [X `, X u ] and Y `, and at test time the resulting predictions Ŷu are evaluated against the held-out labels Y u .


In particular, it successfully controls type I error rates for the practical range of α ∈ (0, 0.1).

with m increased to 100, the LR test drastically fails to control type I error rate.


When twice differentiable, DR-submodularity is equivalent to The above twice differentiable functions are sometimes called smooth submodular functions in the literature [23].

in this paper, we say a differentiable submodular function F is L-smooth w.r.t a norm ⋅ (and its dual norm ⋅ * ) if for all x, y ∈ X we have Here, ⋅ * is the dual norm of ⋅ defined as When the function is smooth w.r.t the 2 -norm we use L 2 (note that the 2 norm is self-dual).


The effects of a wide range of timescales and uncertainty about the causes of changes of the oculomotor plant will largely be hidden if experiments are of a relatively short duration and no uncertainty is produced.

in a recent experiment Robinson et al analyzed saccadic gain adaptation [7] in a way that allowed insight into many timescales as well as insight into the way the nervous system deals with uncertainty.


When we let the variances to be part of parametrization we lose the theoretical guarantees.

the EM algorithm can still be applied, and since the variances are now parameters (rather than being fixed to 1), the model fits better in terms of log-likelihood.


Adversarial training [10,16,18], which injects adversarially perturbed data into training data, is a promising approach.

there is a risk of overfitting to attacks [16,30].


it remains as an open question how one should compute this value for more general configurations.


Nevertheless, it would guarantee regret at most K ln M overall.

now suppose each task is predicted well by some model from a small subset of models of size N M . Running Bayes on all N -sparse allocations would achieve regret ln M N + K ln N . emulating Bayes in this case is NP-hard [RAB07].


As in other fields of AI, deep learning-based end-to-end approaches have made great advances in program synthesis.

compared to other fields such as computer vision, program synthesis provides greater opportunities to explicitly exploit structured information such as execution traces.


[11] provides other variants of the deterministic algorithm, including two ergodic averaging schemes that feature improved theoretical rate of convergence.

these variants performed worse in practice than the original method, and are omitted.


Common approaches to this problem include simply summing up or averaging all the node embeddings in a final layer [11], introducing a "virtual node" that is connected to all the nodes in the graph [25], or aggregating the node embeddings using a deep learning architecture that operates over sets [15].

all of these methods have the limitation that they do not learn hierarchical representations (i.e., all the node embeddings are globally pooled together in a single layer), and thus are unable to capture the natural structures of many real-world graphs.


L ∞ -API cannot return an approximate value function that has a lower Bellman residual than ABP, given the optimality of ABP described in Theorem 5.

even OAPI, an approximate ABP algorithm, performs comparably to L ∞ -API, as the following theorem states.


Note, however, that without any restrictions on the data distribution, d can rise to n. In an effort to overcome scaling problems a range of sparse GP approximations have been proposed [1,8,9,10,11].

none of these has fully achieved the goals of being a nontrivial approximation to a non-sparse GP model and matching the SVM w.r.t.


Therefore, in this section we propose an alternate approach method to setting the beliefs in L[x, y], that optimizes for the accuracy of the final global illuminant estimate.

unlike previous color constancy methods that explicitly model statistical co-dependencies between pixels-for example, by modeling spatial derivatives [4,5,6], or learning functions on whole-image histograms [21]-we retain the overall parametric "form" by which we compute the illuminant in (4).


These two aspects make our setting more challenging than the standard setting for learning mixture distributions.


For odd k, such a reduction is not possible, and one might try a bipartite graph, with either the reduction described above, or with k/2 -tuples and k/2 -tuples (our analysis works for this reduction as well).

with Õ(k/2) clauses, the spectral approach of computing the largest or second largest singular vector of the adjacency matrix does not work.


Current proofs [9,15] show that O * d 3 steps are needed for the random walk to mix.

the constants in these bounds are very large.


In fact, we can consider the empirical version of the integral operator associated to K which is simply defined by The latter operator is an unbiased estimator of T . Indeed, since K x ⊗ K x is a bounded random variable into the separable Hilbert space of Hilbert-Schmidt operators, one can use concentration inequalities for random variables in Hilbert spaces to prove that where • HS is the Hilbert-Schmidt norm (see for example [14] for a short proof).

in general T † n T n does non converge to T † T since 0 is an accumulation point of the spectrum of T or, equivalently, since T † is not a bounded operator.


More recently, powerful graph neural networks that surpass Laplacian and embedding based methods in predictive performance have become popular.

neural network models require relatively larger number of labels to prevent over-fitting and work well.


In general, the statistics of generative field shapes can be influenced by many factors including preprocessing details, sparsity, local optima or details of the learning algorithms.

because of the applied approximation, S5C can avoid the for MAP based approaches required choice of the sparsity penalty [1].


From the statistical point of view, there is no remarkable difference between batch and our mirror-descent procedure.

from the computational point of view, our procedure is quite comparable with the direct stochastic gradient descent.


Ideally, the criteria for selecting k in a frequentist analysis and the prior on k and {γ h } in a Bayesian analysis should guard against such over-fitting.

the impact of the criteria used and prior chosen can be subtle.


Secondly, using either the KDE or k-NN, obtaining the best rates for plug-in methods requires undersmoothing the density estimate and we are not aware for principled approaches for selecting this smoothing parameter.

the bandwidth used in our estimators is the optimal bandwidth for density estimation so we can select it using a number of approaches, e.g.


Causal InfoGAN shares several similarities with VaST, such as using Gumbel-Softmax to backprop through transitions of discrete binary states, and leveraging the structure of the binary states for planning.

vaST is formulated to require the agent actions, and is thus limited to single time step predictions.


and choose the arm with the largest feasible reward given C t−1 as a constraint: The main difference between GLOC and existing GLBs is in the computation of the C t 's.

prior methods involve "batch" computations that involve all past observations, and so scale poorly with t. GLOC takes in an online learner B, and uses B as a co-routine instead of relying on a batch procedure to construct a confidence set.


EA provide a simple mechanism to explore the space of architectures by making a sequence of changes to networks that have already been evaluated.

as we will discuss later, they are not ideally suited for optimising functions that are expensive to evaluate.


exact local computation for the sigmoid function, P(y lXI, ... ,XJ) = 1/(1 + exp[-Bo -L: j BjXj]) , requires the full exponential sum.


Thus for all samples of a batch (dis-)similarity is defined-they either belong to the same compact clique or are far away and belong to different cliques.

pairs of samples with no reliable similarities end up in different batches so they do not yield false training signal for SGD.


Therefore, practical systems may truncate the likelihood-ratio score-space after the 1st-order derivatives, and hence use linear approximations to the Taylor series expansions 3 .

an example of a 2nd-order derivative is V' J-L jk (V'~;k Inp(OIO)) , For simplicity the component posterior ' Y j k (t) is assumed independent of J-L j k. Once the score-space has been defined, an SVM classifier can be built in the score-space.


This observation may appear simplistic, and may not say much more than 'do not use the squared loss' for VI in this setting.

despite this clear failing (2) is precisely the loss used by the majority of approaches to VI for RL [17,35,65,69,20].


For fair comparison, we follow the evaluation procedure of the original two-stream work [20] by sampling 25 frames (and their horizontal flips).

rather than using 10 spatial 224 × 224 crops from each of the frames, we apply fully convolutional testing both spatially (smallest side rescaled to 256) and temporally (the 25 frame-chunks) by classifying the video in a single forward pass, which takes ≈250ms on a Titan X GPU.


(2016) and  discuss the topic in detail.

strong guarantees for the best known estimators hold (with few exceptions mentioned below) under the restrictive assumption that X is either bounded with probability 1 or has sub-Gaussian distribution, meaning that there exists σ > 0 such that for any v ∈ R d of unit Euclidean norm, In the discussion accompanying the paper by Cai et al.


If a multifidelity strategy were to use the second fidelity queries only in X g , then the regret will only have Ψ n (X g ) dependence after n high fidelity queries.

a strategy that only operates at the highest fidelity (e.g.


First, to represent and learn V , we could employ a single output unit, trained on the total utility (reward) using Q-Learning.

we can take advantage of the fact that total utility U pp in equation 1 is a linear combination of performance utility U and power cost −ǫ * P wr.


Two views of every non multi-view anomaly can be generated from a latent vector using view-dependent projection matrices.

since two views of multi-view anomaly 'M' are not consistent, two latent vectors are required to generate the two views using the projection matrices.


The above algorithm is used as a seeding step for Lloyd's algorithm which is known to give the best results in practice.

the theoretical guarantee of the k-means++ comes from analyzing this seeding step and not Lloyd's algorithm.


The former does not optimize temporal aspects of the movement, i.e., duration or the time when costs for specific sub goals of the problem are incurred, assuming them as given a priori.

how should one choose these temporal parameters?


Therefore, its perplexity is significantly high when there are fewer content-related annotations per document than unrelated annotations as with the 20News1 data.

since the proposed method considers the relevance to the content for each annotation, it always offered low perplexity even if the number of content-unrelated annotations was increased.


It has been shown that fictitious play converges to equilibrium (of the stage game G) in k-sum games [17].

fictitious play requires perfect monitoring.


When the number of nodes with more than two common neighbors is less than ten, we define the set S by finding all neighbors with at least one common neighbor (as in the semi-sparse regime).

since the cleaning step works only when S is sufficiently large (so that degrees concentrate), we do not perform any cleaning when |S| < 30.


This rate cannot be improved in general for arbitrary convex loss functions.

this is not the case if the loss functions are uniformly convex, for instance, if all f t have second derivative at least H > 0.


when the number of latent components increases, SCA outperforms other approaches by a large margin.


Theorem 2.1, one must know the norm of a small-error linear filter , or at least have an upper bound on it.

if this parameter is unknown, but instead the noise variance is known (or can be estimated from data), we can build a more practical estimator that still enjoys an oracle inequality.


We say that a representation ρ is reducible if there exist smaller representations ρ 1 , ρ 2 such that ρ ≡ ρ 1 ⊕ ρ 2 where ⊕ is defined to be the direct sum representation: In general, there are infinitely many inequivalent representations.

for any finite group, there is always a finite collection of atomic representations which can be used to build up any other representation using direct sums.


We have presented a Bayesian model of cross-situational world-learning which outperforms both baseline associative models and a more sophisticated translation model on learning from noisy corpus data.

the strength of our model is not just its performance on the corpus, but also a more natural formulation which may contribute to the clarity of our understanding of word learning.


Lastly, note that in our discussion above (and the derivations provided in appendix section A) we assumed each per-sample gradient g n does not depend on the selected mini-batch.

this ignores the influence of batch normalization.


Remark 8 VFE has a tendency to find under-fitting solutions.


The sigmoid function is defined as σ(z) = 1/(1+e −z ), While it is an approximation to the indicator function, it is not a lower bound.

the scaled version of the log of the sigmoid function, log [2σ(z)]/ log 2, is a lower bound on the indicator function (Fig.


For 1D histograms it is known how to achieve the optimal sketch length bound of n = O(k log d): it can be obtained by representing k-histograms using a tree of O(k log d) wavelet coefficients as in [10] and then using the structured sparse recovery algorithm of [1].

applying this approach to 2D histograms leads to a sub-optimal bound of O(k log 2 d).


The diversity of 3D viewpoints and aspect ratios causes dramatic changes in the root filter response.

we have observed that the responses for the part filters are less affected.


These SA algorithms are instances of stochastic gradient descent -a popular choice for convex learning problems.

designing similar updates for the CCA problem is challenging since the gradient of the CCA objective (see Problem (5)) w.r.t.


Image parsing has also been of considerable recent interest [11,13,21,22,24].

it has been difficult to demonstrate that sophisticated compositional models lead to performance advantages on challenging metrics such as the PASCAL object detection benchmark [9].


Their experiments indicate that 2-independent hashing often works, and they state that "the simple and highly efficient 2-independent scheme may be sufficient in practice".

no amount of experiments can show that this is the case for all input.


Master-Slave [8] is also a communication architecture for real-time strategy games, where the action of each slave agent is composed of contributions from both the slave agent and master agent.

both works assume that agents know the global states of the environment, which is not realistic in practice.


We refer the readers to [9,11] for details.

applying Nesterov's algorithm is challenging, because it requires an efficient subroutine for computing projections onto the set of constraints Q 2 .


As we move to heavier tails, establishing such two-sided bounds requires assumptions on the boundedness of the Euclidean norm of the rows of X [15,17,10].

analysis of only the lower bound requires very few assumptions on X.


Thus, the runtime of the Radon machine with N = r h n samples is T R,h (N ) = T L (n) + hr 3 .

(7) the runtime of the base learning algorithm for achieving the same guarantee is T L (M ) with M ≥ N L 0 (ε, ∆).


When the network of interest is singly-connected, prior results about belief propagation imply convergence of consensus propagation.

in most cases of interest, the network is not singlyconnected and prior results have little to say about convergence.


It is possible, and perhaps more motivated, to use two distinct train sets for the CF models and the ensemble.

in our case, we got high performance even in the case of using the same training dataset in both stages.


Specifically, the sample complexity for the generative method depends only on row-wise sparsity of the individual models d 2 ⇥ ⇤ i , and is independent of sparsity s of the differential parameter ⇥ ⇤ diff .

the sample complexity of the discriminative method depends only on the sparsity of the differential parameter, and is independent of the structural complexities of the individual model parameters.


Its main advantage is the efficiency of the corresponding loss-augmented inference algorithm, which has a complexity of O(|P| + |N |).

this gain in training efficiency often comes at the cost of a loss in testing accuracy, which is especially significant when training with weakly supervised datasets [1].


A popular modeling approach assumes the existence of a utility function f such that f (x) gives the utility of an item with feature vector x; f (x i ) > f (x j ) indicates that item i is preferred to item j. Bayesian methods can be used to learn f , for example, by modeling f independently for each user as a draw from a Gaussian process (GP) prior [4].

when data from many users is available, such methods do not leverage similarities in preferences across users.


This distance was previously applied to such statistical problems as homogeneity testing and change-point estimation [14].

these applications so far have only concerned i.i.d.


[2012], we experimented with the five UCI datasets described there.

we present results for PIM and RIN only, as the results on the other datasets mostly followed the results on these and in a way these two datasets are the most extreme.


Manual programming of content ensures high quality and maintains the editorial "voice" (the typical mix of content) that users associate with the site.

it is expensive to scale as the number of articles and the number of site pages we wish to program grow.


The first pair of HSM agents use the same behavior hierarchy as the HAM agent.

they use short-term memory at the most abstract level to learn a strategy for navigating the corridor.


F (x; ⇠) is convex for any ⇠, when f is twice continuously differentiable around the minimum point with positive definite Hessian.

the role of the local geometry is not well understood.


Deep Neural Networks (DNNs) achieved remarkable results in many fields making them the most common off-the-shelf approach for a wide variety of machine learning applications.

as networks get deeper, using neural network (NN) algorithms and training them on conventional general-purpose digital hardware is highly inefficient.


The amount of overlap between any two regions in the cover determines how strongly the corresponding conditionals are tied to each other.

the regions should be small to preserve locality.


The results are very similar to the ones of [1].

for our method, the recommendation in [1] to use v c = 1 leads to significantly worse results in all scores, the v c chosen by our methods are generally larger.


There has long been interest in the nature of eye movements and fixation behavior following early studies by Buswell [I] and Yarbus [2].

a complete description of the mechanisms underlying these peculiar fixation patterns remains elusive.


Note that the application of FISTA to the dual function is not novel per se.

we claim that our theoretical characterization of this classical scheme based on the Hölder continuity assumption in the composite minimization setting is new.


Since we now have M D +|Θ| parameters to fit, instead of just |Θ| for the full GP, one may be worried about overfitting.

consider the case where we let M = N and X = X -the pseudo-inputs coincide with the real inputs.


5 (right), 5 when using the high accuracy environment model, the performance of the encoder-free agent is similar to that of the baseline standard agent.

unlike I2A, its performance degrades catastrophically when using the poor model, showcasing the susceptibility to model misspecification.


Customers are not exchangeable under this distribution, as the number of dishes counted as 1 depends upon the order in which the customers make their choices.

if we only pay attention to the lof -equivalence classes of the matrices generated by this process, we obtain the infinitely exchangeable distribution P ([Z]) given by Equation 4: matrices generated via this process map to the same left-ordered form, and P ([Z]) is obtained by multiplying P (Z) from Equation 5 by this quantity.


When the probability distribution P(X, Y ) is known, the optimal classifier, leading to the minimum misclassification rate, is given by the Maximum A-posteriori Probability (MAP) decision rule.

in practice, estimating the complete joint distribution P(X, Y ) is computationally and statistically impossible for large values of d. Therefore, an alternative approach is to first estimate some low order marginals of the joint probability distribution P(X, Y ) and then design the classifier based on the estimated low order marginals.


So, accuracy is higher when using topics from multilingual anchoring to classify documents.

lORELEI experiments show that multilingual anchoring topics are less interpretable than MCTA topics.


Due to its analytic tractability, computational simplicity, and potential for Bayes optimal inference, VAMP is a promising technique for statistical linear inverse problems.

a key challenge in using VAMP and related methods is the need to precisely specify the distribution on the problem parameters.


The log-normal posterior in combination with a log-uniform prior has a number of attractive features.

the maximization of the variational lower bound with a log-uniform prior and a log-normal posterior is an ill-posed optimization problem.


Constant memory backprop through reversibility Recent work developed reversible versions of residual networks (Gomez et al., 2017;Chang et al., 2017), which gives the same constant memory advantage as our approach.

these methods require restricted architectures, which partition the hidden units.


Traditionally, the subspace method use Euclidian distances.

our experiments show that, as long as the dimensionality reduction preserves enough distance between classes, less computationally expensive distance metrics such as Manhattan distance are equally effective for classification.


Our approach has some similarity with the seminal paper by Pearlmutter and  who also formalized reverse-mode AD in a functional style.

several important aspects are substantially different.


[3] approximate the gradient of the rasterization operation to make the rendering differentiable.

this method is limited to rasterization-based rendering, making it difficult to represent more complex effects that are usually achieved by ray tracing such as global illumination, reflection, or refraction.


Some of these concerns are less applicable to our work, as we leverage learned abstract representations for mapping both visual and language inputs to an underlying symbolic reasoning substrate.

building structured representations for scenes and sentence meanings-the targets of these mappings-in ways that generalize to truly novel situations remains a challenge for many approaches including ours.


Alternatively, the state-space representation used for determining the policy can be augmented with extra dimensions representing the current goal, such that effectively multiple policies can be maintained 5 , or a large "look-up table" of action sequences connecting any pair of start and goal locations can be represented -again leading to inefficient use of experience and potentially excessive representational capacity requirements.

model-based decision-making strategies rely on the ability to simulate future trajectories in the state space and use this in order to flexibly plan in a goal-dependent manner.


There are works [10,9,6] falling into this category.

in general affinity A is barely positive semi-definite.


This implements a nonclassical receptive field [12,18] of a biological neuron as the effective receptive field is larger than that determined by feedforward connections.

with increasing iterations, the size of the effective receptive field will increase unboundedly, which contradicts the biological fact.


For an unobserved latent process x t , an inference procedure needs to be devised to estimate the posterior distribution on the entire sequence x 1 . . . x t . For linear-Gaussian observations, this inference is tractable and is provided by Kalman smoothing.

with generalised-linear observations, inference becomes intractable and the necessary approximations [6] are computationally intense and can jeopardize the quality of the fitted models.


Moreover, it is possible to show through lower bounds on the guaranteed performance that these policies indeed achieve sub-optimal performance.

to demonstrate this, consider the subclass of stationary information flows described in §3.1, with an arrival rate λ that is very large compared to σ 2 4∆ 2 T . In that case, we have seen that the regret lower bound becomes constant whenever the arrival rate λ is independent of T . the -greedy policy, employs an exploration rate that is independent of the number of observations obtained for each arms and therefore effectively incurs regret of order log T due to performing unnecessary exploration.


The synaptic weight w ij is proportional to the concentration of switch template ij, attenuated by the load on A i .

the threshold θ i is dependent on the weights, perhaps implying a lack of generality.


These methods can be regarded as inter-image context learner.

we attempt to apply recurrent connections to each level of hierarchical features to aggregate their context evolutions.


From a biological perspective, it may seem implausible to let threshold dynamics and spike-triggered adaptation currents scale with vast changes in dynamic range.

as noted in [17], there is a theoretical link between spike-triggered plasticity like spike-timing dependent plasticity and spiketriggered adaptation [32].


As in the K-means algorithm, only one reference vector is adjusted for each adaptation step and the update value for the selected reference vector is independent of similarity or proximity.

unlike the K-means algorithm, the adjusted vector is not always the most similar reference vector, and sometimes other similar vectors are adjusted.


Since we consider the edge feature properties of all sub-bands, the HL block mostly shows horizontal edges.

the LH block mainly contains vertical edges.


In practice, it is usually difficult to have a precise guess of β j .

for many application problems, we observe in practice that the eigenvalues of kernel K decays more slowly than that of the target spectral coefficients.


We conjecture that in practice one could run a single instance of the algorithm while gradually increasing T hor and decreasing q.

providing provable guarantees for this modified algorithm seems beyond the current techniques.


Since assumptions of Lipschitz continuity naturally allow one to place bounds on how far the optimum of f is from a certain location, they work to smoothly reduce the value of the acquisition function in a neighborhood of any point reflecting the belief about the distance of this point to the maxima.

assumptions of Lipschitzness are too coarse-grained and it is unclear how their method to estimate the Lipschitz constant and modelling of local penalization affects the performance from a theoretical standpoint.


Another thorny issue in applying standard MAB frameworks in practice is the assumption on a constant set of arms that are available indefinitely.

due to the inherent dynamic nature of many real-world applications, the arms available in each round may change dynamically over time.


1 The synapses shown in Figure 1 are purely bottom-up, directed from simple to complex features.

there are also top-down connections in the visual system, and there is little consensus about their function.


In particular, [3] proved that under suitable conditions the unknown parameters of a noise driven system (i.e., no control) whose dynamics are modeled by linear stochastic differential equations can be estimated accurately with as few as O(log(p)) samples.

the result of [3] is not directly applicable here since for a general feedback gain L even if A 0 and B 0 are sparse, the closed loop gain A 0 − B 0 L need not be sparse.


We have presented a fully nonparametric Bayesian approach to sparse factor regression, modeling the gene-factor relationship using a sparse variant of the IBP.

the true power of nonparametric priors is evidenced by the ease of integration of task-specific models into the framework.


Theorem 1 provides recovery guarantees assuming that L * is exactly rank-r.

in several real-world scenarios, L * can be nearly rank-r. Our algorithm can handle such situations, where M = L * + N * + S * , with N * being an additive noise.


As mentioned above, there is little difference between the predictive accuracies of RAPCF and PGAS.

pGAS is computationally much more expensive.


To solve these problems, one can first discretize the domains and then use conventional search algorithms to determine plans that move the agent to the goal coordinates.

uniform discretizations can prevent one from finding a plan if (a)  they are too coarse-grained (for example, because the resolution prevents one from noticing small gaps between obstacles) and results in large state spaces that cannot be searched efficiently if they are too fine-grained.


Using this approach, the straightforward way to analyze the number of errors is pessimistic since it assumes the difference between the two eigenvectors is concentrated on a few entries.

we show that the perturbation is in fact generated by a random process and thus unlikely to be adversarially concentrated.


A related functional ANOVA GP model [9] decomposes the mean function into a weighted sum of GPs.

the effect of a particular degree of interaction cannot be quantified by that approach.


All tested methods produce results which are, upon cursory visual inspection, largely consistent with the spiketrains.

bayesian binning is better suited than Gaussian smoothing to model steep changes, such as the transient response starting at ≈ 100ms.


We can also express (3a) more succinctly as, This expression looks very much like a multivariate Gaussian density function.

we emphasize that this is not the case since both m 0:t−1 and K 0:t−1 depend (nonlinearly) on the argument x 1:t . In fact, (4) will typically be very far from Gaussian.


For any x ∈ S ∪ {q}, the projection is This is exactly the projection we want.

it requires both S and q, whereas in practice, we will initially have to project just S by itself, and we will only later be given some (arbitrary) q.


While there is an analogy between the inference procedures, in the EM algorithm the parameter learning of the model is conducted analytically, at the expense of the restrictions of the assumed statistical model.

in GNNs the learning is conducted numerically in a data-driven manner [15], for example by backpropagation.


They considered an 2 -penalty and showed that their online algorithm converges to the minimum objective value in the stochastic case (i.e., with distributional assumptions on the data).

the ideas proposed in [12] do not translate to the 1 -penalty.


Our model is similar to discriminatively trained part based model in [6] in that we train SVM classifiers for each part of object and geometric arrangement of parts is captured by a set of "springs".

our learning method is quite different from [6].


The second term scales worse, since one must compute averages over the union of two overlapping cliques and because of the double sum.


Yu [37] proposed a learning rate for stable training through Lyapunov functions.

these methods mainly target Jordan and Elman networks called simple RNNs which, unlike GRUs, are difficult to train long-term dependencies.


It is easy to see that in this case the product model will also be Gaussian.

if each Gaussian has a simple structure, the product can have a richer structure.


From the previous discussions, OCCA captures the input-output relation to minimize the prediction error in bound (1) with the "easy" directions.

pLST minimizes the encoding error in bound (1) with the "principal" directions.


Theorem 2.4 says that for any shift a > 1 there is a parameter α(a) > 4 such that (9) holds.

for the choice a = O(1) one has to set α such that α α−4 = Ω( d k ) and the last term in (9) will be of order O( d 3 k 3 T 2 ), thus requiring T = Ω( d 1.5 k 1.5 ) steps to yield convergence.


( 1), the Fisher vector of the whole image is 2 This is equivalent to performing the sum-pooling for the extracted Fisher coding vectors.

it has been observed [3,12] that the image signature obtained using sum-pooling tends to overemphasize the information from the background [3] or bursting visual words [12].


Typically, the optimal matrix involves negative coefficients, hence departing from the random walk interpretation.

even the optimal choice of symmetric matrix is shown to yield a diffusive rate of convergence, which is already attained by the matrix W M H [7].


Note, that our approach is not equivalent to a variational approximation of the original posterior.

u ws contains the full information of the statistics of the training data.


Naively, categorical random variables with spatial/temporal dependencies can be modeled by a standard HMM with multinomial emission models.

the limited flexibility of each multinomial distribution and the concomitant need for a potentially large number of states to model complex domains may require a large parameter count and lead to overfitting.


It is not surprising, as in those conditions, where one should rely more on the long term statistics, if the learning rate is too high, then subjects will tend to shift more due to recent experience (Fig 2b), which would adversely influence decision optimality.

in a high volatility environment, decision optimality has a linear correlation with the learning rate, suggesting that higher learning rate leads to better performance.


In the margin framework, standard weight decay (l 2 ) regularization seemed to have little impact on margin distributions in Section 2.

in the boosting literature, special types of regularization were developed to maximize margins [Shalev-Shwartz and Singer, 2008]; perhaps a similar development can be performed here?


We can observe that most classes are tightly clustered around their corresponding word vector while the zero-shot classes (cat and truck for this mapping) do not have close-by vectors.

the images of the two zero-shot classes are close to semantically similar classes (such as in the case of cat, which is close to dog and horse but is far away from car or ship).


The twolayer circuit with reciprocal synapses [17,18,19] can be derived from the minimization of the representation error.

the activity of principal neurons in the circuit is a dummy variable without its own dynamics.


We however chose SVGD specifically for BMAML because jointly updating the particles altogether is more efficient for capturing the distribution quickly by a small number of update steps.

mCMC would require to wait for much more iterations until the chain mixes enough and a long backpropagation steps through the chain.


Related concepts such as count-based bonuses have been shown to provide substantial speedups in classic reinforcement learning (Strehl & Littman, 2009;Kolter & Ng, 2009), and several recent works have proposed information-theoretic or probabilistic approaches to exploration based on this idea (Houthooft et al., 2016;Chentanez et al., 2005) by drawing on formal results in simpler discrete or linear systems (Bubeck & Cesa-Bianchi, 2012).

most novelty estimation methods rely on building generative or predictive models that explicitly model the distribution over the current or next observation.


They propose a dense NRSfM method that minimizes a robust discontinuity term over the recovered 3D depth along with 3D shape rank.

their method assumes as input full-length trajectories obtained via the subspace flow tracking method of [16].


However, we conjecture that the worst case is when µ 1 and µ 2 are much larger than the other means: then, the regret is almost the same as in the 2-arm case, and ETC strategies are suboptimal by a factor 2.

the most favourable case (in terms of relative efficiency) seems to be when µ 2 = • • • = µ K : then and T * = 2( √ K − 1 + 1) 2 /∆ 2 , leading to lim sup while Lai and Robbins' lower bound yields 2(K − 1)/∆.


Finally, the algorithm estimates depth for all pixels assuming a constant depth within each superpixel.

our algorithm consists of a single deep network that directly predicts pixel-wise depth (Fig.


• The performance of ERM is similar to that of RF-Oja and RF-ERM in terms to overall runtime.

due to larger space complexity of O(n 2 ), ERM becomes infeasible for large-scale problems; this makes a case for streaming/stochastic approximation algorithms.


Proof We establish the equivalence of ( 9) and ( 11) by showing the equivalence (10) and (11).

by the nonhomogeneous Farkas theorem [9, Theorem 2.4.8] we have that ( 10) is equivalent to either: B'u + w = 0, b'u + ry + 1::; 0, u 2: 0, having solution (u, w), (13) or (14) the second alternative ( 14) contradicts the nonemptiness ofthe knowledgeset {x I Bx::; b}, because for x in this set and u solving (14) gives the contradiction: (15) Hence ( 14) is ruled out and we have that ( 10) is equivalent to (13) which is (11).


They further showed that their algorithm could easily be parallelized and performed better numerically than the dueling bandit algorithm in Yue and Joachims (2009).

since they considered only the unconstrained case in which A = R d , it is not possible to apply their algorithm to the setting considered here, in which the action space is compact.


This allows us to decompose the transition function as a mean value in S plus additive noise s Õ ≥ P M (•|s, a) =∆ s Õ = p M (s, a) + ' P . At first this may seem to exclude discrete MDPs with S states from our analysis.

we can represent the discrete state as a probability vector s t oe S = [0, 1] S µ R S with a single active component equal to 1 and 0 otherwise.


For example, in the first component of Figure 1, the content vector models the appearance of the digit "9".

formally, we assume the content vector is the same for all frames in both the input and the prediction: the pose vector z i t,P is low-dimensional, which captures the location of the digit in Figure 1.


Solving the optimization problems Note that the optimization problems (2) and ( 8  can be solved using Interior-point methods (IPM).

the computational complexity of IPM applied to SOCP with dense matrices grows rapidly with problem dimension, so that large problems of this type arising in signal and image processing are well beyond the reach of these techniques.


Thus, the difference of disagreements of σ * and σ * a↔b with V on such pairs is Suboptimality of approval voting for distances other than the KT distance stems from the fact that in counting the number of approvals for a given alternative, one discards information regarding other alternatives approved along with the given alternative in various votes.

no such information is discarded when only one alternative is approved (or not approved) in each vote.


Then, E[( For many functionals, a Hölderian assumption (Σ(s, L)) alone is sufficient to guarantee the rates in Theorems 5,6 and 7.

for some functionals (such as the α-divergences) we require f , ĝ, f, g to be bounded above and below.


The effect of word frequency in the topic model can be seen in the rank-order correlation of the predicted ranks of the first associates with the ranks predicted by word frequency alone , which is p = 0.49.

the cosine is used in LSA because it explicitly removes the effect of word frequency, with the corresponding correlation being p = -0.01.


the network correctly learns to use the face analysis module when the word "happy" is present in the question.

the face analysis module incorrectly classifies the face as "Angry" misleading the network to give a wrong answer.


Second, to ensure differential privacy by running the exponential mechanism, one needs a priori knowledge of the set U (and thus the universe of items I) independently of the observed data; otherwise the process will not be end-to-end differentially private.

our algorithm does not need to know I in order to provide end-to-end differential privacy.


Finally, prior to undertaking our work on hierarchical apprenticeship learning, we invested several weeks attempting to hand-tune controller capable of picking good footsteps across challenging terrain.

none of our previous efforts could significantly outperform the controller presented here, learned from about 10 minutes worth of data, and many of our previous efforts performed substantially worse.


Specifically, a good learning algorithm for dueling bandits will eventually compare the winner against itself.

comparing one arm against itself does not provide any statistical information, which is critical in TS to update the posterior distribution.


The CountSketch scheme thus constructs a sketching matrix A such that every column has O(lg(1/δ)) non-zero entries.

this construction does not provide a norm-preserving embedding into a Euclidean space (that is, the estimator of x 2 2 cannot be represented as a norm of Ax), which is essential for some applications such as nearest-neighbor search [HIM12].


With a more refined analysis that avoids the use of Hölder's inequality in (6) and a stronger notion of nice episodes called friendly episodes we obtain the bound with the first term in the min.

since a similar analysis has been recently released [16], we defer this discussion to the appendix.


Thus, contrary to the non-decreasing case [3], our regularizers are not norms.

they are norms on the hyperplane {w ⊤ 1 V = 0} as soon as for A = ∅ and A = V , F (A) > 0 (which we assume for the rest of this paper).


Note that an outbreak in some region S does not affect the disease rate outside region S. Thus we can use the same values of α out (S) and β out (S) whether we are assuming the null hypothesis H 0 or the alternative hypothesis H 1 (S).

the effect of an outbreak inside region S must be taken into account when computing α in (S) and β in (S); since we assume that no outbreak has occurred in the past data, we cannot just use the sample mean and variance, but must consider what we expect these quantities to be in the event of an outbreak.


Nevertheless, at least for finite action sets, the tools developed in [1,3,2] look suitable to show that under appropriate conditions these problems can be overcome if the function set is chosen in a judicious way.

the results of these works would become essentially useless in the case of an infinite number of actions since these previous bounds grow to infinity with the number of actions.


In contrast to most modeling work appearing in the NIPS volumes, our model is cast at Marr's implementation level, not at the level of a computational theory.

after introducing our model and showing its predictive power, we discuss an intriguingly similar Bayesian theory of memory adaptation (Kording et al., 2007).


If the data follows the r-spiked model, the optimal step size will be close to 1 if there is no sub-sampling.

due to fluctuations resulting from sub-sampling, we suggest the following step size choice for NewSt: In general, this formula yields a step size greater than 1, which is due to rank thresholding, providing faster convergence.


AdvGAN also proposes to use GANs for creating adversarial examples.

their adversarial examples are still based on small norm-bounded perturbations.


While N N N and N OR N are convex, PSD N K is not.

[10] show that alternating projection with a non-convex set still works under certain conditions, guaranteeing a local convergence.


On one hand, F must be "rich enough" so that the population MMD vanishes if and only if p = q.

for the test to be consistent, F needs to be "restrictive" enough for the empirical estimate of MMD to converge quickly to its expectation as the sample size increases.


Our work is also related to the prior works in cross-domain image generation [31,32,33], which studied transforming an image in one style to the corresponding images in another style.

we focus on learning the joint distribution in an unsupervised fashion, while [31,32,33] focus on learning a transformation function directly in a supervised fashion.


In addition, we are not working with a reproducing kernel Hilbert space since we are considering L 2 .

our definition in Equation 5 defines the "point evaluation" of our membrane potential function.


Having similar payoffs and chance-outcomes under aggregated information sets is natural.

the requirement that information-set-action pairs are the same for leaf nodes mapped to each other is not satisfied by the best heuristic abstraction algorithms used in practice [10,14,24].


For low-dimensional inference problems, algorithms that employ sequential Monte-Carlo (SMC) methods [19] [20] typically yield good results.

unlike the Gibbs samplers mentioned above, SMC-based methods often do not scale well with dimension.


Such work has been extended to probabilistic [7] and sparse formulations [8].

a key limitation of CCA-based approaches is that they only admit efficient global solutions when using the squared-error loss (i.e.


The problem with above algorithm is that it allows only linear classification rules.

linear classifiers may not suffice to obtain in many applications, including the sound localization application.


Then, from equation (13), we obtain that  Combining equations ( 15) and ( 16), we have Assume that the prior probabilities of the classes are the same, i.e., P i = P j = P , which holds for most EEG experiments.

then equation ( 17) becomes from Σ = Combining equations ( 19) and ( 18), we obtain that Let Σi (k = 1, • • • , c) denote the new class covariance matrices computed via equation (8).


MADDPG and COMA both use a centralized critic that takes as input the observations and actions of all agents.

mADDPG and COMA have to train an independent policy network for each agent, where each agent would learn a policy specializing specific tasks [11], and the policy network easily overfits to the number of agents.


Specializing this bound to the case of standard Gaussian designs, the analysis of [10] shows formally that no test can detect θ 0,i = 0, with a fixed degree of confidence, unless |θ 0,i | ≥ cσ/ √ n. (ii) The sample size must satisfy n ≥ s 0 .

indeed, if this is not the case, for each θ 0 with support of size |S| = s 0 , there is a one parameter family {θ 0 (t) = θ 0 + t v} t∈R with supp(θ 0 (t)) ⊆ S, Xθ 0 (t) = Xθ 0 and, for specific values of t, the support of θ 0 (t) is strictly contained in S. there is no fundamental reason to assume the irrepresentability condition (4).


the conditional independence constraints implied by the factorization (3) imply the following .


In the constellation models from [18], [42] parts are constrained to be in a sparse set of locations determined by an interest point operator, and their geometric arrangement is captured by a Gaussian distribution.

pictorial structure models [15], [20] define a matching problem where parts have an individual match cost in a dense set of locations, and their geometric arrangement is constrained by a set of "springs" connecting pairs of parts.


This happens when similar words align well between the two sentences.

since the matrix dimensions vary based on the sentence lengths one cannot simply feed the similarity matrix into a standard neural network or classifier.


Thus, struggles to approximate probability densities with singularities, which are useful in models where sparsity is appropriate.

themethod allows to estimate the gradient for a wider class of variational distributions, including gamma and beta distributions, which are more appropriate to encode sparsity constraints.


Given access to t, the resulting concept class has VC dimension 1.

given instead access to a projection s for the action of the subgroup Z n1 ⇥ {0}, the class e P := {p(•|s) : p 2 P} has 2✏-uniform shattering dimension n 2 .


Moreover, authors in [25] show that the number of negative eigenvalues of the Bethe Hessian gives a more accurate estimate of the rank of A than that based on trimming+SVD.

we see that if the topology is not locally-tree-like but with some noise, for example with some additional cliques, both trimming of the data matrix and Bethe Hessian perform much worse, reporting a wrong rank, and giving a large reconstruction error, as illustrated in Fig.


Alternatively, we could try to limit the number or frequency of queries from each user, forbid adaptive querying, or assume users work independently of each other, remaining oblivious to other users' queries and answers.

it is nearly impossible to enforce such restrictions.


With the changing of the random "noise" vector, the generated samples will change a lot.

the data imputation task requires the imputed value as close as possible to the original incomplete data.


To ask the adequate question, deep learning and reinforcement learning have been recently applied.

these approaches struggle to find a competent recurrent neural questioner, owing to the complexity of learning a series of sentences.


The common choice is principal component analysis (PCA) feature, which is able to reduce the data dimension and identify the most important features [1].

pCA feature is not necessarily discriminative and also may loss the useful information.


Most of the convolutional autoencoders are designed to downsample the spatial dimension in order to increase the receptive field.

the paraphraser maintains the spatial dimension while adjusting the number of factor channels because it uses the feature maps of the last group which has a sufficiently reduced spatial dimension.


The posterior is sharply peaked, with most samples being from the MAP solution, and so our learner does about as well as the MDL learner.

sampling offers an (approximate) predictive posterior over predictions on the held out examples; in a real world scenario, one would offer the top C predictions to the user and let them choose, much like how spelling correction works.


Generative state estimators based on probabilistic filters and smoothers are one of the most popular classes of state estimators.

generative models are limited in their ability to handle rich observations, such as camera images, since they must model the full distribution over sensor readings.


This way of evaluating the BELU score is consistent with [5] and [2], and reproduces the 33.3 score of [29].

if we evaluate the state of the art system of [9] (whose predictions can be downloaded from statmt.org\matrix) in this manner, we get 37.0, which is greater than the 35.8 reported by statmt.org\matrix.


in the Sutton and Barto-models these filtered input signals are only used as an input for the learning circuit (Fig.


The previous samples provide information about the target distribution, so it is reasonable to use them to adapt the kernel.

naively tuning the sampling parameters using all previous samples may lead to an invalid chain, that is, a chain that does not have π as its invariant distribution.


With a sparsity-promoting ψ(x), this reduces to a (soft) thresholding step, and thus ensures a sparse solution.

in each iteration of AC-SA, its output is a convex combination of two other variables.


Deep learning (DL) has obtained unprecedented progress in various tasks, including image classification, speech recognition, and natural language processing [11].

a high-accuracy DL model can be vulnerable in the adversarial setting [12,33], where adversarial examples are maliciously generated to mislead the model to output wrong predictions.


Applications of SVD such as eigenface [20,21] and latent semantic analysis [4] have been illustrated to be very successful.

the basis vectors resulting from SVD have little concrete meaning, which makes it very difficult for us to understand and interpret the data in question.


Nesterov's seminal work [11] has rigorously proved that coordinate descent can reduce the Lipschitz constant of the problem, and thus allows larger step sizes than gradient descent.

due to the sophisticated coupling of primal and dual variable updates in our algorithm, our analysis is currently unable to reflect this property.


This differs from the usual beta process in the subtraction of σ from m k and addition of σ to n − m k + c. This is reminiscent of the Pitman-Yor generalization to the Dirichlet process [11,12,13], where a discount parameter is subtracted from the number of customers seated around each table, and added to the chance of sitting at a new table.

the Lévy measure of the random atoms of µ is still a Lévy measure corresponding to an SBP with updated parameters Note that the update depends only on n, not on Z 1 , .


Exploring many parameterizations of the KF model, we find that the model generally predicts decreasing or constant optimal ISIs as a function of the RI.

mCM necessarily produces an increasing optimal ISI as a function of the RI, consistent with all behavioral data.


These approaches approaches differ significantly from the spectrum based methods, and provide equally important theoretical insight.

their empirical behaviour was never studied, and it is likely that even for graphs generated from the SBM, extremely high values of N would be required for the algorithms to work, due to large constants in the concentration inequalities (see the concluding remarks in [19]).


Unlike in Table 2, L dis outperforms L add , suggesting that disentangling may allow new animations to be learned in a more data-efficient manner.

l dis has an advantage in that it can average the identity features of multiple views of a query character, which L add cannot do.


These methods demonstrate that augmenting visual features with 3D information can enhance object detection in cluttered, realworld environments.

these works do not make use of the contextual relationships between various objects which have been shown to be useful for tasks such as object detection and scene understanding in 2D images.


From the above discussion, we observe that the iteration complexity in stochastic optimization is polynomial in 1 ǫ , making it difficult to find high-precision solutions.

when the objective function is strongly convex and can be written as a sum of a finite number of functions, i.e., where each f i (•) is smooth, the iteration complexity of some specific algorithms may exhibit a logarithmic dependence on 1 ǫ , i.e., a linear convergence rate.


In this way, the hypothesis y = (p) is preferred to y = only if F (x, p; w) > F (x, ; w) = 0, which implicitly sets the detection threshold to zero.

there is no reason to assume that this threshold should be appropriate (in Fig.


While this is similar to what is done by the Σ-SVM, the matrix (I+ Σ λ ) is determined jointly considering both the margin of the data and the spread.

in Σ-SVM, whitening is simply a prepossessing step which can be done independently of the margin.


For pool-based active learning, several effective methods with theoretical guarantees have been developed through maximizing some utility function satisfying adaptive submodularity.

there have been few methods for stream-based active learning based on adaptive submodularity.


Since the second term in equation 8 couples both Z and W and b dec , it is not straightforward to minimize this energy with respect to both.

once Z is given, the minimization with respect to W is a convex quadratic problem.


First we address invariance with respect to W . Obviously the equality constraint is unaltered by a full rank W , so it only remains to check that the dictionary-dependent penalty g (II) is invariant.

since by standard determinant relationships log , where C is an irrelevant constant for optimization purposes, this point is established.


This term provides subtractive normalization that counteracts the use-dependent LTD [4, p. 290].

subtractive normalization cannot prohibit w from running away when the error signal is turned off.


In this case, the optimal sample complexity nmp is On the one hand, this result suggests that the social graph information does not help rating recovery when the number of users is relatively smaller than that of items.

more precisely, when 2n log n ≤ 4γm log m, both (1) and ( 2) are equal to 2m log m/( when 2n log n > 4γm log m, i.e., (1) 2 , the result implies that the social graph information does help rating recovery.


Given the limited amount of device memory on GPUs, we cannot load all training data and model parameters into the device memory for large-scale datasets.

the sequential nature of Gibbs sampling and variational Bayesian inferences allow us to implement a data streaming [5] scheme which effectively reduces GPU device memory space requirements.


Figures 3e and 3f, however, show that when there is a large degree of class overlap the entropy and differential entropy have different behavior -entropy is high both in region of class overlap and far from training data, making difficult to distinguish out-of-distribution samples and in-distribution samples at a decision boundary.

the differential entropy is low over the whole region of training data and high outside, allowing the in-distribution region to be clearly distinguished from the out-of-distribution region.


In our application, an object is a handwritten word and its parts are the letters.

the m ethod we propose is quite general and can easily be extended to two dimensional problems.


A popular approach to neural characterization describes neural responses in terms of a cascade of linear and nonlinear stages: a linear filter to describe stimulus integration, followed by a nonlinear function to convert the filter output to spike rate.

real neurons respond to stimuli in a manner that depends on the nonlinear integration of excitatory and inhibitory synaptic inputs.


Interestingly, the objective of [20] is to remove the parametric assumptions of [21,9] by offering the THRESHOLDASCENT algorithm.

no analysis of this algorithm for extreme bandits is provided.


If we restrict ourselves to the nearest neighbor search, some methods using space partitioning trees such as KD-tree [4], R-tree [5], or their variations have been widely used.

they become impractical for high dimensions because of their poor performance in constructing data structures for queries.


For example, note that if either x i * or A * were known, given y i , this would just be a (matrix/sparse) regression problem.

estimating both x i * and A * simultaneously leads to both computational as well as statistical complications.


Although TRPO-SimHash picks up the sparse reward on HalfCheetah, it does not perform as well as VIME.

the performance of SimHash is comparable with VIME on MountainCar, while it outperforms VIME on SwimmerGather.


It has been shown that also for k-ISA, scalings and permutations as above are the only indeterminacies [11], given some additional rather weak restrictions to the model.

a serious drawback of k-ISA (and hence of ICA) lies in the fact that the requirement fixed group-size k does not allow us to apply this analysis to an arbitrary random vector.


These two terms would appear alone in a straightforward representational model of the joint distribution over sensory stimuli and values.

in considering a representational subsystem within a reinforcement learning agent, where the overall goal is to maximise accumulated reward, it seems reasonable that the demand for representative or predictive fidelity depend on the value associated with the stimulus; this dependence is reflected here by a value-based weighting of the log probabilities, which we assume will weight the more valuable cases more heavily.


The disadvantage of this form of generative model is that there is no simple expectation-maximisation (EM) [1] scheme for estimating the model parameters.

a simple iterative scheme is available [3].


Under mild conditions, StARS is partially sparsistent.

even without these conditions, StARS has a simple interpretation: we use the least amount of regularization that simultaneously makes a graph sparse and replicable under random sampling.


The success of survey inspired decimation relies on the fact that marginals carry some signal about the likely assignments of variables.

the factor graph becomes more dense as the constraint density approaches the phase transition threshold, making it harder for survey propagation to converge in practice.


The result shows that simply composing templates that mostly describe normal medical findings can lead to high automatic evaluation scores since the majority reports describe normal cases.

this kind retrieval-based approaches lack of the capability of detecting significant but rare abnormal findings.


Typically, the designer assigns his or her own reward to the agent.

there is ample work which demonstrates the benefit of assigning reward which does not match the designer's.


Beta prior distribution of context change can be initialized as a uniform distribution, (α, β) = (1, 1).

based on a preliminary experiment we set it to (α, β) = (1, 50): this means we initially assume a context change rate of once every 50 words in average, which will be updated adaptively.


Alternative approaches take inspiration from biological spike-time dependent plasticity (STDP) [20,21], and reward-modulated STDP process [22,23,24].

it is generally hard to guarantee convergence of these bottom-up approaches, which do not consider the complex effects network dynamics nor the task information in designing of the learning rule.


For efficient implementation of RNN, several model compression techniques have been developed, such as pruning [15], quantization [16], and matrix decomposition [17].

these techniques need efficient data rearrangement and decompression; therefore, they are not explored in this work.


Recall that the evidence maximization procedure upon which ARD is based involves integrating out the unknown sources before optimizing the hyperparameters γ.

if some p(γ) is assumed for γ, then we could just as easily do the opposite: namely, we can integrate out the hyperparameters and then maximize S directly, thus solving the MAP estimation problem max S p (B|S) p (S; Σ s ) p(γ)dγ ≡ min where each A i is derived from the i-th covariance component such that C i = A i A T i , and g(•) is a function dependent on p(γ).


parameters W and binary hidden variables {z i } N i=1 [1].

given hidden variables, the problem is convex w.r.t.


Since the variables within a block are described as a low-dimensional dynamical system, the updates of the densities for the Gibbs sampling can be computed efficiently via a standard particle filter [10,11].

simulations of the method show that the mixing between blocks can still take considerable time to converge.


8,12,13,15,17,18,20 Based on these roughly similar anatomical and physiological properties, cholinergic and noradrenergic systems have been attributed correspondingly similar general computational roles, such as modulating the signal-to-noise ratio in sensory processing.

9,10 the effects of ACh and NE depletion in animal behavioral studies, as well as microdialysis of the neuromodulators during different conditions, point to more specific and distinct computational roles for ACh and NE.


This implies that, in principle, the predicted interval equals the universal interval.

for some outcomes the assigned weight will be extremely small.


discuss the use of an additional "missing" tree node to handle these cases [9].

this approach can effectively make repeated searches over subsets of trees, making it more expensive both in theory and practice.


Probabilistically-correct inference should then implement selection, when data that is known to be irrelevant is excluded to the advantage of the relevant information (eg Dayan and Zemel, 1999;Palmer, 1994).

in other circumstances, it will be appropriate to take advantage of the information about the target that is available in the neurons with large fields, even if this means allowing some influence on the final decisions from distractors.


Note that, if we do not restrict the form of Y, then a trivial solution to this problem is to learn identity mappings by setting y = Φ(x ) = x and Ψ(x, y ) = y .

given that y has the "form" of a set of landmark detections, the model is strongly encouraged to learn those.


When P k,α and P k,β are two N × N matrices, then P is a N 2 × N 2 matrix.

as we will see in the next subsection, we actually never compute P explicitly.


This method is computationally slower than using equation 7 and is vulnerable to worse results if the learnt input noise variance Σ x is very different from the true value.

it gives proper consideration to the uncertainty surrounding the test point and exactly computes the moments of the correct posterior distribution.


In this case, the green decision boundary should obtain zero test error even if it is estimated from a finite number of samples.

for finite training data, the SVM solution will make errors and will do so increasingly as the data is scaled along the x-axis.


The same kernel function can be derived from a large margin classification viewpoint [6].

to our knowledge, the preference kernel has not been used previously for GP-based models.


These results tend to show that ErrP could be a potential tool to improve the quality of the brain-computer interaction.

it is to note that in order to isolate the issue of the recognition of ErrP out of the more difficult and general problem of a whole BCI where erroneous feedback can be due to nonoptimal performance of both the interface (i.e., the classifier embedded into the interface) and the user himself, the subject delivered commands manually.


The best known algorithm for active learning of rectangles (2, δ)-learns a very restricted class of distributions (continuous product distributions which are sufficiently balanced in all directions) with an active label complexity of Õ(d 3 p(ln(1/η)p(ln(1/δ))), where p(•) is a polynomial (Hanneke, 2007b).

for a general distribution, active label complexity cannot be significantly better than passive label complexity.


For finite dimensional spaces and self-concordant losses, an optimal parameter-free stochastic algorithm has been proposed in [2].

the convergence result seems specific to finite dimension.


For each domain, for each k, there were λ values for which the performance was worse than the baseline.

for many sets of hyperparameters, the performance exceeded the baselines.


However LSTD is concerned with finding a least-squares linear function approximation, it has not yet been developed for general γ and λ, and has update time quadratic in the number of features/states.

our algorithm "exactly" coincides with TD/Q/Sarsa(λ) for finite state spaces, but with a novel learning rate derived from statistical principles.


For finite state space problems, the Expectation Maximization (EM) algorithm is a popular method for solving the MLE problem.

in continuous space problems, see [CM05], the EM algorithm is difficult to use mainly because the Expectation part relies on the estimation of the posterior path measure which is intractable in many situations.


It is important to point out that each posterior density estimate at point n depends solely on the corresponding measurement x n and does not depend on any other x k , k = n. This means that even if we partition independent measurements into arbitrary subsets, posterior density estimation is accomplished locally, within each subset.

in the M-step all measurements X affect the choice of θ because of the dependence of each term in the completed log likelihood on the same θ.


However, the bootstrap tests require computation of the test statistic multiple times (equal to number of bootstrap samples b; we use b = 200 in our experiments).

the proposed test compute the statistic once, and is much faster (∼200 times).


The variational parameters ω i are specific to the tasks used during meta-training, and will not be useful for a new task.

since the KL-divergence loss (Eqn 3) encourages the pre-update parameters to be close to the prior, all of the variational parameters ω i are driven to the prior at convergence (Fig 5a).


The choice of θ 0 strongly influences the non-discrimination constraint.

as the example shows, it allows R θ to exploit features that exhibit potential proxy discrimination.


For example, high quality POS taggers [1], parsers [2], sentiment analyzers [3] are readily available for English.

this is not the case for many other languages such as Hindi, Marathi, Bodo, Farsi, and Urdu, for which annotated data is scarce.


We will assume a noisy-OR gate, and thus our model is closely related to causal power.

we propose to model human estimates of P(C -+E ) as causal support, the log posterior odds in favor of Graphl (h e = 1) over Grapho (h e = 0) : Via Bayes' rule, we can express P( he = l 1 X) in terms of the marginal likelihood or eviden ce, P(X lhe = 1), and the prior probability that C is a cause of E , P(h e = 1) : P(h e = l 1X) ex P( Xl he = I)P(h e = 1).


Hence we choose another popular technique -particle filter.

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


To understand this condition, note that if L n were actually strongly convex, then both these RSC inequalities would hold with α 1 = α 2 > 0 and τ 1 = τ 2 = 0.

in the high-dimensional setting (p n), the empirical loss L n can never be strongly convex, but the RSC condition may still hold with strictly positive (α j , τ j ).


All these methods above prune the network in a fixed way, obtaining a static model for all the input images.

it is obvious that some of the input sample are easier for recognition, which can be recognized by simple and fast models.


The proof hinged on the fact that all spanning subgraphs with same edge cardinality that satisfied the sufficiency condition for existence of any -PSNE were equally good with respect to our deterministic submodular function, and we created an instance with exponentially such spanning subgraphs.

we might be able to circumvent Theorem 3 by breaking the symmetry, e.g., by using data that specifies multiple distinct -Nash equilibria.


It is important to point out that, for most forms of Pr[x | y], the model is analytically intractable [21].

when Pr[x | y] has an exponential form, such as Pr[x | y] = f (x)e −f (x)y , the model has several interesting properties [12,13].


However, to see why it is difficult to compute the exact value of α in the nonparametric case, suppose we have computed the minimum cost of paths up to step t − 1 and we would like to compute the values of α for step t. The cost of a path that ends in state c is obtained by examining, for all states i, the cost of a path that ends at i at step t − 1 and then transitions to state c at step t. Thus, we must consider the transition from i to c. If there are existing transitions from state i to state c, then we proceed as in a standard forward-backward algorithm.

we are also interested in two other cases-one where there are no existing transitions from i to c but we consider this transition along with a penalty λ 1 , and another where an entirely new state is formed and we pay a penalty λ 2 .


To sample the θ i , we could launch a thread per row.

as the number of columns is much larger than the number of rows, we launch a thread to generate the gamma variates for each column, and then separately compute a normalizing constant for each row by multiplying the matrix with a vector of ones using CUBLAS.


First, in influence maximization, the state of each user is often assumed to be binary, either adopting a product or not [1,3,4,5].

such assumption does not capture the recurrent nature of product usage, where the frequency of the usage matters.


Human long-term memory can store a remarkable amount of visual information and remember thousands of different pictures even after seeing each of them only once [25,1].

it appears to be the fate of visual memories that they degrade [13,30].


Even by imposing the above constraints, this number grows rapidly with P i and W i .

since different assignments share many common sub-assignments, the number of unique likelihood computations is much lower, namely P i • (W i + 1).


However, the EPG loss for this family of tasks is unlikely to be at all effective on a wildly different kind of task, like playing Space Invaders.

standard RL losses do have this level of generality -the same loss function can be used to learn a huge variety of skills.


A particularly nice feature of our bounds is that their computational cost is relatively low, provided that the number of possible values of each variable in the factor graph is small.

the computational complexity is exponential in the number of possible values of the variables, which limits application to factor graphs in which each variable has a low number of possible values.


Unfortunately, it is difficult to incorporate large amounts of detailed statistical knowledge about the problem into such an approach.

machine learning researchers, especially those working on independent components analysis (lCA) and related algorithms, have focused on the case of multiple microphones in simplified mixing environments and have used powerful "blind" statistical techniques.


Recent work focuses on algorithms whose runtimes do not depend on properties of A.

classical literature typically gives runtime bounds that depend on the gaps between A's singular values and become useless when these gaps are small (which is often the case in practice -see Section 6).


At test time, the bound can be computed exactly, as the gradients no longer need to be stored.

if desired, it is possible to use a different estimator (specifically, the geometric estimator) for the ∞ norm to calculate high probability bounds on the adversarial problem, which is discussed in Appendix E.1.


It is worth noting that such normalization is accomplished without modeling joint distributions of response across orientations.


Specialized algorithms have also been proposed for accommodating proximal terms [9], and for further acceleration through the condition number [10][11][12][13].

not all empirical risks are separable in its plain form, and in many cases dualization is necessary for achieving separability.


These approaches are easy to train and inference is computationally cheap.

a high entropy posterior over classes could indicate uncertainty in the prediction due to either an in-distribution input in a region of class overlap or an out-of-distribution input far from the training data.


They have a fixed input size and typically perceive only small local contexts of the pixels to be classified as foreground or background.

multi-Dimensional Recurrent NNs (MD-RNNs) can perceive the entire spatio-temporal context of each pixel in a few sweeps through all pixels, especially when the RNN is a Long Short-Term Memory (LSTM).


In machine learning problems the data often live in a vector space, typically a Euclidean space.

there are many other kinds of non-Euclidean spaces suitable for data outside this conventional context.


The multi-task aspect of their work focused on finding common feature weights across multiple, related tasks.

our work focuses on classification and learns different metrics with shared components.


ψ can be modeled as a parametric noisy-channel, where the parameters of ψ can also be learned during training.

we model ψ as dropout [18] (multiplicative Bernoulli noise) because it provides an easy and straightforward method for noisy-transformation of e 1 into ẽ1 without complicating the training process.


Given T , the c m, variables are deterministic-simply look up the th level of the mth path in the infinite collection of paths.

not having observed T , the distribution of c m, will be defined by the nested Chinese restaurant process, conditioned on all the c q, for q < m. Now suppose we are given a corpus of M documents, w 1 , .


Recurrent Neural Networks (RNNs) have been found to be successful in a variety of sequence learning problems [4,3,9], including those involving long term dependencies (e.g., [1,23]).

most of the empirical success has not been with "plain" RNNs but rather with alternate, more complex structures, such as Long Short-Term Memory (LSTM) networks [7] or Gated Recurrent Units (GRUs) [3].


In principle, it would be possible to eliminate all nonlinearities by using Schur complements and to reformulate (5) as a linear SDP, which is formally tractable.

it is folklore knowledge that general-purpose SDP solvers are yet to be developed that can reliably solve large-scale problem instances.


The cost of a kernel MVM is increased by a factor P/C < 2, which in most hierarchies in practice is close to 1.

it would be wrong to claim that hierarchical classification in general comes as cheap as flat classification.


Variance reducing techniques have also been applied to these settings, including smoothed stochastic variational inference (SSVI) [25] and variance reduced stochastic gradient MCMC (VRSGMCMC) algorithms [13,8,7].

convergence guarantees for SSVI have not been developed, while VRSGMCMC algorithms are typically much slower than sEM-vr due to the intrinsic randomness of MCMC.


(2002) discussed the concentration of spectral properties of Gram matrices and of the residuals of fixed projections.

these results gave deviation bounds on the sampling variability the eigenvalues of the Gram matrix, but did not address the relationship of sample and population eigenvalues, or the estimation problem of the residual of peA on new data.


Sequentially learning to place items in multi-position displays or lists is a task that can be cast into the multiple-play semi-bandit setting.

a major concern in this context is when the system cannot decide whether the user feedback for each item is actually exploitable.


In mathematical modeling of this diffusion process, Gaussian noise has been predominantly used as a model for zigzagging upon a constant drift toward a choice [3,13].

when we consider two competing Poisson signals, a simpler statistical test can be used instead of estimating the direction of the drift.


For example, Munro and Hernandez showed that their model could retrieve a stored pattern sequence even in a noisy environment [9].

the previous works have not mentioned the reason why TAH is effective.


This is quite natural and may look straightforward at a glance.

if we simply consider the population version of the objective function of (4), we have which is not equivalent to the classification risk R(g) defined by (1).


We have yet to thoroughly investigate the clinical ramifications of this work.

for the daunting task of risk stratifying patients already at an elevated risk for C. diff, an AUC of 0.79 and an odds ratio of >25 are quite good.


Prior work [Kulesza and Pereira, 2007] shows that approximate inference may not be sufficient for learning a good statistical model, even with rigorous approximation guarantees.

the successful application of various approximate inference algorithms motivates a deeper exploration of the topic.


In fact, the result follows solely from the structure of the regularizer.

we require L 2 to be convex in its first argument to ensure a convex problem below.


Still, layer 2 provides the best predictions by a small margin, giving many voxels a green tint.

auditory cortex (AC) shows a clear preference for layers 1 and 3, giving it a purple tint.


The difference between the spike rates on B1+ and B1encodes the B1 filter output.

the B1+ and B1-spike rates do not represent the ON (positive half-wave rectified) and OFF (negative half-wave rectified) components of the binocular filter outputs, since they may both be non-zero at the same time.


The local nature of EP appears to make it an ideal candidate for performing Bayesian learning on large models in large-scale dataset settings.

eP has a crucial limitation in this context: the number of approximating factors needs to increase with the number of datapoints, N , which often entails a prohibitively large memory overhead.


In the standard eigenvoice method, this is done by first breaking down the adapted speaker supervector s to its R constituent Gaussians s 1 , .

. . , s R . the use of kernel PCA does not allow us to access each constituent Gaussians directly.


We also show that our theoretical criterion for a weak learner to improve the overall model applies well in practice. . We are thus finding the first order optimal weak learner, which gives the "steepest descent" in the loss at the current model predictions.

we should note that once ¨becomes non-infinitesimal, no "optimality" property can be claimed for this selected ¢ .


The proof of the following lemma follows closely the proof of Lemma 5.3 in [8].

it considers a multiplicative risk bound rather than additive.


For example, we do not require finite moments.

as in the mixture of Gaussians case some sort of separation between the distributions is needed, this is the role of the disjoint supports.