This approach has been facilitated by hardware developments such as graphics processing units (GPUs).

this approach increases the inference and training times and consumes more memory.


As log-convex quadratic forms do not correspond to normalizable Gaussian graphical models, the log-convex case appears to be less interesting as the MAP problem is unbounded from above.

the situation is entirely different for constrained (over some convex set) log-quadratic maximization.


The study of electrical properties of materials starts off with a topic (in purple) that seems devoted to Physical Chemistry.

following the development of Quantum Mechanics in the 30s, this line of research became more closely aligned with Physics than Chemistry, and it disappears from the sub-tree.


We feed in ground truth optical flow to COVST, which is impractical for real applications.

our model estimates optical flow from source videos.


Independent Component Analysis (ICA) is a popular method for extracting independent features from visual data.

as a fundamentally linear technique, there is always nonlinear residual redundancy that is not captured by ICA.


These modeling techniques typically involved grouping entities (eg., nodes in a graph) such that interactions between these entities (eg., edges in a graph) are governed by their corresponding clusters.

these approaches do not model the nuances of decision making such as confusions of decision makers which is crucial to our work.


This additional model is also trained through amortized variational inference.

we share its prior p ξ (z|h) and approximate posterior q ξ (z|b, h) with those of the "primary" model (b is a deterministic function of x per Eq.


This includes simulated environments, such as playing Atari games (Mnih et al., 2015), and defeating the best human player at the game of Go (Silver et al., 2016), as well as robotic tasks such as helicopter control (Ng et al., 2006), hitting a baseball (Peters and Schaal, 2008), screwing a cap onto a bottle (Levine et al., 2015), or door opening (Chebotar et al., 2016).

a common challenge, especially for robotics, is the need to engineer a reward function that not only reflects the task at hand but is also carefully shaped (Ng et al., 1999) to guide the policy optimization.


When the underlying graph is a tree, the log partition function may be computed exactly via the sum product algorithm in time linear in the number of nodes [15].

when the graph contains cycles, a generalized version of the sum product algorithm known as loopy belief propagation may either fail to converge or terminate in local optima of a nonconvex objective function [26,20,8,13].


The action a * in line 6 is the maximal valued action in state s ′ , according to the value function Q A .

instead of using the value Q A (s ′ , a * ) = max a Q A (s ′ , a) to update Q A , as Q-learning would do, we use the value Q B (s ′ , a * ).


The intracellular recording therefore can be used to obtain a ground truth labeling for the spikes originating from one neuron that can be used to evaluate the performance of human sorters and automatic spike sorting algorithms that sort extracellular recordings [13].

by this method ground truth can only be determined for one of the neurons whose spikes are present in the extracellular recording, and this should be kept in mind when evaluating the performance of spike sorting algorithms on such a data set.


Finding the exact u min 1 is difficult because of the partial observability.

it is hopeful to find a good approximation to u min 1 .


This shows that indeed the forward model regularizes the inverse model and helps generalize better.

when the number of training examples is increased to 100K both models are at par.


For GMMs some innovative gradient-based methods have also been suggested [22,26], where the PD constraint is handled via a Cholesky decomposition of covariance matrices.

these works report results only for low-dimensional problems and (near) spherical covariances.


We found that if the true model is in the model class, the (downward) bias in a maximum entropy estimate from finite observations is proportional to the ratio of the number of parameters to the number of observations, a relationship which is identical to that of the (naive) histogram estimators [8,9].

we also show that if the model is misspecified (i.e.


(See, for example, [3] and references therein.)

we are not aware of any general result for random DAGs analogous to that of Friedgut [8].


Let m = cn 2 , then clearly this depiction has an O(m log m) running time.

our native implementation makes use of a stable comparison-free linear time sort and thus takes O(m) time and space.


Differently, their affinity matrix is additionally supervised by ground-truth sparse pixel similarities, which limits the potential connections between pixels.

many graphical model-based methods have successfully improved the performance of image segmentation.


With the notation f (x) = x/ x 2 , we define the AMP iteration over vectors v t ∈ R n by v 0 = y, f (v −1 ) = 0, and Our main conclusion is that the behavior of AMP is qualitatively similar to the one of power iteration.

we can establish stronger results in two respects: 1.


For example, the Dobrushin criterion is that ||R|| 1 < 1, which can be easier to verify in many cases, since ||R|| 1 = max j i |R ij | does not require the computation of singular values.

for symmetric matrices, it can be shown that ||R|| 2 ≤ ||R|| 1 , meaning the above result is tighter.


Their policy selection criterion was designed for the case when only the linear reward parameters change.

in our experiments, tasks could differ in three different ways: (1) only reward functions change, (2) only transition functions change, and (3) both reward functions and transition functions change.


Recently, supervised learning has been developed and used successfully to produce representations that have enabled leaps forward in classification accuracy for several tasks [1].

the question that has remained unanswered is whether it is possible to learn as "powerful" representations from unlabeled data without any supervision.


Observe that ℓ 1 penalty encourages sparsity of the signal at each time point and enables a selection over the relevant coefficients; whereas the total variation penalty is used to partition the interval [0, 1] so that βk is constant within each segment.

there are also some drawbacks of the procedure, as shown in Lemma 1 below.


We can try to more quantitatively describe the correctness of the inpainting procedure using as metrics the discriminator score and the leastsquares rigid-body alignment error with respect to the true native structure.

the GAN solutions are found by explicitly trying to optimize the discriminator score; hence the corresponding score will be artificially inflated relative to the baselines.


If neither solution satisfies c T α ≥ (δ Var( Ŷ )) 0.5 , by the contrapositive of Theorem 2, we can be sure that the model does not contain any proxies.

the converse does not hold, i.e., we cannot be sure that the model has a proxy even if a solution to Problem 2 satisfies c T α ≥ (δ Var( Ŷ )) 0.5 .


[4] target the image multilabeling problem but model the label noise for each label independently.

our proposed CRF model represents the relation between all noisy and clean labels while the inference over latent clean labels is still tractable.


The evolution of s (l) with l tells us the ability of the average network to separate two input points in terms of Euclidean distance.

again, for tanh and ↵-ReLU (↵ < 1) nonlinearities, s varies only polynomially with l. (l) measures the size of gradient at layer l, and through it we track the dynamics of gradient backpropagation, be it explosion or vanishing.


However, the number of mixture components in the output Y space must be pre-specified and the number of parameters is linear in the number of mixture components.

with N h stochastic hidden nodes, SFNNs can use its distributed representation to model up to 2 N h mixture components in the output Y . SFNNs contain binary stochastic hidden variables h ∈ {0, 1} N h , where N h is the number of hidden nodes.


Since the type of problem that is faced in each round is not a function of the past data, but only of the regularization, the coefficients of the value-to-go function can still be computed recursively.

extending the analysis beyond quadratic loss and constraints is difficult; the self-dual property of the 2-norm is central to the calculations.


., and the likelihood of any such sequence turns out to be independent of the dwell times (assuming the dwell times total no more than time t): If λ < 1, this implies the optimal trajectory has the system remaining at state a.

if λ = 1 then all trajectories of all lengths have the same likelihood.


If K is correctly specified, then the variance components parameters (τ, σ 2 ) can be estimated unbiasedly by maximizing the Restricted Maximum Likelihood (REML) [12]: where V = τ K + σ 2 I, and 1 a n × 1 vector whose all elements are 1.

it is worth noting that REML is a model-based procedure.


Recently, [12] proposed to overcome this issue by imposing additional physical constraints on the pose estimated by the predictor.

these constraints were imposed at inference, which required to solve a non-convex optimization problem for each test example.


To avoid the complication of dealing with spike train observations, neuroscientists often use summarizing statistics such as mean firing rate to compare two point processes.

this approach implicitly assumes a model for the underlying point process, and therefore, the choice of the summarizing statistic fundamentally restricts the validity of the inference procedure.


Yet, the integral over the action space is hard to perform for continuous actions.

we will show how we can approximate the value function without the evaluation of this integral.


So far we do not know the theoretical properties of these limit functions and thus cannot present any theoretical reason to prefer one over the other.

we think that the diagonal dominance of the Brand kernel can be problematic.


contributes to the approximation according to the following update equation : We call this new algorithm LSQ due to its similarity to LSTD.

unlike LSTD, it computes Q functions and does not expect the data to come from any particular Markov chain.


Because Python plays an important role in the ML community many popular ML frameworks are Python-based.

the language's characteristics make it difficult to implement a highperformance AD-enabled ML framework in Python directly.


In such cases we have divergence for every 0: > 0 as described in [1] for,,( = 0.9.

contradicting the argument in [1] the TD(O) algorithm converges for all "( :::; 0.88 if the learning rate is chosen appropriately.


In practice, the first C eigenvectors may not necessarily be those which carry most information about the clustering structure of the data set.

kernel MaxEnt will seek to pick those eigenvectors with the blockwise structure corresponding to cluster groupings, because this will make the sum of the elements in K y as close as possible to the sum of the elements of K x .


Both the spectral clustering and the geometric clustering algorithms mentioned above have been widely used in practice, and have been the subject of extensive theoretical and experimental studies over the decades.

these algorithms are designed for the centralized setting, and are not applicable in the setting of large-scale datasets that are maintained remotely by different sites.


One explanation why we do not see a large improvement in the latter cases is that the automatically generated sense-specific search terms happened to return relatively high-precision images.

in the other three cases, the term generation fails while our model is still able to capture the dictionary sense.


The reason is that the combination of words in this query is likely to activate one or more latent variables related to the concept of presidential campaigns.

once this generalization is made the model has "lost" the information about the specific word Camejo and it will only show up in highly ranked documents if this word happens to frequently occur in these topics (unlikely in this case given that this candidate received relatively little media coverage compared to the coverage given to the candidates from the two main parties).


Their method is able to handle variations in pose, illumination and expression.

their WSL appearance model treats pixels within the target region independently, and therefore does not have notion of the "thing" being tracked.


Interestingly, the persistent algorithms do not yield better results on this task.

we observe that the performance of deterministic EMF RBM training is at least comparable with both CD-1 and PCD.


[7] also suffers from the slow nuclear norm minimization when estimating the second and third order moments.

we use tensor method only for initialization, i.e., we require ✏ to be a certain constant.


On one hand, because of the positive externality, the platform operator is able to move the user population towards the profit maximizing population.

due to self-reinforcing preferences the impact of mistakes is amplified: if rewards are generated on suboptimal arms, the positive externality causes more users that prefer those arms to arrive in the future.


One can show that which is a set of smooth vector fields on φ(R n ) in which the vector field at each point φ(x) displaces φ(x) infinitesimally.

since φ is a diffeomorphism, we have that φ(R n ) = R n . we write v : φ(R n ) → R n to emphasize that the velocity fields in the tangent space are defined on the deformed domain, so that v is a Eulerian velocity.


In [14] authors propose a heuristic to identify the additive structure.

satisfactory theoretical certificates on cumulative regret or sufficiently practical algorithms with acquisition functions that can be efficiently optimized are lacking.


A function approximation scheme in the context of BA planning has been considered by Duff [7], in an offline actor-critic paradigm.

this was in a discrete setting where counts could be used as features for the belief.


Most prior work on label corruption robustness assumes that all training data are potentially corrupted.

it is usually the case that a number of trusted examples are available.


This pruning heuristic enforces the budget constraint in a brute-force way, and can be equally applied to any kernel-machine.

the natural question is how much will the pruning heuristic affect the classification accuracy of the kernel-machine it is applied to.


Had we directly taken the first D s = 8 columns from the permuted data matrix, we would obtain the same non-zero entries as in K 1 and K 2 , if we exclude elements in K 1 and K 2 whose IDs > D s = 8. in this example, the element 10{8} in sketch K 1 is excluded.

since the columns are already permuted, any D s columns constitute a random sample of size D s . This means, by only looking at sketches K 1 and K 2 , one can obtain a "random" sample of size D s . By statistics theory, one can easily obtain an unbiased estimate of any linear summary statistics from a random sample.


For the ReLU activation we get a stronger bound with only quadratic dependence on the depth.


We also introduces the marginal distributions Observe incidentally that the probabilistic framework of the continuous ranking problem is quite similar to that of distribution-free regression.

as shall be seen in the subsequent analysis, even if the regression function m(x) = E[Y | X = x] can be optimal under appropriate conditions, just like for regression, measuring ranking performance involves criteria that are of different nature than the expected least square error and plug-in rules may not be relevant for the goal pursued here, as depicted by Fig.


In our case, the displacement vector field components can take on both positive and negative values, and are naturally centered in the sense that across a large variety of motions, the movement in one direction is as probable as the movement in the opposite one.

given a pair of frames, the optical flow between them can be dominated by a particular displacement, e.g.


For the higher-dimensional motion tracking example, the embedded HMM has some difficulties exploring the full posterior distribution, due, we think, to the difficulty of creating pool distributions with a dense enough sampling of states to allow linking of new states at adjacent times.

the particle smoother was even more severely affected by the high dimensionality of this problem.


16 is used to efficiently compute a reasonable estimate for α M L from an arbitrary initialization.

its convergence is similar to other interior point methods in that small components of α M L will continually decrease but never equal zero.


In this section, we describe the application using the nonparametric prior to the miRNA target prediction problem.

the method is applicable in general settings where there is a way to model properties of one entity from properties of its interacting entities.


Under certain assumptions, Gaussianity in particular, the optimal hyperplane, specified by the projection w * and bias b * , is easily computed using standard statistical techniques based on class means and sample covariances for linear classifiers.

in the absence of such assumptions, one must resort to searching for the optimal hyperplane.


A naive implementation of the CPF-AS algorithm will give rise to O(T 4 ) computational complexity, since at each time step t = 1, . . . , T , a matrix of size T × T needs to be factorized.

it is possible to update and reuse the factors from the previous time step, bringing the total computational complexity down to the familiar O(T 3 ).


Since this conditional distribution of a i is Markov, we can make use of the forward filtering-backward sampling procedure to sample it.

a i is a continuous-time MJP so a direct application of the typical forward-backward algorithm is not possible.


In the limit of infinite importance samples, we also predict AIR to have zero regularizing effect since f1 (under some assumptions) can always approximate any posterior.

for practically feasible values of k, we show in Tables 2  and 3 that AIR is a highly effective regularizer.


The optimization problem in (2.1) can be solved by the alternating direction method of multipliers (ADMM) with a global convergence guarantee [20].

aDMM does not take full advantage of the problem structure in (2.1).


This is a very effective approach since it scales easily to a large number of classes.

the method does not attempt to understand the scene semantics.


These result minimizes the • 2 error, while our result minimizes the Frobenius norm, which is always higher, and may be higher by a factor of d. After appropriate weighting, we can apply the uniform sampling of size O(k/ε 2 ) to get a coreset with a small Frobenius error [14], as in our paper.

in this case the probability of success is only constant.


For VEM, X was set to 0.0001 (almost uniform) since this showed a significant improvement in performance.

eM showed less sensitivity to initialization, and we used X = 1 which resulted in the best results.


If the dynamics of the gradient method are such that the iterates remain in some bounded domain (or at least have a sufficiently slowly increasing norm), then this would not be an issue.

we are not a-priori guaranteed that this would be the case: Since the optimization problem is unconstrained, and we are not assuming anything on the structure of f θ , it could be that the parameters w, V diverge, and no meaningful algorithmic result can be derived from Thm.


Initially this density is uniform, as in RANSAC, but as regions of high likelihood are discovered, we update it so that it gives a strong bias toward producing good draws again, increasing the efficiency of the sampling process.

having found local maxima, we must still be able to escape and find the global maxima.


We note that this issue has been addressed before in literature [8,12] by way of landmark selection heuristics.

we guarantee that our predictor will select a small number of landmarks while incurring bounded generalization error.


Variants of this problem have been studied in the context of applications to numerical linear algebra [15], graphical model learning [27], nonrigid structure from motion [16], spectral estimation and Prony's problem [11], sparse PCA [29], blind source separation [28], dictionary learning [24], graphical model learning [3], and sparse coding on manifolds [21].

in contrast to the standard sparse regression problem (Ax = b, b = 0), for which convex relaxations perform nearly optimally for broad classes of designs A [14,18], the computational properties of problem (1) are not nearly as well understood.


Specifically, we compute ↵ i,j for patch i as the mean over all pixels p in that patch of the following quantity: Where Ov(p) denotes the set of features for positive patches that contain the pixel p. It is admittedly difficult to analyze how well these heuristics approximate the adaptive bandwidth approach of [4], and even there the setting of the bandwidth for each datapoint has heuristic aspects.

empirically our approach leads to improvements in performance as discussed below, and suggests a potential area for future work.


Typically for MT-DFS, we observe an order of magnitude speed-up over naïve linear scan and other popular data structures such as SR-trees.

mT-DFS starts to slow down as the dimension of the datasets increases.


It is well known that this type of regularization implies a prior assumption about the distribution of the parameter (e.g., L 1 -regularization implicitly assumes a Laplacian prior distribution) [12].

strong sparsity-inducing regularization, which is common when there are many more potential features than data samples (i.e., the so-called small n/p regime) can severely hinder the interpretation of model parameters (Fig.


Let us notice that the "signed margin", pus, is not derivable at point O.

according to the results of convex analysis (see for instance [2]), it is possible to define the "sub derivative' of Pus since it is a continuous and convex function.


(2008) it is obvious that the constant γ in (5) can be found in analytical form when S = {k}.

we kindly warn the reader again that the proofs of these last three cited articles (Kozachenko and Leonenko, 1987;Goria et al., 2005;Leonenko et al., 2008) contain a few errors, just like the Wang et al.


Implementing a Vector Quantization score estimation is straightforward, and is the primary source of our speedup.

a straightforward implementation cannot leverage the full speed-up potential available with Vector Quantization.


The bushes area consists of many small derivatives which are explained better by a small blur model than by a no-blur model.

the car consists of very few vertical edges.


Properties of Cumulants: Cumulants are similar to moments and can be expressed in terms of certain polynomials of the moments.

cumulants have additional properties which allow independent random variables to be algebraically separated.


Interestingly, training an HRL policy this way can do quite well.

in the harder tasks (Ant Push, Ant Fall) the issue becomes difficult to ignore.


As a consequence, on one hand, the large margin preference guides the scaling of the learned kernel to be as large as possible.

any kernel, even the one resulting in a bad performance, can give an arbitrarily large margin by enlarging its scaling.


ICA's main distinction compared to sparse coding and autoencoders is its use of the hard orthonormality constraint in lieu of reconstruction costs.

we will now present a proof (consisting of two lemmas) that derives the relationship between ICA's orthonormality constraint and RICA's reconstruction cost.


In [27], RL is directly used to improve the performance of agents in terms of the task completion rate of goal-oriented dialogs.

the importance of previous references has not yet been explored in the visual dialog task.


This assertion is proven below, in theorem 3.1, for the case of the hinge loss.

even if the solution involves a finite number of active hidden units, the convex optimization problem could still be computationally intractable because of the large number of variables involved.


An electroencephalogram (EEG) typically contains several types of rhythms and discrete neurophysiological events that describe instantaneous brain activity.

the neural activity taking place in a brain region is very likely dependent on activities that took place in the same region at previous time instances.


However, their approach requires the computation of the score function tensor which uses the density of the data-generating measure.

the data generating measure is unknown and also difficult to estimate for high-dimensional feature spaces.


We compared to random forests (RF) [9], an ensemble method that consistently performs well for datasets this size [10].

rF makes no attempt to respect the monotonicity constraints, nor is it easy to check if an RF is monotonic.


Examples of spiking neuron models considered in this paper include the ideal IAF neuron, the leaky IAF neuron and the threshold-and-feedback (TAF) neuron [15].

the methodology developed below can be extended to many other spiking neuron models as well.


Sparse learning is an essential topic in machine learning, which has attracted considerable interests recently.

it can be shown that the solution of the L 0 regularization problem in (1) achieves good prediction accuracy if the target function can be approximated by a sparse w. a fundamental difficulty with this method is the computational cost, because the number of subsets of {1, . . . , d} of cardinality k (corresponding to the nonzero components of w) is exponential in k. Due to the computational difficult, in practice, it is necessary to replace (1) by some easier to solve formulations below: where λ > 0 is an appropriately chosen regularization condition.


When we have access to all data modalities, we can use Equation ( 6) for exact posterior inference.

when some of the input modalities are missing, the inference is intractable, and we resort to the variational method.


. . , (x m , y m ) of m examples, where Note that by upper bounding ζ Q , we are taking into account all moments of W Q .

the PAC-Bayes theorem [2,3,4,5] currently only upper bounds the first moment 1 When H is a continuous set, Q(h) denotes a density and the summations over h are replaced by integrals.


Directly analyzing the optimal payoff is hard.

schapire [16] observed that the payoffs can be very well approximated by certain potential functions.


This enables us to use Theorem 1 to obtain rates of 1/n on the expected loss itself.

we cannot expect the eigenvalues to be bounded away from zero in very high dimensional spaces, limiting the applicability of the result of low-dimensional spaces were, as discussed above, other results also apply.


BP is based on a convex relaxation of the ℓ 0 norm, i.e., replacing w 0 with w 1 , which leads to an attractive, unimodal optimization problem that can be readily solved via linear programming.

oMP is a greedy strategy that iteratively selects the basis vector most aligned with the current signal residual.


R | sup x2X |h(x)|  1}, and the Wasserstein distance (also known as the Kantorovich-Rubenstein or earth mover's distance), d W k•k , generated by The primary impediment to adopting an IPM as a sample quality measure is that exact computation is typically infeasible when generic integration under P is intractable.

we could skirt this intractability by focusing on classes of test functions with known expectation under P . For example, if we consider only test functions h for which E P [h(Z)] = 0, then the IPM value d H (Q, P ) is the solution of an optimization problem depending on Q alone.


The accuracy of the estimation easily influences 3d detection of small objects; oftentimes, it is nearly impossible for prior approaches to detect.

benefiting from the parametrization method and 2D projection loss, the proposed cooperative model maintains the consistency between 3D and 2D, substantially reducing the estimation variance.


Our framework includes softmax and a slight generalization of the recently-proposed sparsemax as special cases.

we also show how our framework can incorporate modern structured penalties, resulting in more interpretable attention mechanisms, that focus on entire segments or groups of an input.


This does not mean though that all these Web pages share a common topic.

if two web pages point to web page like the one of the Learning with Kernels book, it is likely to express a common interest for kernel methods.


It works quite well for most applications with large number of labeled examples per class.

if we know that the classes are related to one another, priors which respect these relationships may be more suitable.


As DNS retrains the pruned network after every pruning operation, we are not able to report its error rate of the pruned network before retraining.

as can be seen, similar to LWC, the total number of iterations used by DNS for rebooting the network is very large compared with L-OBS.


Early research in human concept attainment suggested that learners do benefit from the opportunity to actively select examples during learning [11].

it proved very difficult to establish cri-  teria for assessing the magnitude of the active learning benefit (e.g., compared to theoretical ideals, or to passive learning).


Further, the number of constraints in C, and with it the number of operations per period, can grow over time.

if |A| is tractably small and Q has some special structures (e.g.


Their estimation method is close to our AMP algorithm.

the analysis is for a linear tensor completion with/without noise and is a different direction from our general nonparametric regression setting.


Major differences in task design complicate direct comparisons among the studies.

our empirical finding of human reward under-estimation is broadly consistent with the notion that humans do not always veridically represent reward statistics.


Acknowledging that attribute classifiers are often unreliable, recent work abandons purely semantic attributes in favor of discovering mid-level features that are both detectable and discriminative for a set of class labels [11,22,26,15,30,27,1].

there is no guarantee that the discovered features will align with semantic properties, particularly "nameable" ones.


Specifying a model prior is a daunting task, so almost invariably, the model prior is taken to be uniform (but see [15] for an exception).

information regarding the parameter is much easier to include, although still challenging (e.g., [16]).


They project the data onto a hyperplane, so the reduced coordinates are easy to interpret.

these methods are unable to deal with nonlinear correlations in a data set.


However, the existing method tends to perform poorly once the correctness of the model is violated.

the proposed method overall worked reasonably well and it consistently outperformed the passive learning scheme.


This indicates that running algorithms more steps does help reduce the skewness of estimated values and improve the overall performance.

the expression of Var[ Dj ] in Lemma 3.5 also indicates that the degree of improvement diminishes quickly as N j grows.


In this paper, we derived the learning rules for variational Bayesian ICA with missing data.

the complexity of the method is exponential in L. this exponential growth in complexity is manageable and worthwhile for small data sets containing missing entries in a high dimensional space.


We adapt hypernetworks to RHNs by directly modifying the RHN cell using ( 5): If RHN Cell and RHN CellHyper had the same state sizes, we could simply stack them.

as the hypernetwork is much smaller than the main network by design, we instead must upscale between the networks.


In the first glance, since (2) has only one variable, one may think it is easier to solve (2) than ( 1), or at least (2) can be solved by directly utilizing efficient algorithms developed for nonsymmetric NMF.

the state-of-the-art alternating based algorithms (such as ANLS and HALS) for nonsymmetric NMF utilize the splitting property of (1) and thus can not be used for (2).


For example, the preceptron algorithm makes no update when there is no error.

there is a family of algorithms which more aggressively update the loss when there is a margin mistake.


A related setting is adaptive submodularity [7,2,6,13], which is a probabilistic setting that essentially requires that the conditional expectation over the hypothesis set of submodular functions is itself a submodular function.

we require that the hypothesis class be pointwise submodular (i.e., each hypothesis corresponds to a different submodular utility function).


As we can see in Figure 2, when d is low, the held-out likelihood computed by our method does a fairly good job in recovering the correct number.

as the true number of eigenvalues rises our method underestimates the true number (although it is still fairly close).


If we consider a Bayesian setting with some prior on the set of realizations [2,4,14], we can sample a subset of realizations from the prior to estimate f worst .

this method does not provide any guarantee for the estimation.


This linear model predicts that the variance of the posterior distribution is always lower than that of individual cues.

data from several psychophysical studies contradict this prediction, necessitating non-linear computational strategies to deal with the inputs.


Notice that, unlike the previous experiment, since the data matrix is high-rank, LRMC has a large completion error, similar to synthetic experiments.

sSC-Lifting error is less than 0.1 for ρ = 0.1 and less than 0.55 for ρ = 0.7.


In all cases, Ad-aBoost detectors have the lowest error, but at a tremendous computational cost.

chainBoost cascades are always the fastest, at the cost of the highest classification error.


because they are the result of a natural physical process, and therefore we only have the observed input-output pairs for supervision.

there are scenarios where we do know the analytic form and so are able to compute the ground truth gradients (or higher order derivatives), alternatively sometimes these quantities may be simply observable.


The standard technique is therefore to derive a monotonic upper bound on the regret and tune the learning rate optimally for the bound.

our approach, inspired by the approach for combinatorial games of Koolen and Van Erven [16, Section 4], is to have our master aggregate the predictions of a discrete grid of learning rates.


We would like to model P (r A , w A ), the joint probability of observing an image defined by r A together with annotation words w B .

we hypothesize that the observation {r A , w B } came from the same process that generated one of the images J * in the training set T . we don't know which process that was, and so we compute an expectation over all images J∈T .


The value of β mK is usually smaller than mK and the authors in [20] have provided an expression for computing β mK based on the spectral norm σ of the data matrix X/ √ n = (x 1 , .

. . x n )/ √ n. in practice the value of σ cannot be computed exactly.


Empirical results have shown its favorable performance in comparison with several other popular clustering algorithms.

the inherent relationship between subspace selection and clustering in this framework is not well understood, due to the iterative nature of the algorithm.


Preliminary comparisons of the new algorithm with BBP were carried out on spin glass-like problems and indicate that the new algorithm is convergent when BBP is not.

the effectiveness of the new algorithms remains to be seen.


One can show that, providing ε + and ε − are respectively concave and convex functions of g, then the loss (4) is convex in g. is an admissible estimate of P (Y = 1|x).

the relaxed loss (4) is optimistic, below the neg-log-likelihood of g. This optimism usually L(g(x),1) L(g(x),1) Figure 2: Losses for positive examples (plain) and neg-log-likelihood of g(x) (dotted) vs. g(x).


Since it is possible to detect below the threshold with non-efficient algorithms, proving formally the converse of Conjecture 1 would require major headways in complexity theory.

[9] provides already non-rigourous arguments that the converse hold.


Our framework is similar in spirit to the label embedding methods based on reducing the label space dimensionality [10,21,25].

our framework offers the following key advantages: (1) computational cost of training our model scales in the number of ones in the label matrix, which makes our framework easily scale in cases where the label matrix is massive but sparse; (2) our likelihood model for the binary labels, based on a Bernoulli-Poisson link, more realistically models the extreme sparsity of the label matrix as compared to the commonly employed logistic/probit link; and (3) our model is more interpretable -embeddings naturally correspond to topics where each topic is a distribution over labels.


As in IBHC, we sequentially inserted data points into existing trees with a random order.

instead of inserting them via SeqInsert, we just put data points on top of existing trees, so that no splitting would occur.


It is unclear if there exists a general approach for dealing with unknown η in the active learning setting that does not increase substantially the labelled example complexity.

as we will demonstrate, in the context of specific active learning algorithms variants of this approach can be used to solve the problem.


We observed that as long as n o values are a few times greater than the expected number of data points in each cluster, the final results remain almost the same with or without this preprocessing.

this approximation decreases the running time of the algorithm by a factor n/n o .


This problem is also addressed in [2] in an unsupervised setting.

they have not considered any mechanisms to force their auxiliary latent variables to represent only the domain-specific information.


This would seem to imply that the system can not be stable around such an equilibrium.

as we will show, gradient descent GAN optimization is locally asymptotically stable, even for natural parameterizations of generator-discriminator pairs (which still make up concave-concave optimization problems).


Following Oja's work, many multineuron circuits were proposed to extract multiple principal components of the input, for a review see [3].

most multineuron algorithms did not meet the same level of rigor and biological plausibility as the single-neuron algorithm [2,4] which can be derived using a normative approach, from a principled objective function [5], and contains only lo-cal Hebbian learning rules.


No improvement can therefore be expected in this area.

unlike cross-validation, stability can also be defined in settings where no label information is available.


In the meantime, distinctiveness of the caption, which, on the other hand, requires the image to be the best matching among all images for the caption, has not been explored.

distinctiveness is crucial for high-quality captions.


In the absence of noise, the tensor power method correctly recovers the components under a random initialization followed by deflation.

perturbation analysis of tensor power method is much more delicate compared to the matrix case.


The spatial module alone is not as effective 263 as the attribute and relation module.

the unsupervised learning of the spatial knowledge 264 still can significantly help the object recognition through those undefined knowledge.


In other words, we assume that the reward function does not change within a trajectory.

the whole trajectories are assumed be generated by one or more agents whose reward functions are distinct from each other.


Traditionally, computational models of cognition have been compared using one of many goodness-of-fit measures.

use of such a measure can result in the choice of a model that over-fits the data, one that captures idiosyncracies in the particular data set (i.e., noise) over and above the underlying regularities of interest.


In particular, the FID score [22], the mode score [23] and the Inception score [24] use hidden features/labels of a pretrained CNN classifier as φ, and measure the performance of generative modeling algorithms by comparing p(z) and q(z) under this projection.

because we want to study the exact difference between p(z) and q(z), we choose φ to be interpretable high level features inspired by experimental work in cognitive psychology, e.g.


The parameters p and α are often heuristically selected on an application-specific basis.

type II methods, with origins as empirical Bayesian estimators, implicitly utilize a more complicated penalty function that can only be expressed in a variational form [18].


All other curves have a slope of 1 ± 0.1, indicating linear scaling with the number of training instances.

fITC and SSGP are used here with a fixed number of inducing inputs and basis functions.


Experiments show that μ2 is more accurate and has lower variance than μ1 (see Figure 1).

the U-statistic estimator μ2 needs O(n 2 ) memory rather than O(n).


Such latent feature representation has been used in the past to describe entities [7,10,12] and IBP is an appropriate nonparametric prior to infer the number of latent features.

unlike IBP our model utilizes interaction scores as priors and so the model is not exchangeable anymore.


There has been a long-standing interest in the GP community to overcome the cubic scaling of inference in standard GP models [17,18,12,13,8].

none of these approaches actually dealt with the harder tasks of developing scalable inference methods for multi-output problems and general likelihood models.


Under mild conditions, PCP guarantees that the two components X and E can be exactly recovered through solving: To solve the problem in (1), iterative optimization methods such as Accelerated Proximal Gradient (APG) [15] or Augmented Lagrangian Multiplier (ALM) [14] methods are often used.

these optimization methods are implemented in a batch manner.


We also use two-streams to model video [34], but apply them for video generation instead of action recognition.

our approach does not explicitly use optical flow; instead, we expect the network to learn motion features on its own.


For instance, spectral mixture kernels (Wilson & Adams, 2013b) were introduced for flexible kernel learning and extrapolation, by modelling a spectral density with a scale-location mixture of Gaussians, with promising results.

wilson & Adams (2013b) specify the number of mixture components by hand, and do not characterize uncertainty over the mixture hyperparameters.


Given that the kernel of Y 1 is not uniquely defined, the goal is no longer to estimate K exactly, but one possible kernel that would give rise to the same DPP as K. The route that we follow is similar to that followed by [25], which is based on a method of moments.

lack of symmetry of K requires significantly different ideas.


Following [2], RBFAOO ran with a 10-20GB cache table (134,217,728 entries) and overestimation parameter δ = 1.

sPRBFAOO allocated only 95,869,805 entries with the same amount of memory, due to extra information such as virtual q-values.


Other kernel methods with linear complexity have been proposed using functional gradient descent [14,5].

because these methods use a model strictly the same size as the entire dataset, they fail to estimate the predictive covariance, which requires Ω(N 2 ) space complexity.


These final values resulted in clipping a small fraction of rs, and none of ds.

at the beginning of training, when the learning rate was larger, it proved important to increase r max slowly: otherwise, occasional large gradients were observed to suddenly and severely increase the loss.


As shown in Figure 3, only clustering ensembles, majority voting methods, and the proposed BGCM algorithm work at the meta output level where raw data are discarded and only prediction results from multiple models are available.

majority voting can not be applied when there are clustering models because the correspondence between clusters and classes is unknown.


Given a matrix A ∈ R n×m , the linear operator vec(A) yields a vector x ∈ R nm , which is obtained by stacking the columns of A.

given a vector x ∈ R nm , the operator unvec (n,m) (x) yields a matrix A ∈ R n×m .


Generally, this will result in a bound on the value of a stochastic policy.

if the optimal policy is the same for all of the possible samples from the posterior, then we will get a bound for that particular deterministic policy.


The previous section shows how to optimize the label predictors F while the nodes N , edges E and label sets L which specify the structure of the tree are fixed in advance.

we want to be able to learn specific tree structures dependent on our prediction problem such that we minimize the Algorithm 2 Learning the Label Tree Structure Train k One-vs-Rest classifiers f1 , .


that minimizes the empirical error, i.e., such that g(a (n) , v (n) ) = y (n) on as many examples as possible.

as our primary goal is to use AVTS as a self-supervised proxy for audio-visual feature learning, we define g(.)


All the keypoints lie on top of the human actors, and consistently track the body across identities and poses.

the model cannot discern frontal and dorsal sides of the human body apart, possibly due to weak cues in the images, and no explicit constraints enforcing such consistency.


When we have s nodes, for the SDCA algorithm, dividing the examples into s computing nodes does not yield any speed-up.

we can divide the features into the s nodes (that is, each node will hold d/s of the features for all of the examples).


However, solving a large number of smaller systems is still a bottleneck, and decoding the optimal solution from the sub-problems might be difficult.

we propose to use the Concave-Convex Procedure (CCCP) [33], which we now briefly review.


Methods using k ∈ {0, 6, 12} are relatively slow (although still enjoying a linear rate), and tend to have similar behaviour, especially when ∆ is small.

methods using k ∈ {18, 24, 29} are much faster, with a behaviour nearly independent of θ and ∆.


Variance reduction techniques such as SAG, SVRG and SAGA have been proposed to overcome this weakness, achieving linear convergence.

these methods are either based on computations of full gradients at pivot points, or on keeping per data point corrections in memory.


Gabor wavelets, the DCT) in which those signals are sparse or nearly sparse.

an arbitrary class of signals can be sparse in unknown bases, some of which give better encodings than others.


The above convergence result for CDSGD is limited to the case when the objective functions are strongly convex.

most practical deep learning systems (such as convolutional neural network learning) involve optimizing over highly non-convex objective functions, which are much harder to analyze.


[18] performs very poorly when used in conjunction with the PLS classifier, but becomes more competitive when used with an SVM.

even then their method performs much worse than our method for nearly all object classes, as it is difficult to model the underlying domain shift in feature space.


One reason for the collapse of 1 -norm MKL is that kernels deployed in real-world tasks are usually highly sophisticated and effectively capture relevant aspects of the data.

sparse approaches to MKL rely on the assumption that some kernels are irrelevant for solving the problem.


In Figures 2(a) and 2(b), samples are generated according to a power-law distribution with power α = 2 over k = 1, 000 categories.

the underlying distribution in Figure 2(c) is a piecewise power-law.


Of course, the Hessian of a quadratic function can be easily computed by hand.

here we want to illustrate that even for this simple example, running times can vary dramatically.


The presence of the Dirac delta mass function makes the application of variational approximate inference algorithms in spike and slab Bayesian models troublesome.

there exists a simple reparameterization of the spike and slab prior that is more amenable to approximate inference methods.


Our method differs from them in following aspects: 1) DA-GAN aims to synthesize photorealistic and identity preserving profile faces to address the large variance issue in unconstrained face recognition, whereas TP-GAN ( 13) tries to recover a frontal face from a profile view and Apple GAN ( 28) is designed for much simpler scenarios (e.g., eye and hand image refinement); 2) TP-GAN ( 13) and Apple GAN (28) suffer from categorical information loss which limits their effectiveness in promoting recognition performance.

our proposed DA-GAN architecture effectively overcomes this issue by introducing dual discriminator agents.


Probably most closely related to Wasserstein++ is VAE-GAN [38], combining VAE [24] with vanilla GAN [14].

whereas the VAE part and the GAN part minimize different divergences (Kullback-Leibler and Jensen-Shannon in the case of VAE and vanilla GAN, respectively), WAE and WGAN minimize the same cost function, so Wasserstein++ is somewhat more principled conceptually.


We build our scholar model with a solver that has suitable architecture for solving a task sequence and a generator trained in the generative adversarial networks framework.

our framework can employ any deep generative model as a generator.


As opposed to random initialization, components created during this sequential construction are often truly needed, as the decisions of creating new components are based on knowledge accumulated from previous samples.

it is still possible that some components introduced at early iterations would become less useful and that multiple components may be similar.


Here, we tackle the following question: "Given the row and column marginals of a hidden binary matrix H, what can one infer about H?".

optimization-based methods for addressing this question, e.g., least squares or maximum likelihood, assume a generative model for the hidden matrix and output an estimate H of H. this estimate gives little guidance as to the structure of the feasible solution space; for example, H may be one of many solutions that achieve the same value of the objective function.


If W = 0, we get 7% training error for distinguish class 0 and class 1.

it can be improved to 1% with W 2 = 0.6.


On the other hand, [25] shows that ) is sufficient for recovering multiple components from noisy tensors.

[25] assumes exact computation of rank-1 tensor approximation, which is NP-hard in general.


[7], which provides data-dependent margin guarantees for a general family of hypotheses, with an arbitrary factor graph decomposition.

with the exception of [11], both aforementioned works do not focus on producing computationally appealing methods.


Linear dynamical systems (LDSs) are useful in describing dynamical phenomena as diverse as human motion [9], financial time-series [4], maneuvering targets [6,10], and the dance of honey bees [8].

such phenomena often exhibit structural changes over time and the LDS models which describe them must also change.


They are often used in their depthwise-separable (Chollet, 2016) form (g = N ).

the networks with half, or quarter that number of groups perform substantially better for a modest increase in parameters.


In these work, limited attribute observation settings only at training time have been considered.

it is natural to assume that the observable number of attributes at prediction time is same as the one at training time.


The reconstruction of z is then produced by a (symbol) decoder D : [L] m → R d , which maps the symbols back to ẑ = D(E(z)) ∈ R d . Since z is a sample from Z, the symbol stream E(z) is drawn from the discrete probability distribution P E(Z) .

thus, given the encoder E, according to Shannon's source coding theorem [8], the correct metric for compressibility is the entropy of E(Z): Our generic goal is hence to optimize the rate distortion trade-off between the expected loss and the entropy of E(Z): min where F is the architecture where z has been replaced with ẑ, and β > 0 controls the trade-off between compressibility of z and the distortion it imposes on F . we cannot optimize (3) directly.


For example, the Iterative Closest Point algorithm [4] is one of the most popular algorithms for alignment.

it does not generate the one-to-one match between the rigid structures.


These can be naively computed with 6rb FFTs.

as before, by sharing FFT of the forward and backward inputs, and the fft of the parameters, this can be lowered to (4br + 4r + 2b) FFTs.


This result is somewhat surprising, as it has been observed by practitioners that using larger batches in deep learning degrades the quality of the model, as measured by its ability to generalize (Keskar et al., 2016).

our method differs from the experiments performed by Keskar et al.


4 The analysis above demonstrates that optimal policy design and the best achievable performance depend on the information arrival process: while policies such as UCB1 and -greedy may be rate-optimal in some cases, a myopic policy can achieve rate-optimal performance in other cases.

the identification of a rate-optimal policy relies on prior knowledge of the information flow.


Conveniently, the gradient update and projection operators are independent of the on-policy and off-policy updates and can be applied in either case.

as we will see below, the gradient update operator causes significant instability in the off-policy update, to the degree that divergence is a common phenomenon (much more so than with full projections).


The estimation error bound in Theorem 1b is typically sharper than that in Theorem 1a.

for specific structures, using application of Theorem 1b requires additional bounds on ER * (P Ω (W )) and Ψ R (T R ) besides w 2 G (E R ).


Pattern classification using template matching techniques is a powerful tool in implementing human-like intelligent systems.

the processing is computationally very expensive, consuming a lot of CPU time when implemented as software running on general-purpose computers.


The figure indicates that the music data sets mix fairly well, as the performance of GSN quickly saturates.

for the Wikipedia data, the performance could probably be even further improved by letting the MCMC chain run for more than M = 100 steps.


In these cases, active learning is not helpful, even asymptotically.

in the general case, this ratio is unbounded, and so is the potential for improvement from using active learning.


Marginals computed with Gibbs sampling (run for about 10 8 iterations) are clearly very inaccurate (far from the 45 degree line), an indication that the Markov Chain had not mixed as an effect of the relatively large weights that tend to create barriers between modes which are hard to traverse.

samples from PAWS provide much more accurate marginals, in part because it does not rely on local search and hence is not directly affected by the energy landscape (with respect to the Hamming metric).


When a link is created from i to σ, the probability of reaching σ directly from i increases.

due to the renormalization constraints, the probability of reaching σ via longer paths may decrease.


The total number of triangles, over all 4 classes, is Θ(N 3 ).

our goal is not to account for all 4 classes; instead, we will focus on ∆ 3 and ∆ 2 while ignoring ∆ 1 and ∆ 0 .


One might argue that the points which are far from the decision boundary do not provide any information anyway.

there is some merit in not only keeping the output label invariant under the transformation Lt, but also the real-valued output.


It is impossible to do this literature justice here, but some examples include [10,7,12,8,11,5,4,9].

most of this work addresses only very specific online learning methods, and usually quite simple ones (such as ones that switch between only a finite number of parameter values using a specific, simple, decision rule, e.g., [4]).


Independent of our work, [18] recently proved a representer type of theorem for spectral regularization functions.

the framework they consider is different than ours in that they are interested in sensing the underlying high-dimensional matrix using given measurements.


In the Logistics domain, specifically, it is easy to see that the probability of successfully loading a container onto a truck using robots of k (1 ≤ k ≤ m) different manufacturers is (1 − 0.7 k ).

robots of all five manufacturers are used in a plan when ρ = 0.4, whereas using those of three manufacturers is enough.


The resulting box was then expanded (via a statistical technique) to get better results.

the test data from Muskl was used to tune the parameters of the algorithm.


Historically, multi-matching has received relatively little attention.

independently of, and concurrently with the present work, Huang and Guibas [18] have recently proposed a semidefinite programming based solution, which parallels our approach, and in problems involving occlusion might perform even better.


1, we first notice that the same terms: appear on the RHS of the update rules of both algorithms.

while Q-learning uses the same conservative learning rate α k for both these terms, SQL uses α k for the first term and a bigger learning step 1 − α k = k/(k + 1) for the second one.


In [7,18] the authors show that coordinate descent methods are very efficient for solving lasso type problems.

an obvious way to update each element of ∆ to solve for the Newton direction in (5) needs O(p 2 ) floating point operations since Q := W t ⊗W t is a p 2 ×p 2 matrix, thus yielding an O(p 4 ) procedure for approximating the Newton direction.


Moreover, [14] explicitly put the orientation and scale of each feature in the codebook, so that object center location can be inferred directly.

these works treat orientation and scale as independent of the feature descriptor and use them to post-verify whether a feature found to be consistent in terms of the appearance desciptor would also be consistent in terms of scale.


This is one of the classical problems in statistics.

sometimes, like in DA, the interesting question is with regards to similarity rather than equality.


Note the Theorem 2.6 only provides limiting behavior without specifying the convergence rate.

if we are willing to add perturbations, the following theorem not only establishes convergence but also provides a sharp convergence rate: Theorem 2.7 ( ).


For such distributions, the problem of revenue maximization becomes trivial, since any posted price is optimal.

as follows from Theorem 2.3, since the expected revenue of such distributions is infinite, almost never do the empirical revenues uniformly converge to the true revenues.


One might say that VFE "underfits" in this case.

we can show that VFE still recognises a good solution: When we initialised VFE with the FITC solution it consistently obtained a good fit to the model with correctly identified lengthscales and a noise variance that was close to the full GP.


(1982)   suggested that feedforward inhibitory connections subtracting a linear prediction generated from nearby receptors implement such compression, resulting in biphasic center-surround receptive fields.

feedback inhibitory circuits are common in early sensory circuits and furthermore their dynamics may be nonlinear.


Hence, they inevitably suffer from the semantic gap, which is defined in [8] as the lack of coincidence between low level visual features and high level semantic interpretation of an image.

joint analysis of multimodal data offers improved search and cross-view retrieval capabilities e.g.


Generative methods formulate the likelihood of the observed firing rates conditioned on the state and use Bayesian inference methods such as the Kalman filter [21] or particle filter [3] to estimate the system state from observations.

direct (or discriminative) methods learn a function that maps firing rates over some preceding temporal window into hand kinematics.


1 Testing at one interval per stage is not possible with a utility function based on statistical model selection criteria, such as MDL, which require computation of the maximum likelihood estimate [10].

it can be done with a utility function based on mutual information [5].


At a high level, this is because the empirical means consists of d coordinates, each of which has a significant amount of noise.

their squared distance is just a single number which is a sum of d quantities, and we can leverage concentration in the amount of noise contributed by these d summands to save a √ d factor.


Generative Stochastic Networks Like GibbsNet, generative stochastic networks (GSNs, Bengio et al., 2013) also directly parameterizes a transition operator of a Markov chain using deep neural networks.

gSNs and GibbsNet have completely different training procedures.


Let F i be the σ-field generated by all the random variables until episode k i , step h. Then, τ i=1 is a martingale difference sequence w.r.t the filtration {F i } i≥0 .

by Azuma-Hoeffding and a union bound, we have that with probability at least 1 − p/(SAH): ) for some absolute constant c. Because inequality (4.4) holds for all fixed τ ∈ [K] uniformly, it also holds for Putting everything together, and using a union bound, we see that with least 1 − p probability, the following holds simultaneously for all (x, a, h, k) if we choose b t = c H 3 ι/t for the same constant c in Eq.


Yet, recent work in neuroscience has showed that the structural wiring of the brain did not correspond to a very sparse network [20], thus questioning the underlying assumption of sparsity often used to estimate brain network connectivity.

for the problem of finding differences between networks in two populations, sparsity may be a valid assumption.


If sampling were involved in the update rule the learning rate would have to be decreased in the standard manner (Lt at = 00, Lt a; < (0) in order to fulfil the condition for stochastic approximation algorithms.

for a fixed set of updates and certain synchronous RL algorithms with linear feature-based function approximation Theorem 1 predicts the existence of a constant learning rate.


Slow updates are also one of the main reason why CMS, despite being theoretically inferior, is preferred [7].

cMS has only logarithmic update cost, which is desirable, but local CMS summaries cannot be combined (since they are not reducible).


Note that we are using each R t as the target regression variable in this formulation, even though we only observe r t for each state.

to compute Equation 3 we need only retain sufficient statistics A, b and ( Each can be updated incrementally using r t (the latter two using traces).


Recall that the learning problem is to select the functions f α ∈ F α so as to minimize the empirical risk At first blush, this appears challenging, since evaluating A(θ) requires solving a message-passing optimization.

we can use the dual representation of A from Theorem 2 to represent min F R(F ) in the form To optimize Eq.


This frustrates the process of learning in environments with sparse rewards.

agents that learn a high level decomposition of sub-tasks are able to explore the environment more effectively by exploring in the abstract action space rather than the primitive action space.


For the whole network, RNP allocated more computations on faces images than background images, at approximately a ratio of 2, which clearly demonstrates the effectiveness of RNP.

since the first convolutional layers and fully connected layers were not pruned, to get the absolute ratio of pruning rate, we also studied the pruning of a certain convolutional layer.


These algorithms are generally simple and efficient; one needs only to construct a matrix based on local feature analysis of the training data and then computes its largest or smallest eigenvectors using standard numerical methods.

methods like generative topographic mapping [9] and self-organizing maps [10] are prone to local optima in the objective function.


Our approach partly involves the text retrieval, because we search for candidate sentences for each image of a query sequence from training database.

we then create a final paragraph by considering both compatibilities between individual images and text, and the coherence that captures text relatedness at the level of sentence-to-sentence transitions.


In higher dimensions, this can be a significant cost, even relative to the fixed O(N 3 ) cost of inverting the Gram matrix.

as our experiments show, typically only the first few orders of interaction are important for modeling a given function; hence if one is computationally limited, one can simply limit the maximum degree of interaction without losing much accuracy.


For the p-value, the statement dir L (Y ), µ = 0 is implied by the stronger null hypothesis µ ⊥ L. We can also use Lemma 1 to give a two-sided confidence interval for dir L (Y ), µ ; specifically, dir L (Y ), µ lies in the interval [L α/2 , L 1−α/2 ] with probability 1 − α.

in general this cannot be extended to a two-sided interval for P L µ 2 .


Recall that the conditional mutual information I(X i ; X j |X S ) = 0 iff given X S , the random variables X i and X j are conditionally independent.

thus, (11) seeks to identify non-neighbors, i.e., node pairs which can be separated in the unknown graph G. since we constrain the conditioning set |S| ≤ η in (11), the optimal conditioning set may not form an exact separator.


When the gradient noise is large, smaller gradient steps must be taken to avoid unstable dynamics of the iterates.

a smaller step size increases the number of iterations that must be performed to reach convergence.


This algorithm achieves the same approximation as KwikCluster, in a logarithmic number of rounds, in expectation.

it performs significant redundant work, per iteration, in its effort to detect in parallel which vertices should become cluster centers.


Typical mechanism design approach may seek to design online learning mechanisms such that truthful biddings form an equilibrium (or even better, are dominating strategies) even if bidders are non-myopic, and to get small regret given truthful bids.

designing truthful mechanisms that learn in repeated auctions seems beyond the scope of existing techniques.


These metrics generalize easily and allow for likelihood-based comparisons of different models or selection of model parameters such as the number of topics.

this adaptability comes at a cost: these methods only measure the probability of observations; the internal representation of the models is ignored.


Furthermore, we remark that we this assumption is required only for establishing concentration results.

our contrastive estimator is still valid even when this assumption is violated.


While HMC is motivated by smooth distributions, the inclusion of an acceptance probability means HMC does asymptotically sample correctly from piecewise distributions 1 .

since leapfrog numerical integration of Hamiltonian dynamics (see [9]) relies on the assumption that the corresponding potential energy is smooth, such cases lead to high rejection probabilities, and poor performance.


For example, the model on the left produces reasonably looking faces on CelebA, but too many dark images.

the model on the right produces more artifacts, but more varied images.


The resulting solutions share many properties with previous sparse coding models, used to model early sensory processing [7].

unlike these sparse coding models, the learned representation depends on: (i) the relation between the input and variable of interest; (ii) the trade-off between encoding quality and compression.


Upon the completion of the action, the actor transfers to a state s t+1 and receives a reward r t . As we are interested in learning complex motor tasks consisting of a single stroke [23], we focus on finite horizons of length T with episodic restarts [1] and learn the optimal parametrized, stochastic policy for such reinforcement learning problems.

we assume an explorative version of the dynamic motor primitives [22,23] as parametrized policy π with parameters θ ∈ R n . in this section, we will keep most derivations sufficiently general that they would transfer to various other parametrized policies.


State-of-the-art sparse variational inference methods trade modeling accuracy against complexity.

the complexities of these methods still scale superlinearly in the number of basis functions, implying that that sparse GP methods are able to learn from large datasets only when a small model is used.


More open-ended question asking can be achieved by non-goal-driven systems trained on large amounts of natural language dialog, such as the recent progress demonstrated in [20].

these approaches cannot capture intentional, goal-directed forms of human question asking.


Last, in theory, an injective mapping f is necessary for the theoretical guarantees.

we observe that it is not mandatory in practice as we show in Section 5.5.


For symmetric matrices, B ≤ α ⇐⇒ |λ l | ≤ α ∀l, where λ l are the eigenvalues of B.

letting i p denote the unit vector along the p-th coordinate of R n , the distance between the p, q-th rows of f (S) can be written as Similarly, we have that Thus pairwise distances between the rows of f L (S) approximate those between the rows of E. the distortion term δ √ 2 is additive and must be controlled by carefully choosing f L (•), as discussed in Section 4.


To bound the probability, a normal technique is to bound the centroid region and the tail region separately.

the challenge is that the s-concave distribution is fat-tailed (Theorem 5).


It is easy to see that the maximum utility play for this sequence (and the lowest 2-memory bounded policy regret strategy) is choosing the same action at every round.

such an action sequence admits linear external regret.


Some works addressed this problem in a generic setting to achieve better trade-off between arbitrary relevance and dissimilarity functions [11,9,51,8,21].

they used only pairwise dissimilarities to characterize the overall diversity property of the list, which may not capture some complex relationships among items (e.g., the characteristics of one item can be described as a simple linear combination of another two).


By scanning the data in this table, the cost of histogram building for a feature will change from O(#data) to O(#non_zero_data).

this method needs additional memory and computation cost to maintain these per-feature tables in the whole tree growth process.


A plausible algorithm based on this insight is to first find a set of near maximizers, and then run the exponential mechanism on this set.

finding this set directly in a differentially private manner is very challenging.


In general, the KG model with DBM matches the second-order trend of human data the best, with ε-greedy following closely behind.

there still exists a gap on the absolute scale, especially with respect to the probability of staying with a successful arm.


Thus we can directly update the factor P (W ij,l |D n ) in a single step.

the last equation is still problematic, since it contains a generally intractable summation over an exponential number of values, and therefore requires simplification.


On small graphs, it is possible to minimize the zero-avoiding KL-divergence KL(θ||ψ) by computing marginals using the junctiontree algorithm.

as minimizing this KL-divergence leads to exact marginal estimates, it doesn't provide a useful measure of marginal accuracy.


Discussion It can be seen from theorem 1 that factorizations can be computationally efficient when ř k dppΓ k q is small.

factorizations can potentially be inefficient when scc `pΓ k q is large for any Γ k in the data.


Our previous experiments validate the efficiency of the decentralized algorithms on 8 nodes with 8 bits.

we wonder if we can scale it to more nodes or compress the exchanged data even more aggressively.


Yu and Neely (2018); Deng and Yin (2016)).

when neither of the properties is assumed, the basic dualsubgradient type algorithm gives a relatively worse O(1/" 2 ) convergence time (e.g.


The multiplicative nature of PoE models make them able to form complex densities: in contrast to mixture models, each expert has the ability to have a strongly negative influence on the density at any point by assigning it a very low component density.

maximum Likelihood Estimation (MLE) of the model requires differentiation of a normalizing term, which is infeasible even for low data dimensionality.


If H is dense in the space of continuous functions C(X) then for all P we have a(λ) → 0 if λ → 0 (see [3]).

in non-trivial situations no rate of convergence which uniformly holds for all distributions P is possible.


1 We note that some authors also add a term P i∈V θi(xi) to f (x; θ).

these terms can be included in the pairwise functions θij (xi, xj), so we ignore them for simplicity.


The most related method of IsoHash is ITQ [7], because both ITQ and IsoHash have to learn an orthogonal matrix.

isoHash is different from ITQ in many aspects: firstly, the goal of IsoHash is to learn a projection with isotropic variances, but the results of ITQ cannot necessarily guarantee isotropic variances; secondly, IsoHash directly learns the orthogonal matrix from the eigenvalues and eigenvectors of PCA, but ITQ first quantizes the PCA results to get some binary codes, and then learns the orthogonal matrix based on the resulting binary codes; thirdly, IsoHash has an explicit objective function to optimize, but ITQ uses a two-step heuristic strategy whose goal cannot be formulated by a single objective function; fourthly, to learn the orthogonal matrix, IsoHash uses Lift and Projection or Gradient Flow, but ITQ uses Procruster method which is much slower than IsoHash.


Although we both assume the tasks to share similarities in their value functions, [21] consider only linear approximators and adopt a hierarchical Bayesian model of the corresponding weights' distribution, which is assumed Gaussian.

our variational approximation allows for more general distribution families and can be combined with nonlinear approximators.


Compact Representation: After further investigation, we find that the non-local module contains a second-order feature space (Sect.3.1), which is used widely in previous computer vision tasks, e.g., SIFT [15], Fisher encoding [17], Bilinear model [14] [5] and segmentation task [2].

such second-order feature space involves high dimensions and heavy computational burdens.


By using only ¨ © ¨' , the algorithm simply "throws away" the entire structure of the previous tree.

we can also construct new MSTs built from all nodes ¨ © © of the previous tree.


In the second step, we minimize the reconstruction loss as well as the perplexity of generated samples evaluated by the language model.

since x is discrete, one can use the REINFORCE (Sutton et al., 2000) algorithm to train the generator: using a single sample to approximate the expected gradient leads to high variance in gradient estimates and thus unstable learning.


Hence the constraint A ≥ 0 is not enough to lead to a well-defined notion.

the geometric viewpoint we are developing does not so far include the positivity constraint Ψ ≥ 0 on the generating vectors of the simplicial cone.


These extensions have the advantages of maintaining computational tractability as convex optimization problems.

their utility is limited inherently by the sizes of kernel matrices .Weinberger et.


The experiments show that if there are no events then the well-studied UCB1 algorithm [2] performs the best.

when many different queries experience events, the performance of our algorithm significantly outperforms prior techniques.


• We provide a general structural result (Lemma 2) showing that, as in [7,18,19], our main algorithm exhibits a linear-quadratic solution error recursion.

we show that by using our nonuniform sampling strategies, the factors appearing in such error recursion enjoy a much better dependence on problem specific quantities, e.g., such as the condition number (Table 2).


Bayesian learning via Markov chain Monte Carlo (MCMC) methods is appealing for its inborn nature of characterising the uncertainty within the learnable parameters.

when the distributions of interest contain multiple modes, rapid exploration on the corresponding multimodal landscapes w.r.t.


Developing lower bounds in the interactive setting appears to be significantly challenging, as algorithms may choose to get any deterministic information adaptively by querying, and standard lower bounding techniques based on Fano-type inequalities [9,31] do not apply.

one of our major contributions in this paper is to provide a general framework for proving information-theoretic lower bound for interactive clustering algorithms which holds even for randomized algorithms, and even with the full knowledge of f + , f − and k. our algorithms are computationally efficient and are parameter free (works without knowing f + , f − and k).


To verify the performance of the algorithms with respect to the optimal solution in largescale, we remain within the noiseless setting.

the timing and the convergence behavior of the algorithms remain qualitatively the same under polarization and additive Gaussian noise.


Most recommender systems rely on collaborative filtering.

this approach suffers from the cold start problem: it fails when no usage data is available, so it is not effective for recommending new and unpopular songs.


A slight variation of this has been shown to work as long as (α − γ)/ √ α = Ω(log n/ √ n) and the average degree grows faster than poly-logarithmic powers of n [10].

(a) spectral clustering solves a harder problem than Problems 1 and 2, and (b) eigen-decompositions can be expensive, particularly for very large graphs.


When ↵ 1, the prior corresponds to a bias toward a particular ✓ topic distribution.


These models are consistent with the results of many diverse psychophysical studies.

little is known about the neural representation and manipulation of such Bayesian information, particularly in populations of spiking neurons.


We need to exploit the convexity of the K functions in the e-family instead of exploiting the concavity of f = log.

not only does the reverse-bound have to upper-bound the log-sum, it should also have the same form as the Jensen-bound above, i.e.


For example, convolutional operations coupled with pooling strategies capture shift-invariant spatial information while recurrent operations robustly capture high-level trends in sequential data.

this approach requires significant effort for engineering custom network modules and layers to achieve invariance to specific nuisance factors, making it inflexible [19].


We expect this outcome since BWC's classifier, because it is safe, initially assumes that all queries are intent-shifting and thus needs time to learn that in fact no queries are intent-shifting.

bWC's regret dominates the other approaches, especially as the fraction of intent-shifting queries grows.


In addition to the strong theoretical performance guarantee, DUDE can be implemented as a computationally efficient sliding window denoiser; hence, it has been successfully applied and extended to some practical applications, e.g., [1,3,4,2].

it also had limitations; namely, the performance is sensitive on the choice of sliding window size k, which has to be hand-tuned without any systematic rule.


Step size h allows us to quantify the rate of change of intersection if τ is increased from 0 to ∞, and since z t is decreasing, k r will evaluate to a high value for two points from the same subspace.

k r is always low for points not from the same subspace or that are outliers.


T with fixed γ for different functional spaces.

in the previous subsection we presented our method when considering a general set of transformations H. In this section we propose several possibilities for the choice of a convex set H. On the one hand, we propose to define H as a set of linear transformations from Ω S to Ω T . using the kernel trick, we propose to consider non-linear transformations.


Thus, X s0,π is approximately normally distributed for each s 0 ∈ S if H is sufficiently large.

if γ = 1, X s0,π = H t=0 γ t R(s t , π(s t )) can be rewritten as a linear combination of n t=0 f (s t ) for n = 0 to H as follow: Notice that a linear combination of independent or correlated normally distributed random variables is still normally distributed.


Specifically, graph convolutional networks [11] are used to propagate information on our learned graph.

our method focuses on learning graph representations rather than developing message passing methods on the graph.


In the Bayesian logistic regression application analyzed at the end of Section 4 of this paper, the number of arithmetic operations required to compute the gradient ∇U is Θ(d), and is the same number of operations required to evaluate the target function U itself.

in other applications it can take 2d times as many arithmetic operations to compute the gradient ∇U as it takes to compute the target function U .


Our quantitative results on the benchmark datasets show that the structure recovered by our approach is consistent with classes defined by human labelers better than or at the level of other clustering approaches.

the dimensions in the image benchmarks do not have much associated meaning, and the our approach was designed for clustering, not classification.


Even in this case, finding the optimal set B is known to be NP-hard.

for the case where f is assumed to be non-negative, the EMAX objective is a non-negative, submodular, non-decreasing function of B.


It still holds that the PG sampler is ergodic, which intuitively can be explained by the fact that the collection of variables that is left out is chosen randomly at each iteration.

it has been observed that the PG sampler can have very poor mixing, especially when N is small and/or T is large [2,3].


A partial list includes the error reduction schemes by Fienup [2], alternating minimization [14], Kaczmarz method [17], and generalized approximate message passing [15].

most of them fall short of theoretical support.


For large scale collections (WIKI-Small, WIKI-50K and WIKI-100K), the solvers with competitive predictive performance are OVA, M-SVM, PD-Sparse and (π, κ)-DS.

standard OVA and M-SVM have a complexity that grows linearly with K thus the total runtime and memory usage explodes on those datasets, making them impossible.


One natural idea is to pick a cluster proportionally to its size (which is essentially the same as querying the cluster of a node chosen uniformly at random).

we show that a better strategy is to query a cluster proportionally to the square root of its size.


Monte Carlo Markov Chain (MCMC) sampling methods (e.g., Gibbs sampling) are the standard approaches to train these models, which theoretically can achieve very accurate results.

mCMC methods can be slow to converge and their convergence can be difficult to diagnose.


This model assumes shared relevant and irrelevant features among tasks.

some tasks are allowed to have specific relevant features.


When γ i is equal to 1, the gate receives the modulation of the cell's state.


To enhance the generation quality, some works [8,34] utilize adversarial learning [13] to facilitate video prediction task, i.e., adding an adversarial loss [13] on the prediction module.

paired regression and adversarial loss still CANNOT solve image blur and motion deformation problems in principle.


The visual feedback midway through the movement provides information about the lateral shift on the current trial and allows for a correction for the current lateral shift.

the visual system is not perfect and we expect some uncertainty in the sensed lateral shift Ü × Ò× .


State-of-the-art techniques in both classes are not ideal for use in contexts where performing inference quickly and reliably on large volumes of streaming data is crucial for timely decision-making, such as autonomous robotic systems [9][10][11].

many classical clustering methods [12][13][14] scale well with the size of the dataset and are easy to implement, and advances have recently been made to capture the flexibility of Bayesian nonparametrics in such approaches [15].


Back-propagation (BP) is the foundation for successfully training deep neural networks.

bP sometimes has difficulties in propagating a learning signal deep enough effectively, e.g., the vanishing gradient phenomenon.


Recent eye tracking studies in natural tasks suggest that there is a tight link between eye movements and goal directed motor actions.

most existing models of human eye movements provide a bottom up account that relates visual attention to attributes of the visual scene.


[8] propose a kernel density estimate method to detect the points lying far from the data manifolds in the finallayer hidden space, which does not change the structure of the classification network with little computational cost.

carlini and Wagner [3] show that each of these defense methods can be evaded by an adversary targeting at that specific defense, i.e., by a white-box adversary.


One of the motivations for considering (x, a)-rectangular sets in RMDP is that they lead to tractable solutions in the conventional reward maximization setting.

in the robust regret minimization problem that we propose in this paper, even if we assume that the uncertainty set is (x, a)-rectangular, it does not guarantee tractability of the solution.


Bounded response is obviously a far more modest requirement.

importantly, the definition of bounded response allows the possibility of arbitrary leverage; that is, no bound is imposed on the magnitude of a perturbed input (i.e.


The recently proposed additive noise model [1] for structure learning addresses both limitations; by taking advantage of observed nonlinearity and non-Gaussianity, a unique directed acyclic structure can be identified in many contexts.

it too suffers from limitations: (i) for certain distributions, e.g.


Traditionally, formal learnability arguments have been used to claim that such learning is impossible without the aid of innate language-specific knowledge.

recently, researchers have shown that statistical models are capable of learning complex rules from only positive evidence.


Straightforward application of Deep Belief Nets (DBNs) to acoustic modeling produces a rich distributed representation of speech data that is useful for recognition and yields impressive results on the speaker-independent TIMIT phone recognition task.

the first-layer Gaussian-Bernoulli Restricted Boltzmann Machine (GRBM) has an important limitation, shared with mixtures of diagonalcovariance Gaussians: GRBMs treat different components of the acoustic input vector as conditionally independent given the hidden state.


Note that A1 only requires that ∇f (x) 2 is bounded and A2 assumes a mild condition on the stochastic gradient.

for strongly convex optimization we need to assume a bound on the stochastic gradient ∇f (x, ξ t ) 2 .


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

they require quite different theoretical analysis; unlike prior work, our estimator is constructed and analyzed entirely in the frequency domain, and then related to the data domain via Parseval's identity.


The FTAL algorithm is designed to achieve logarithmic regret rate for exp-concave problems, exploiting the curvature information of such functions.

our algorithm is aimed for optimizing general convex functions with possibly no curvature; while FTAL performs FTL over the second-order approximation of the functions, Online Lazy Newton instead utilizes a first-order approximation with an additional rank-one quadratic regularizer.


To address this issue, more sophisticated linear methods such as canonical correlation analysis (CCA) [7], and the partial least squares method [11] have been proposed.

all linear approaches have a fundamental shortcoming -the space of images, which is highly non-linear and thought to form a manifold, may not be well represented by a linear subspace.


This segmentation can be performed by simply combining all consecutive readings that are within a certain distance from each other (10m in our implementation).

it might be desirable to associate GPS traces to a street map, for example, in order to relate locations to addresses in the map.


In principle, the method is applicable to larger and more general graphical models.

how to make the tuning of scale parameters practically feasible in such models is still to be explored.


we prefer to make them separate, as we mostly rely only on (iii).


In fact, the first bound (4) has been extensively studied.

given the results of the previous section, we can now provide a much simpler proof.


At the beginning (step 1), the proposed active model can accurately find the right region such that the matting algorithm [7] can distinguish the foreground and background layers by color distributions.

both the scribbles from the users are not sufficient to generate the mattes.


As a final remark, a tighter variational bound is not guaranteed to always result in a better posterior approximation since the variational family limits the quality of the solution.

in the context of variational EM, where one performs gradient-based hyperparameter optimization on the log marginal likelihood, our bound gives more reliable results since higher orders of K can be assumed to approximate the marginal likelihood better.


As soon as the algorithm makes a mistake, it can easily figure out what the target function is.

class H needs exponentially many ⊥'s in the KWIK framework to be learned.


Specifically, the optimum solution of θ is obtained by solving the sub-problem 3 ) , which is equivalent to a constrained problem by introducing a set of non-negative slack variables ξ min θ,ξ The constrained optimization problem is similar to that of a linear SVM [7].

the difference is that we have the additional term This term indicates that the estimation of the scene classification model is influenced by the topic discovery procedure, which finds an optimum posterior distribution q ⋆ .


Statistical computations can then be performed based on probability theory on Banach spaces [14].

the methods proposed in [4] cannot guarantee that different probability distributions can always be distinguished by a statistical test.


Generalized linear models are often fit via maximum a posteriori (MAP) estimation [11,19,13,20].

as we scale to larger populations of neurons, there will inevitably be structure in the posterior that is not reflected with a point estimate.


This branch of computational chemistry provides invaluable tools for in-depth analysis but is currently not suitable for high-throughput reactivity tasks and is far from being able to recapitulate the knowledge and ability of human experts.

most rule-based expert systems for high-throughput reactivity tasks use a much more abstract representation, in the form of general transformations over molecular graphs [2,7,8,9,10].


In the extreme of sampling every tangent plane, this solution is exact and therefore accurate.

it suffers from very high computational cost.


However, the results of our algorithm, which is completely generic, are comparable.

the output of LDPC is a point cloud (rather than a graph).


Moreover, and unlike coordinate descent, SEGA allows for general sketches from essentially any distribution D. Another stream of work on designing gradient-type methods without assuming perfect access to the gradient is represented by the inexact gradient descent methods [9,11,45].

these methods deal with deterministic estimates of the gradient and are not based on linear transformations of the gradient.


The day-ahead prices π t ∈ R 24 + per unit of energy committed are known at the beginning of the day.

the hourly amounts of wind energy ω t+1 ∈ R 24 + generated over the day are uncertain.


In comparison to the constant-factor algorithms for general submodular functions, our approach is more efficient because we have explicit access to the objective function and its gradient.

general submodular functions assume a simple function oracle and need to employ sampling to estimate function and gradient values in the polytope interior.


In addition, the policy-update stage requires the definition of π(ŝ a k ) for all n states in the set of sample transitions.

kBSF only performs O(m 3 ) operations to evaluate a decision policy and O(m 2 |A|) operations to update it.


J τ determines the maximum allowable instantaneous speedup of one portion of a time series relative to another portion, within the same series or across different series.

the length of time for which any series can move so rapidly is constrained by the length of the latent trace; thus the maximum overall ratio in speeds achievable by the model between any two entire time series is given by min(J τ , M N ).


One most recent work in this direction is DEVISE [12], which learns embeddings that maximize the ranking loss, as an additional layer on top of the deep network for both images and labels.

these models impose structure only on the output space, and structure on the learned space is not explicitly enforced, which is our goal.


Recent years have witnessed the superiority of non-convex sparse learning formulations over their convex counterparts in both theory and practice.

due to the non-convexity and non-smoothness of the regularizer, how to efficiently solve the non-convex optimization problem for large-scale data is still quite challenging.


Note the two algorithms are similar when q(β) has low variance.

when the uncertainty modeled in q(β) is high, these two approaches lead to different approximations of the posterior.


On the other hand, discriminative methods, such as linear discriminative analysis (LDA), are better suited for classification tasks.

discriminative methods are usually sensitive to corruption in signals due to lacking crucial properties for signal reconstruction.


[8] gives solutions to a wide range of problems.

this work does not directly apply to our setting, because we need to maintain not only subsets S t but also continuous variables x t , and both of them affect regret.


In the factorial model we have The solution of the E step is therefore a product of Gamma distributions with parameters α + 1 and β + |s  A coefficient that has a small value after t iterations but is not exactly zero will have in the next iteration a large reweighting factor λ (t+1) i , which increases the chance that it will be set to zero in the next iteration, resulting in a sparser representation.

a coefficient having a large value after t iterations corresponds to a feature that is very salient in the signal x.


One simple fix is to choose at random between arms in the first L rounds, use these samples to form the best guess, in a straightforward way, and then run UCB1.

in the first L rounds this algorithm incurs regret of Ω(L), which is very suboptimal.


However, in order to recover the exact gradient under any potential set of stragglers, the required redundancy factor is on the order of the number of straggling nodes, which could mean a large amount of overhead for a large-scale system.

we show that one can converge to an approximate solution with a redundancy factor independent of network size or problem dimensions (e.g., 2 as in Section 5).


Comparing models with different numbers of states by computing Bayes factors can be cumbersome and time consuming.

nonparametric Bayesian methods for models with an unknown number of model parameters based on Dirichlet or Chinese restaurant processes have been highly popular in recent years [e.g.


We believe that this protocol represents both an interesting direction for practical applications involving networks of electronic devices and a significant step in the policy gradient literature.

there is an important outstanding issue that needs to be addressed to assess the potential of this approach: whether or not parameters can be adapted fast enough for this protocol to be in applications.


Note that the accuracy of the artificial observation approach gets very close to our approach for a large number of artificial observations.

in the last step of increasing the artificial observations, the accuracy decreases.


This has been extended to include certain empirical Bayesian methods [8,12].

these results assume a single dipole with fixed, known orientation (or alternatively, that d c = 1), and therefore do not formally handle source correlations or multi-component dipoles.


In other words, we want to minimize H(z|s) and H(s) at every time frame.

we know from information theory that H(z, s) = H(z|s) + H(s).


The reward maximization problem cannot be solved analytically in general.

it is possible to use an iterative approach.


In [3], the resubstitution estimator for H (α) was used.

since this estimator is biased, we use a leave-one-out cross-validation (LOOCV) estimator, which is unbiased and facilitates our theoretical analysis.


For example, if the training data are documents, then the classifiers cannot accept test data from a video space.

in practice, we often face the problem where the labeled data are scarce in its own feature space, whereas there are sufficient labeled data in other feature spaces.


Moreover, if the network is made larger and the number of parameters thereby increased, this credit assignment problem becomes still more difficult; thus we expect the performance of stochastic gradient methods to scale up with network size more poorly than deterministic methods.

under some circumstances stochastic methods can be equally as effective as direct ones in training even large networks, generating near-identical learning curves (see, e.g., Fig.


Great success has been achieved in obtaining powerful discriminative classifiers via supervised training, such as decision trees [34], support vector machines [42], neural networks [23], boosting [7], and random forests [2].

recent studies reveal that even modern classifiers like deep convolutional neural networks [20] still make mistakes that look absurd to humans [11].