Problem (2) is a linear program solvable by a general purpose method in O(m 3 ) time.

if all potential dictionary elements are no longer than k words in length, we can use problem structure to achieve a run time of O(k 2 n) per step of ADMM, i.e., linear in the document length.


The RMA preprocessing method was used to produce gene expression values from these images.

the Welsh dataset [25] for the second task is already in the form of gene expression values.


In case ¢k yield a quadratic form, then a closed form update exists.

in general we have: (6) In our experiments, ¢k is a I-hidden layer perceptron.


In this regard, it appears to be similar to many sparse PCA methods.

cUR takes a randomized algorithmic approach, whereas most sparse PCA methods are framed as convex optimization problems.


When this QP is solved, the estimate Â obtained may be unstable.

any unstable solution allows us to derive a linear constraint which we then add to our original QP and re-solve.


When the training sample size was 2000, kNN provided comparable results to the NB method.

when the training sample size was 500, the kNN method obtained results similar to or slightly better than those of SVM.


Therefore, different disease sub-types are likely to appear in different ratios in the different hospital.

if patients in two hospitals acquired the same sub-type of a disease, parts of their medical records will be similar.


We note that for the specific problem of super-resolution, Càndes derived a deconvolution algorithm which finds the global minimum of (2) without discretization error and proved that the algorithm can recover the true parameters under a minimal separation condition on the parameters [6].

we are unaware of an extension of this approach to more general applications of mixture models.


We start with the observation that the most natural formulation of averagecost ALP, which follows immediately from taking limits in the discounted-cost formulation and can be found, for instance, in [1,2,4,10], can be interpreted as an algorithm for approximating of the optimal average cost.

to obtain a good policy, one needs a good approximation to the differential cost function.


Below this scale, no information can be extracted; therefore, when the algorithm hits this "floor" for one coordinate, it will switch to the other.

it is possible to find other examples which show that the lack of consistency is not necessarily tied to the discontinuous nature of the conditional densities.


We observe that at the minimal error, both in 2 and 1 senses, the solution is sparser than the true vector (κ = 0.2).

adjusting the sparsity to the true one slightly increases the error 2 norm.


iv) =⇒ iii): Fix y and construct the gauge function Then P κ (y) = y, hence P f (P κ (y)) = P f (y) = P f +κ (y) by iv).


Based on the obtained expression, we note from Lemma 1 that the target goodness can now be bounded in terms of both values that characterize the similarity function in the source domain.

replacing the worst margin term in the bound by constant γ prevents us from taking it into account when attempting to design a new adaptation algorithm based on the obtained bounds.


PCA transforms the features into a small number of uncorrelated variables.

the supervised FSDR approaches include supervised principal component analysis [9], sliced inverse regression [10], and kernel dimension reduction [11].


For point loss functions, the instantaneous penalty L t (•) is encoded using a data point (x t , y t ) ∈ R d × {−1, 1} as L t (w) = P (x t , y t , w).

for (surrogates of) non-decomposable loss functions such as pAUC and Prec @k the definition of instantaneous penalty itself is not clear and remains a challenge.


If the data currently assigned to a k-means center appear to be Gaussian, then we want to represent that data with only one center.

if the same data do not appear Algorithm 1 G-means(X, α) 1: Let C be the initial set of centers (usually C ← {x}).


Third, for the initialization step, the best low-rank approximation of a matrix is unique and finding it is trivial.

for tensors, finding the best low-rank approximation is notoriously difficult.


Since the space T θ1 (D) is infinite dimensional, this optimization is not straightforward.

since f ∈ L 2 , it has a Fourier decomposition, and we can solve the optimization problem over a finite number of Fourier coefficients.


For the LDA model, we vary the number of hidden variables (i.e., topics) as {10, 20, 30, 40}.

our method is designed to optimize for the number of hidden variables, and does not need this input.


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

despite their apparent advantages over EM, the adoption of MoM algorithms in practical applications is still limited.


EPCG uses the point cloud representation, same as our method.

in the original work EPCG has only been evaluated in the unrealistic setup of having 100 random views per object and pre-training from 8 fixed views (corners of a cube).


Also, some of the corner points disappear under different lighting condition.

performance of the kernels is comparable to the existing methods, thus demonstrating the effectiveness of modeling faces as attributed pointsets.


As before, we identify that λ 1 and λ 2 use P.area and P.perimeter, respectively.

we now know that λ 3 uses P.ratio, which is a composition of P.intensity and P.perimeter.


Using a scale sensitive losses, such as the cross entropy loss, does address this issue (if the outputs are scaled down toward zero, the loss becomes trivially bad), and one can obtain generalization guarantees in terms of norm and the cross entropy loss.

we should be careful when comparing the norms of different models learned by minimizing the cross entropy loss, in particular when the training error goes to zero.


To optimize (10), one can use the convex-concave procedure (CCCP) [25] which has been proposed specifically for latent SVM learning [24].

cCCP tends to be slow on large problems.


The task of ranking has been of significant interest.

most of the literature [e.g., 11, 14, 24, 1], only focuses on calibration functions (in the form of regret bounds) for bipartite ranking, which is more akin to cost-sensitive binary classification.


A classical example of this is a concern that any metric used to regulate financial risk may become invalid as soon as it is widely used, because actors in the financial market may attempt to game the metric to avoid regulation [14].

much of the work on model feedback in fields like finance, education, or macro-economic theory has focused on negative results: there is an emphasis on understanding when feedback can happen and promoting awareness about how feedback can interact with policy decisions, but there does not appear to be much focus on actually fitting feedback.


Competence may not be observable as in Example 2.

when the group size is not too large, for example a group is a household, then it is natural to assume that the family members are able to choose the max-informed representative.


The Euclidean version of (1) where M = R d and g is the Euclidean inner-product has been the subject of intense algorithmic development in machine learning and optimization, starting with the classical work of Robbins and Monro [26] to the recent spate of work on variance reduction [10; 18; 20; 25; 28].

when (M, g) is a nonlinear Riemannian manifold, much less is known beyond [7; 38].


The walkback training will then destroy these modes.

in DAE's and NET's, since the destructive process corresponds to the addition of unstructured noise that knows nothing about the generative process, it is not clear that such an agnostic destructive process will efficiently seek out the spurious modes of the reverse, generative process.


We observe that this ratio stays almost the same for RL with different decoders.

the run time for the Clarke-Wright and Sweep heuristics increases faster than linearly with the number of nodes.


Related work: When k = 2, k-submodularity is called bisubmodularity, and [20] applied bisubmodular functions to machine learning problems.

their algorithms do not have any approximation guarantee.


Then, Ω(f ) can be the norm of a Reproducing Kernel Hilbert Space (RKHS), which means that there exist an Hilbert space H and a kernel function k : The reason for using an RKHS norm is the so-called representer theorem [5]: the function minimizing the corresponding regularized loss can be expressed as a linear combination of the kernel function evaluated at the labeled points.

it is not straightforward to find the kernel associated with an RKHS norm.


Learning a representation which can predict future video without labels has applications in action recognition and prediction and, when conditioned on the action of the agent, amounts to learning a predictive model that can then be used for planning and decision making.

learning to predict physical phenomena poses many challenges, since real-world physical interactions tend to be complex and stochastic, and learning from raw video requires handling the high dimensionality of image pixels and the partial observability of object motion from videos.


Relation-based nets have shown remarkable effectiveness to learn relations for physical reasoning [19,20,21,22,23,24].

they are not designed for action-conditioned dynamics learning.


In many cases, the maximum of a concave surrogate function can only be solved using other convex solvers and as a result the efficiency of the CCCP highly depends on the choice of the convex solvers.

we show that by a suitable transformation of the network we can compute the maximum of the concave surrogate in closed form in time that is linear in the network size, which leads to a very efficient  ) ⇥ fv j (w (k) ) 4 Experiments We conduct experiments on 20 benchmark data sets from various domains to compare and evaluate the convergence performance of the four algorithms: PGD, EG, SMA and CCCP (EM).


For any sample (s, ā, ō, r, s ), the naive form would be The action ō is the minimizing opponent's action in computing π(s ).

unfortunately, the number of terms in the summation within the first update equation is exponential in N . the vector φ(s, ā, ō) − γ ā ∈ Ā π(s , ā )φ(s , ā , ō ) can be computed on a component-by-component basis avoiding this exponential blowup.


It would be interesting to analyze our algorithm under non-orthogonal CP model.

we would like to point here that even with fully observed tensor, exact factorization is known only for orthonormal tensors.


Many modern data analysis problems involve inferences from streaming data.

streaming data is not easily amenable to the standard probabilistic modeling approaches, which require conditioning on finite data.


Gazefollowing is used in [16] to improve models of free-viewing saliency prediction.

they only estimate the gaze direction without identifying the object being attended.


The added computational cost lies in the computation of the importance weights for importance sampling and bridge sampling.

this boils down to computing free-energies which are mostly pre-computed in the course of gradient updates with the sole exception being the computation of qi,t (x i,t−1 ) in the importance sampling step.


Blei et al do not address the specific problem considered here, of using both page structure and hyperlink structure in web page classification.

they do apply their technique to two closely related problems: they augment a page classification method with local features based on the page's URL, and also augment content-based classification of "text nodes" (specific substrings of a web page) with page-structure-based local features.


Specifically, according to the MLE, Σ −1 is estimated by solving the optimization problem which is obtained by applying − log to the probability density function of the Normal distribution.

if the number of samples is lower than the dimension of the vectors, i.e., m < n, then S in (1) is rank deficient and not invertible, whereas the true Σ is assumed to be positive definite, hence full-rank.


Under simplified assumptions, they concluded that random orthogonal initialization of weights will give rise to the same convergence rate as unsupervised pre-training, and will be superior than random Gaussian initialization.

a good initial condition such as orthogonality does not necessarily sustain throughout training.


Typically the optimal ρ is in the order of KL( ŵX dπ||dπ)/n, and hence the rate of convergence given on the right-hand side is no better than O( 1/n).

the more interesting case is when there exists a constant b ≥ 0 such that This condition appears in the theoretical analysis of many statistical estimation problems, such as least squares regression, and when the loss function is non-negative (such as classification).


proposed the maximum margin planning (MMP) where Bellman-flow constraints are introduced to consider the margin between the experts' policy and all other possible policies.

an entropy based method is first proposed in [1] to handle the stochastic behavior of the expert.


the initial condition for one must make an important modification to the algorithm.


The former is an online algorithm specially designed to minimize the average rank in feeds sorted in reverse chronological order and the latter is an offline algorithm specially designed to maximize the time at the top in feeds sorted in reverse chronological order.

because REDQUEEN assumes that the feed is inverse chronologically sorted and posts with intensity / rank chrono (t), we also compare our method TPPRL against a stronger heuristic RQ ⇤ , which posts with intensity / rank priority (t).


This shows that when the set of feasible actions is strongly convex, a directional hint can improve the regret bound beyond what has been known to be achievable by an approximation hint.

we note that our results require the hints to be always valid, whereas the algorithm of Rakhlin and Sridharan [19] can adapt to the quality of the hints.


The most common way this is approached, in pedigrees [20] and elsewhere [21], is via block Gibbs sampling.

block Gibbs sampling does not apply readily to our model.


models in unsupervised learning was also demonstrated in earlier studies in [21,3].

these earlier methods did not perform well in practical prediction tasks with real-world data without using additional strong generative models.


Although it is always desirable to invent an exact algorithm that could be mathematically proved to obtain a better scalability property, it is beneficial to demonstrate the value of larger number of variables with an industrial application.

for a problem with billions of variables, there are existing practical approaches to reduce it into a smaller number of variables and then solve it with traditional approaches designed for centralized algorithm.


Our estimation procedure of the Hessian has similar motivation as the one done in Hessian eigenmaps [3].

in their approach they do not fix the zeroth-order term.


Then for j ∈ A we have where (a) follows by using Lemma 5 to bound T j (n) ≤ τ ji when Z i < ∆ji .

the total number of pulls for arms j for which Z i ≥ ∆ji /2 is at most n. (b) follows by bounding τ ji in expectation using Lemma 6.


In other words, if we had a lookup table of all possible input → output mappings for a neuron, it would be a complete portrayal of that neuron's functional form.

such infinite tables are not only practically infeasible, but are also problematic to process into a set of conclusions.


(For example, a Dalmatian belongs to the same group as the wolf according to a biological taxonomy, as both are canines.

in terms of visual attributes, it can be grouped with the leopard, as both are spotted; in terms of habitat, it can be grouped with the Siamese cat, as both are domestic.


Our theorem extends their result to classification problems and exponential decay spectrum.

we have to use a stronger assumption that f * P ∈ F φ so that the low noise condition can be applied to derive the variance condition.


This explains the "heuristic" used in [1,2] where the personalized PageRank vector is divided by the degrees of vertices to generate a sharp drop.

our choice of Λ = αI appears to be more justified, without the need of such post-processing while retaining a probabilistic foundation.


Our SSL methods based on Ω H,p , p = 1, 2 outperform consistently the clique expansion technique of Zhou et al [11] on all datasets except 20newsgroups 3 .

20newsgroups is a very difficult dataset as only 10,267 out of the 16,242 data points are different which leads to a minimum possible error of 9.6%.


An exception to this is the recent work [11] that demonstrates that PGD with non-convex regularization can offer consistent estimates for certain high-dimensional problems.

the work in [11] is only able to analyze penalties such as SCAD, MCP and capped L 1 .


The Wasserstein distance is inherently based on a notion of distance between images which in all implementations of Wasserstein GANs (WGAN) so far has been the 2 distance.

the imaging literature contains a wide range of metrics used to compare images [4] that each emphasize different features of interest, such as edges or to more accurately approximate human observer perception of the generated image.


If the objects in the set are randomly sampled from some distribution, theoretical results such as central limit theorem [14] or confidence set construction [20] have been proposed, providing the basis for the practical use of Wasserstein barycenter.

calculating the Wasserstein barycenter of m measures includes repeated computation of m Wasserstein distances.


A consequence of claim 3 is that BMMF will find the top M MPCs using 2M calculations of max marginals.


In a sense, our model is quite related to the DenseCap model for image captioning [23], itself similar to STNs.

we do not aim at explicitly predicting line positions, and STNs are not as good with a large amount of small objects.


On the other hand, if the minimum step length τ is computed naively by Lemma 5, it takes O(n 2 |P|) computations, which could be a bottleneck of the algorithm.

this bottleneck can be eased by introducing a working set approach: only a fixed number of constraints in the working set are evaluated at each step, while the working set is updated, say, every 100 steps.


Obviously, the choice of which is more appropriate, a feature graph or metric space, is application dependent.

it is less obvious how to incorporate feature dissimilarities in a metric space.


TD(λ) is known to converge when used with linear function approximators, if states are sampled according to the policy being evaluated -a scenario called onpolicy learning (Tsitsiklis & Van Roy, 1997).

the absence of either of these requirements can cause the parameters of the function approximator to diverge when trained with TD methods (e.g., Baird, 1995;Tsitsiklis & Van Roy, 1997;Boyan & Moore, 1995).


Most of the research on these methods has studied how to solve one-shot search problems.

search is often a repetitive process, where one needs to solve a series of similar search tasks, for example, because the actual situation turns out to be slightly different from the one initially assumed or because the situation changes over time.


This scale made a number of tensor recovery algorithms, for example Tucker decomposition and PARAFAC [12], impractical to apply on the dataset.

our recovery algorithm took 2430 seconds to finish on a standard workstation for truncation level r = 100.


Prism learning or Blindness may interfere this alignment and cause loss of the capability of accurate prey.

juvenile barn owl could recover its sensory map alignment by shifting its auditory map.


Since neither the empirical covariance estimator nor the CSP algorithm is robust to this kind of outliers, it dominates the solution.

the resulting pattern is meaningless as it does not capture motor imaginary related activity.


For normally distributed synthetic datasets, our experiments indicate that two variations of the CONCORD-ISTA method show little performance difference.

ccista 0 was marginally faster in our tests.


The parameters of generative models such as ARIMA are typically estimated via the maximum likelihood technique, which often leads to non-convex optimization problems.

our objective is convex and leads to an optimization problem with a unique global solution that can be found efficiently.


The above theorem requires an infinite number of spikes in order to start decoding.

we would like a real-time decoder that outputs the 'best guess' at every time t in order for us to act on the estimate of the signal.


Intuitively, the acquisition function α n (x) should be high in areas where the maxima is most likely to lie given the current data.

α n (x) should also encourage exploration of the search space to guarantee that the recommendation x N is a global optimum of f , not just a global optimum of the posterior mean.


A recent work [16] addresses the extension to structures with decomposable norm regularization.

the scope of matrix completion extends for low dimensional structures far beyond simple low-rankness or decomposable norm structures.


In cases where a bound u max on m t=1 A t F t is known, we can restrict t to [0, u max ] and discretize problem (8) over this interval.

the conclusion of Lemma 2 does not hold for a finite horizon and we need to impose additional linear constraints y[t] ≤ y[t − 1] to ensure the monotonicity of y.


4, that is, if the nonlinearity is exponential.

for other nonlinearities this may still be a useful approximation, and gives us a principled way of evaluating the goodness of fit of a learned subspace.


In both cases, testing for statistical significance against the CONV model was not possible since those results were obtained from [4].

the higher variability and non-Gaussianity of the Copper data may be the reason of why the simplest MOGP model (SM-LMC) achieves the best results.


They show that the CST policies are not good enough to use immediately, as the agents do worse than those given pre-learned skills for the first few episodes.

very shortly thereafter the CST agents are able to learn excellent policies-immediately performing much better than skill chaining agents, and shortly thereafter even exceeding the performance of agents with pre-learned skills.


have studied active model selection, where the goal is also to identify a model with lowest risk [5].

in their setting costs are associated with obtaining predictions ŷ = f (x), while in our setting costs are associated with obtaining labels y ∼ p(y|x).


Typically, for η 0 < 1 more spikes are required for convergence than for η 0 > 1.

the opposite occurs if we consider timesteps as time units.


The top six eigenvalues of its gradient covariance matrix are well separated from the rest as seen in Figure 4(a).

the function is far from smooth when projected onto the leading 1D or 2D active subspace, as Branin Franke Sine Norm Sixhump StyTang Hart3 SE 6.02e-3 8.73e-3 8.64e-3 6.44e-3 4.49e-3 1.30e-2 SKI 3.97e-3 5.51e-3 5.37e-3 5.11e-3 2.25e-3 8.59e-3 D-SE 1.83e-3 1.59e-3 3.33e-3 1.05e-3 1.00e-3 3.17e-3 D-SKI 1.03e-3 4.06e-4 1.32e-3 5.66e-4 5.22e-4 1.67e-3 Table 1: Relative RMSE error on 10000 testing points for test functions from [24], including five 2D functions (Branin, Franke, Sine Norm, Sixhump, and Styblinski-Tang) and the 3D Hartman function.


Piepenbrock & Obermayer (1999) suggested an interesting model in which varying a single parameter spans a spectrum from cortical competition to cooperation.

the nature of competition in their model makes it hard to predict the outcome of adaptation completely, except in some special cases.


In addition, it is of great significance to find an appropriate metric to evaluate whether a photo is aesthetically good or not.

the traditional image evaluation metrics may not work well in this situation [32].


Cliques have no v-shapes, so to improve upon existing results we had to exploit the acyclicity operation (F 3 ).

for the average-case, the proof of Theorem 4.1 exploits the v-structure operation (F 1 ).


Practically, such reparameterizations have the closed-form of the entropy in general, and thus, the gradient computation and the optimization is relatively easy.

such parameterization cannot perfectly fit the posterior when it does not fall into the known distirbution family, therefore, resulting extra approximation error to the true posterior.


1 regularization of the likelihood), this computational complexity could be reduced.

[1] could only produce some quantitative results on a very small dataset with only 200 words.


Our VPNs are related to Value Iteration Networks [35] (VINs) which perform value iteration (VI) by approximating the Bellman-update through a convolutional neural network (CNN).

vINs perform VI over the entire state space, which in practice requires that 1) the state space is small and representable as a vector with each dimension corresponding to a separate state and 2) the states have a topology with local transition dynamics (e.g., 2D grid).


GLMLasso was also the only algorithm that scaled to the p = 5000 setting.

it should be pointed out that GLMLasso is not necessarily consistent and it is highly depending on the choice of g j (.).


This corresponds to one discriminator for each agent which discriminates the trajectories as observed by agent i.

these discriminators are not learned independently as they interact indirectly via the environment.


The privacy constraints here are similar to the local differential privacy setting studied in [13] in the sense that there are multiple privacy barriers, each one separating each individual party and the rest of the world.

the main difference is that we consider multi-party computation, where there are multiple functions to be computed, and each node might possess a different function to be computed.


Given a (η, Φ)-mixable loss , we verify that Algorithm 3 is well defined; for simplicity, assume that dom = A and L is twice differentiable on ]0, +∞[ n . From the definition of an entropy, |Φ| < +∞ on ∆ k , and thus the entropic dual Φ t is defined and finite on all R k (in particular at θ t ).

from Proposition In what follows, we focus on a particular instantiation of Algorithm 3 where we choose β t := −η t−1 s=1 ( x s (A s ) + v s ), for some (arbitrary for now) (v s ) ⊂ R k . The (v t ) vectors act as correction terms in the update step of the AGAA.


That the majority of the components is positive stems from the fact that the underlying signals in calcium imaging are all made up of photons, and they elicit activity above a baseline as opposed to fluctuating around it.

not all positive sources are cells that could be extracted by an algorithm (some could be neuropil, other noise, or non-captured cells); hence we model them as generic gross non-negative contamination sources.


The complexity of control and prediction of Poisson traffic is reduced by the memory-less property of the Poisson process: its expected future depends on the arrival intensity, but not on the process history.

the long-range dependence of self-similar traffic makes it possible to improve predictions of the process future by observing the history.


The performance of B-CNN is the worst for infrequent AUs due to the limited positive samples in each mini-batch.

the proposed IB-CNN improves CNN learning significantly with limited training data.


Up to now, search-based MAP solvers were developed primarily as sequential search algorithms.

parallel, multi-core processing can be a powerful approach to boosting the performance of a problem solver.


This involves computing ∇g along all m = |Y| of its components, which may be intractable.

for the 2 2 smoothing, the gradient ∇h µ 2 2 (z) is given by the projection of z/µ onto the simplex, which selects a small number, denoted K z/µ , of its largest coordinates.


In this section we describe a Sparse Encoding Symmetric Machine (SESM) having a set of linear filters in both encoder and decoder.

everything can be easily extended to any other choice of parameterized functions as long as these are differentiable and maintain symmetry between encoder and decoder.


Then for any δ ∈ (0, 1), best-arm MAB algorithms can identify i with probability at least 1−δ based on at most 2 i =i ∆ −2 i log(1/δ) total samples (see the paper [9] for a brief survey and [10] for an application to clinical trials).

if samples are allocated uniformly to the alternatives under the same conditions, then the most natural procedures require K max i =i ∆ −2 i log(K/δ) samples before returning i with probability at least 1 − δ.


The approximate factors must have the same functional form as Q but they need not be normalized.

the exact factors ψ ik with i = 1, . . . , n and k = y i , corresponding to the likelihood, (2), only depend on f k (x i ), f yi (x i ) and z i .


The difference between RL's competition between multiple actions and SR's motivation of a single action might seem trivial, particularly if an extra, nUll, action is included in the action competition in RL, so the subject can actively choose to do nothing.

there is substantial evidence from experi-ments in which drive states (eg hunger, thirst) are manipulated, that motivation in the SR sense works in a sophisticated, intrinsically goal-sensitive, way and can exert unexpected effects on instrumental conditioning.


More generally, the inference technique of [7] applies to any model selection method whose outcome can be described in terms of quadratic conditions on Y .

their technique cannot be used to construct confidence intervals for the selected coefficients or for the size of the effects of the selected groups.


Stochastic Gradient Descent (SGD) is the most widespread algorithm of choice for practitioners of machine learning.

the objective functions typically found in deep learning problems, such as feed-forward neural networks and Restricted Boltzmann Machines (RBMs), have inhomogeneous curvature, rendering SGD ineffective.


While the novelty pressure in NS-ES does help it avoid local optima in some cases (discussed below), optimizing for novelty alone does not result in higher reward in most games (although it does in some).

it is surprising how well NS-ES does in many tasks given that it is not explicitly attempting to increase reward.


Marked point processes offer a probabilistic framework for modeling the rate at which the observed events occur.

our scientific questions pertain to discrete and continuous states that are not directly observable.


Thus, withoutreplacement sampling is shown to be strictly better than with-replacement sampling, after sufficiently many passes over the data.

this leaves open the question of why without-replacement sampling works well after a few -or even just one -passes over the data.


[9] take the approach of creating features from scores, enabling decisions to be trained via regular back-propagation.

they have only decisions and do not build higher level representations.


3AB we employed a budget that yielded an optimal cell-type ratio matching that of midget to parasol cells in the primate retina [18].

the general structure of the resultant RF power spectra in Fig.


Further, our approach does not require BKT's assumption that learning a skill is conditionally independent of the practice history of other skills.

the simplicity of BKT allows one to conduct modeling on a relatively large scale.


( 8) implies that if we ignore the gradient of the noise component, z n j , the tendency of increasing the SNR of z j will attempt to increase the variance of the signal component, z s j , instead of increasing the feature correlation of the lower layer.

we find in practice that such modification to the gradient causes optimization difficulties, preventing the training process from converging.


The seminal work of [6,11] triggered a line of work on quantifying the inefficiency of computer systems, ranging from network routing, resource allocation and more recently auction marketplaces [10].

the notion of the price of anarchy suffers from the pessimism of worst-case analysis.


0 if log f is continuous and has bounded gradient.

alpha-annealing might not be ideal in practice.


Building on this idea, algorithms have been proposed for answering queries on probabilistic Kripke structures [10] and on influence diagrams that define such structures [8].

these algorithms have not addressed the fact that as agents interact with the world over time, the set of observation sequences they could have received (and possibly the set of beliefs they could arrive at) grows exponentially.


Then, the graph must satisfy the following constraint: In words, if at least one of i and j is a ghost node, B(i, j) must be zero.

if neither of i and j is a ghost node, B(i, j) must be nonzero.


All of these definitions have similar meanings, and they are typically sufficient for the purpose of understanding a single estimator.

they are not mathematically rigorous, and it is difficult to use them to discuss the breakdown point of composite estimators.


( 19) is the solution to the following problem: Thus in the t iteration, where vectors u i t and u i t+1 denote the i-th row of matrices U t and U t+1 , respectively.

according to Lemma 1, for each i we have Thus the following inequality holds: Combining Eq.


Although this modeling is indirect, recurrent networks nonetheless can achieve state-of-the-art results on many robotics [18,23], vision [34,50], and natural language tasks [15,20,38] when training succeeds.

recurrent model optimization is hampered by two main difficulties: 1) non-convexity, and 2) the loss does not directly encourage the internal state to model the latent state.


In most cases, the k-means and k-medoid approaches perform similarly.

for both batch sizes k-medoid often does shows a small improvement over k-means and appears to have a significant advantage in FuelCell.


In both cases, this is equivalent to pre-process the data with a Gaussian smoothing kernel with standard deviation σ = √ β [17].

smoothing the data with a Gaussian kernel would mix gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF).


A recent benchmark [18] indicated that Local Subspace Affinity (LSA) [21] gave the best performance in terms of classification accuracy, although their result was subsequently surpassed by [5,10].

we argue that most of the previous approaches do not simultaneously fulfil the qualities desirable of motion segmentation algorithms.


Although the projection strategy can overcome this problem, it requires a costly procedure to compute the inverse of an B × B matrix wherein B is the budget size, typically in the cubic complexity of B.

the merging strategy needs to estimate the preimage of a vector in the feature space, leading to a significant information loss and requiring extensive computation.


• These methods strongly rely on the knowledge of the length L of the filters.


For example, for a restricted Boltzmann machine (RBM) [23], the 1-neighbourhood of any pairwise clique includes the entire graph.

hence, the complexity of LAP is exponential in the size of V. it is linear for conditional LAP, without sacrificing consistency.


This allowed us to conduct a fair comparison with the low density separation (LDS) algorithm of [19], which is an enhanced version of the so-called Transductive SVM.

deriving "out-of-sample" extensions for our method is straightforward.


By ignoring anything but most frequent words, and sometimes stop words as well, it is possible to preserve most of the text while drastically reducing the number of embedding vectors and parameters.

for any given task, there is a risk of removing too much or to little.


For some data sets, the sheer size of the data dictates that one use a cluster of machines.

there are a host of problems in which, after appropriate preprocessing, the data necessary for statistical analysis may consist of a few terabytes or less.


On the one hand, SRL is stable and data efficient.


A classic result of Kruskal [10] has been employed to prove the identifiability of a wide class of latent variable models, including hidden Markov models and certain restricted mixtures of latent tree models [11][12][13].

these techniques cannot be directly applied to parsing models since the tree topology varies over an exponential set of possible topologies.


Several works characterize convergence of EM to stationary points of the log-likelihood objective under certain regularity conditions (Wu, 1983;Tseng, 2004;Vaida, 2005;Chrétien and Hero, 2008).

these analyses do not distinguish between global maximizers and other stationary points (except, e.g., when the likelihood function is unimodal).


[34] use a generator trained with a GAN as a decoder in a compression system.

they rely on vanilla GAN [14] only rather than considering different W d -based generative models and they do not provide an analytical characterization of their model.


The prevailing model in this field is the continuous-time Markov process (CTMP), a model that provides an initial distribution over states and a rate matrix parameterizing the rate of transitioning between states.

this model does not scale for the case where a CTMP state is a joint state over many variable states.


Because the precise mechanism by which neural responses generate hemodynamic responses is an active area of research [7], strong conclusions cannot be drawn based on simulated fMRI data alone.

establishing "ground truth" validity for connections estimated by GC on fMRI data require concurrent, brain-wide invasive neurophysiological recordings during fMRI scans, a prohibitive enterprise.


The structure of log depends on the probabilistic model used; in the worst case, log can always be represented as a sum of m Kronecker product vectors.

many models admit a far more compact structure where dramatic savings can be realized as we demonstrate in the following sections.


By appropriately tracking cross terms, these results can also be applied to more general (non-tetrahedral) polynomials in Gaussian random variables [23].

our random process L(a, w) involves a nonlinear phase term ψ(Aw) which is not a polynomial, and hence is not amenable to a direct appeal to existing results.


A common choice is the regression loss function i ( f (x i ) − c i ) 2 , which encourages the model to predict cost accurately.

as we care only about the relative order of program run times rather than their absolute values in the selection process, we can instead use the following rank loss function [6]: We can use the prediction f (x) to select the top-performing implementations.


it seems that images for (* * * 5747 *) code do not correspond to any predefined category.


When the Gaussian width (σ target ) becomes much greater width of the Gaussian proposal distribution (σ proposal ), RwM produces brown noise.

mC 3 has a tendency to produce 1/f noise when the acceptance rate is high (Figure 3C black line).


In this study we use one neural network architecture which suffices to achieve good results in terms of FID on all considered data sets.

given data sets of higher complexity and higher resolution, it might be necessary to significantly increase the number of parameters, which in turn might lead to larger quantitative differences between different methods.


Also in Figure 4 is the effect of a varying cost, c(t), under uniform Currently most mobile internet access providers appear to be charging a flat fee for call costs (typically in the U.K. about 15 cents per minute).

when demand on their systems rise they may wish to incorporate a varying cost to flatten peak demands.


This approach provides a unified framework for detection and post-processing (non-maximum suppression), and handles issues related to the object with variable aspect ratios naturally.

object localization is an inherently difficult task due to the large amount of variations in objects and scenes, e.g., shape deformations, color variations, pose changes, occlusion, view point changes, background clutter, etc.


Furthermore, given observation Y l (t), assume that the transformation by (1) has modeling and measurement uncertainty in Gaussian distribution, i.e., where w stkt (t) is Gaussian with zero mean and variance Σ l stkt , i.e., N (•; 0, Σ l stkt ).

thus, the likelihood of observation Y l (t) at state s t and mixture k t is Refereeing to (3) and ( 5), the posterior distribution of Θ(t) given Y l (t) is The time-varying noise parameter is estimated by MMSE, given as, it is difficult to obtain the posterior distribution p(Θ(t)|Y l (0 : t)) analytically, since p(µ l stkt (t), µ l n (t)|Y l (t)) is non-Gaussian in µ l stkt (t) and µ l n (t) due to the non-linearity in (4).


If ε = 0, this is equivalent to the classical spatial scan statistic [1][2]: we are testing for regions where q in is greater than q out .

in many real-world applications (including the epidemiological and fMRI datasets discussed later) we expect some fluctuation in the underlying baseline; thus, we do not want to detect all deviations from baseline, but only those where the amount of deviation is greater than some threshold.


Then, if we solve (5) with s = 8 r log p n and g = 8 then, with probability at least 1 c 1 exp( c 2 n 2 s ) c 3 /q 2 , we have the error bound: Let us briefly compare the result from Corollary 2 with those from single-structured regularized estimators.

since the total sparsity of ✓ ⇤ is bounded by k✓k 0  ms g + s, "clean" `1 regularized least squares, with high probability, gives the bound [11]: the support of ✓ ⇤ also can be interpreted as comprising s g + s disjoint groups in the worst case, so that "clean" `1/`2 group regularization entails, with high probability, the bound [11]: (sg+s)m n + q (sg+s) log q n ◆ .


Abadi and Andersen [2] used adversarial training to teach two neural networks to encrypt a short message, that fools a discriminator.

it is hard to offer an evaluation to show that the encryption scheme is computationally difficult to break, nor is there evidence that this encryption scheme is competitive against readily available public key encryption schemes.


For inference of average treatment effect, we see that at the low noise levels CEVAE does slightly worse than the other methods, with CEVAE nh = 0 doing noticeably worse.

similar to the counterfactual case, CEVAE is significantly more robust to proxy noise, achieving quite a low error even when the direct proxies are completely useless at noise level 0.5.


An assumption of the sparse coding model is that the coefficients of the representation are independent.

in the case of natural images, this is not the case.


Notably, OLPOMDP (d = 0) does not perform well with this feature set.

for planning depths 3 ≤ d < 6, the PGRD agents with the recency parameterization achieve optimal objective return faster than the corresponding PGRD agent with the observation-action parameterization.


We note that these constraints can be removed by simply redefining U t (b t ) = ∞ ∀b t = b i t . A naive approach to minimizing (4) would take O(K T ) for K locations per frame.

we can efficiently solve the above problem in O(T K 2 ) by using dynamic programming through a forward pass recursion [3]: By storing the pointers in (6), we are able to reconstruct the least cost path by backtracking from the last frame T . We note that we can further reduce this computation to O(T K) by applying distance transform speed ups to the pairwise term in (3) [11].


In a cluster, data points are close to each other and the neighborhood is small, so the corresponding eigenvalues are small.

for a noise point, corresponding eigenvalues are much bigger.


Therefore, over time we see an improved validation score, even after convergence, due to lucky evaluations.

those apparent improvements are not reflected on the test set.


It is once again natural to wonder whether some approximation of BP might underlie learning in the brain [22,5].

none of the algorithms proposed as approximations of BP have been tested on the datasets that were instrumental in convincing the machine learning and neuroscience communities to revisit these questions.


This result was hinted at in [2], as in high dimensional case, the random draw from the unit sphere is likely to produce orthogonal directions.

we do not require dimensionality to be high for our result.


To the best of our knowledge, we are the first to introduce the notion of entrywise PDFs for binary matrices and to develop implicit sampling techniques for computing them efficiently.

our work is related to the problem of sampling from the space of binary matrices with fixed marginals, studied extensively in many domains [2,6,7,9,21], primarily due to its applications in statistical significance testing [14,17,20].


Moreover, different computer architectures and CNN architectures afford different optimization strategies making most implementations highly specific.

regardless of implementation details, all of the approximations we present reduce both the number of operations and number of weights required to compute the output by at least a factor of two, often more.


2 This motivated further development, including a recent actor-critic algorithm proven to converge when the critic uses linear function approximation [Maei, 2018], as well as several methods using the approximate off-policy gradient such as Deterministic Policy Gradient (DPG) [Silver et al., 2014, Lillicrap et al., 2015, ACER [Wang et al., 2016], and Interpolated Policy Gradient (IPG) [Gu et al., 2017].

it remains an open question whether the foundational theorem that underlies these algorithms can be generalized beyond tabular representations.


For the ease of presentation, we discuss how to develop MKL-DR subject to constraint (4).

the derivation can be analogously applied when using constraint (3).


For the prediction of v t given v 1:t−1 , we (i) first obtain a sample from q φ (h of the current hidden state ; (iii) make a prediction for v t using p θ (v t |h 1:t , v 1:t−1 ).

synthesizing samples is conceptually simper.


We would like to include a direct training signal for this instance in the optimization procedure above.

e(θ) is defined in terms of bag-level error, not instance-level error.


One reason why subjects might employ sampling is that, in generative models more interesting than the toy linear, Gaussian one used here, Bayesian reasoning is notoriously intractable.

the approximation from a small number of samples (or in the extreme case considered here, one sample) would be noisy and poor.


As a result, it would be accurate in predicting the best arm k * over bandits, but may have an arbitrarily bad performance in predicting the best arm for each bandit, and thus, may incur a large error ℓ(n).

gapE focuses on the arms with the smallest gaps.


Including the entropy into the learning cost function can be seen as adding a regularizer that promotes a compressible representation of the network or feature representation.

two major challenges arise when minimizing D + βR for DNNs: i) coping with the non-differentiability (due to quantization operations) of the cost function D + βR, and ii) obtaining an accurate and differentiable estimate of the entropy (i.e., R).


For any distribution P in our proposed family, an event stream is almost surely infinite.

when we observe the process only during a time interval [0, T ], the number I of observed events is almost surely finite.


As with bandit problems, the states of the arms evolve independently given the actions taken, suggesting that there might be efficient algorithms for large-scale settings, based on calculating an index for each arm, which is a real number associated with the (belief-)state of that arm alone.

while bandits always have an optimal index policy (select the arm with the largest index), it is known that no index policy can be optimal for some discrete-state restless bandits [17] and such problems are in general PSPACE-hard even to approximate to any non-trivial factor [10].


The behavior when the two frequencies are close to each other differs in the linear and nonlinear cases.

in both cases a sharp selectivity in frequency is observed.


Extremely small values < 10 −8 resulted in numerical instabilities, as shown in Figure 2 (right).

when > 10 −1 , the approximation in (6) becomes substantially inaccurate.


When neurons compute noiselessly, this task may be achieved by exploiting the fact the set of patterns x ∈ X to satisfy the set of constraints W (i) • x (i) = 0.

it is not clear how to accomplish this objective when the neural computations are noisy.


We could have instead used J i y i x i , which would be more standard.

this would make the parameter vector J invariant to scaling, complicating the identifiability analysis.


Thus, Adept-norm maximizes mean responses at the expense of less scatter.

adept-avgdist produced a lower mean response than that of Adept using the full objective function (Fig.


The first loss is the negative log-likelihood of the ground-truth correspondences: This loss has the advantage that it explicitly learns (3) as the probability of a match.

it is not sensitive to the size of a correspondence error v − gu.


Theorem 3.3 suggests that it is a good heuristic to include linear features in SVGD, because Gaussianlike distributions appear widely thanks to the central limit theorem and Bernstein-von Mises theorem, and the main goal of inference is often to estimate the mean and variance.

the more commonly used Gaussian RBF kernel does not have similar exact recovery results for the mean and variance, even for Gaussian distributions.


The primary contribution of this paper is a theoretical analysis that substantially relaxes the strength of this second assumption to just a form of "expansion" of the underlying distribution (a natural analog of the graph-theoretic notions of expansion and conductance) that we show in some sense is a necessary condition for co-training to succeed as well.

we will need a fairly strong assumption on the learning algorithms: that the h i they produce are never "confident but wrong" (formally, the algorithms are able to learn from positive data only), though we give a heuristic analysis of the case when this does not hold.


Sketching is a powerful dimensionality reduction tool for accelerating statistical learning algorithms.

its applicability has been limited to a certain extent since the crucial ingredient, the so-called oblivious subspace embedding, can only be applied to data spaces with an explicit representation as the column span or row span of a matrix, while in many settings learning is done in a high-dimensional space implicitly defined by the data matrix via a kernel transformation.


The recently proposed additive noise model has advantages over previous directed structure learning approaches since it (i) does not assume linearity or Gaussianity and (ii) can discover a unique DAG rather than its Markov equivalence class.


If the causal effects are shown to be identifiable, their magnitudes can be obtained by statistical estimation, which for common models often reduces to solving systems of linear equations.

from the Bayesian perspective, the causality detection problem may be viewed as that of model selection, where a model M x→y is compared with M y→x .


Method Average Score DQN [66] 343 ± 18 A3C (continuous) [36] 591 ± 45 A3C (discrete) [41] 652 ± 10 Gym Leader [44] 838  Full World Model (V and M) The representation z t provided by V only captures a representation at a moment in time and does not have much predictive power.

m is trained to do one thing, and to do it really well, which is to predict z t+1 .


The number of iterations required for convergence is O(log( d )/gap).

this method can be very slow when the gap is small.


Over the past twenty years or so, the attention of cognitive neuroscientists and computationally minded psychologists has tended to focus on habit-based control, due in large part to interest in potential links between dopaminergic function and temporal-difference algorithms for reinforcement learning.

a resurgence of interest in purposive action selection is now being driven by innovations in animal behavior research, which have yielded powerful new behavioral assays [3], and revealed specific effects of focal neural damage on goaldirected behavior [4].


We use MCMC simulations in a computer to sample for our Bayesian learners, and so considering only finite spaces above is acceptable.

the theory we present here holds for any hypothesis, input and output space that may be handled by a computer with infinite resources (see [11; 12] for more precise descriptions).


Just like in the exponential family case, g t the log-partition function ensures that p(x; θ) is normalized.

no closed form solution exists for computing g t exactly in general.


same point of view, colors, objects), which is related to the replay alignment mechanism that enforces remembering the instance.

meRGAN-JTR remembers bedrooms in general as the generated image still resembles a bedroom but not exactly the same one as in previous steps.


In recent years, deep reinforcement learning (DRL) has attracted attention in a variety of application domains, such as game playing [1,2] and robot navigation [3].

exploration remains a major challenge for environments with large state spaces, deceptive local optima, or sparse reward signals.


6: end for Return: x k . Algorithm 4: ReLU pxq Input: x x 1 1: Branch: Algorithm 5: ReLU pxq Input: x x 1 1: Branch: Figure 1: Two programs that implement ReLU pxq: Both programs are correct and return the same value.

the program on the right violates Assumption 3.1 since the gradient of the constraint function at x 0, ∇px 3 1 q 3x 2 1 0. where each p z is a polynomial; I Sz is the indicator function on the set S ; and S z consists of all x where the program executes branch z when given x as input.


This observation allows to reconstruct the Ising graph perfectly with only a logarithmic number of samples and in time quasi-quadratic in the number of variables.

bresler's algorithm suffers from two major practical limitations.


Most research in GPSSMs has focussed on the state estimation problem, i.e., computing a posterior of the latent state given the model.

the key challenge in GPSSMs has not been satisfactorily addressed yet: system identification, i.e., learning the model.


6) When asked to grasp an object, we command the arm to move the camera to two or more positions, so as to acquire images of the object from these positions.

there are inaccuracies in the physical positioning of the arm, and hence some slight uncertainty in the position of the camera when the images are acquired.


The effects of stress, strain, and NA on future reward discounting indicate that stress, high anxiety, and elevated noradrenaline are all detrimental for learning delayed future rewards.

since the effects of NA and stress on reward discount factors are more pronounced for DBA/2 mice, γ-s might be sensitive to noradrenaline at higher levels than β-s are.


. . y [r,I] ): Input variables, such as "feature vectors" in a purely discriminative model.

a CGPM is required to satisfy the following conditional independence constraint: (1) Eq (1) formalizes the notion that all dependencies across members r ∈ N are completely mediated by the population parameters θ and member-specific variables z r . elements x [r,i] and x [r,j] within a member are generally free to assume any dependence structure.


The constraint causes some minor complications with the assumptions on the base learning algorithm.


Our main motivation is to consider an important class of models in applied economics, namely, dynamic industry models of imperfect competition.

we believe our methods can be useful in other contexts as well.


Despite the nonconvexity of both the objective and regularizer, the theorem above shows that with a near minimal number 1 We would like to note that n0 only approximately characterizes the minimum number of samples required.

a more precise characterization is since our results have unspecified constants we avoid this more accurate characterization.


Belief propagation (BP), originally proposed by Pearl [1], has gained in popularity as a method of approximate inference, and in the last decade has led to a number of more sophisticated algorithms based on conjugate dual formulations and free energy approximations [4,5,6].

the progress on approximate inference in systems with continuous random variables has not kept pace with that for discrete random variables.


There are simple examples such as learning intervals for which active learning has no advantage.

these negative examples are more or less "artificial".


For comparison, one can think of the vanilla stochastic attention of which variance is independent of inputs. )

as we mentioned, this model cannot express different amount of uncertainties over features.


One may argue that we can also equip multiple NICs on a server to connect a Fat-Tree network.

it leads to more switches and several times higher network cost.


Given that spikes are discrete events in time, it seems more natural to use a Poisson [10] or other point-process model [19] or, at coarser timescales, a count-process model.

it is unclear what (if any) advantage such more realistic models confer.


The optimisation strategy we suggest could be sensitive to local minima, we did not try a range of different initialisations to explore this phenomena.

by initialising with the uniformly-spaced strategy we ensured that we increased the objective function relative to the standard strategy.


Classifying instances in the original instance space by comparing them to the target classes' single examples x and x , leads to overfitting.

our approach projects the instance space by W and only then applies a nearest neighbor distance measurement to the projected single examples W x and W x .


An interesting trend emerges: in the early blocks of the stage, the distribution of class selectivity for both models appears to be closely matched.

with increasing depth, the distributions begin to separate, and by conv4-6-relu the distributions appear more distinct with GE-θ exhibiting less class selectivity than ResNet-50.


We have only considered classification tasks in this paper, but a continuous key-value cache component can be added to models performing other image-based tasks, such as object detection or segmentation, as well.

different tasks might require different similarity measures (Equation 1) and different ways of combining the predictions of the cache component with the predictions of the underlying model (Equation 3).


Because shot boundaries can be seen as arrivals over discrete, non-overlapping temporal intervals, a Poisson process seems an appropriate model for shot duration [3].

events generated by Poisson processes have inter-arrival times characterized by the exponential density which is a monotonically decreasing function of time.


Large neural networks have recently demonstrated impressive performance on a range of speech and vision tasks.

the size of these models can make their deployment at test time problematic.


By evaluating the derivative of the log likelihood on only a small subset of data points, we can drastically reduce computational costs.

using stochastic gradients comes at a cost: While the resulting estimates are unbiased, they do have very high variance.


Several lines of work have shown that the plain Robbins-Monro algorithm could be accelerated for strongly-convex finite sums, e.g., SAG [1], SVRG [2], SAGA [3].

these only apply to separable objective functions.


For function F and any U ∈ {U|σ min (X U) ≥ γ}, we have: Lemma 4.2 tells function f is smooth if spectral norm of U is not very large.

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


In particular, recent works have applied GP-based Bayesian quadrature to the estimation of the marginal likelihood [8,9,10,11], and GP surrogates to build approximations of the posterior [12,13].

none of the existing approaches deals simultaneously with posterior and model inference.


In the three plots involving feature y 1 it can be seen that the directions of the response vector (i.e., the vector composed of the slow feature values at a particular point in time) cluster at class-specific angles, which is characteristic for What-information.

these phase plots tend to form loops in phase space (instead of just straight lines from the origin), where each point on this loop corresponds to a position within the trajectory.


In motion segmentation [7,20] or illumination invariant face clustering [8], the data belong to a high dimensional space.

the instances belonging to each cluster approximately span a low-dimensional subspace (usually, of dimension 3 or 4).


Recent successes of generative adversarial networks in the image domain [25] have motivated their use in modeling discrete sequences like text.

discreteness introduces problems in endto-end training of the generator.


In case of single MNL models (no mixture), computationally and statistically tractable learning from pair-wise comparisons is feasible.

even learning mixture with two MNL components is infeasible in general.


So Kolmogorov complexity (see below) determines the relatedness between tasks.

the bounds hold only for ≥ 8192 tasks (Theorem 3).


At each iteration of the algorithm, we update each value in the slice based on adjacent values, as before.

it is now the case that some of the adjacent nodes lie off of the slice.


In the context of image-denoising, feedforward neural networks have been shown to have good performance [6,20,11].

their work has not included a feedback component and has no generative ability.


Due to the low-rank constraint in our optimization framework, we seek a small value of eigengap(C) for a good optimal value.

we can set a stopping criterion for our method using eigengap(C) < T for a small threshold, T . due to the noise reaching a small threshold cannot be guaranteed, therefore, a practical stopping criterion adopted by our method is when eigengap(C) has stoped decreasing.


Of course, in general this question cannot be answered.

experience shows that the assumption that the distribution is noise-free is almost never satisfied.


Due to the relative entropy bound, the algorithm achieves a smooth and stable learning process.

the episodic REPS algorithm uses a sample based approximation of the KL-bound, which needs a lot of samples in order to be accurate.


We found that this approach works well when all the factors have small variances, as in this case the link function of the observation model is only mildly non-linear.

with growing variances of the factors (larger dynamic ranges of neurons) spectral clustering performance quickly degrades.


This has the advantage of not requiring any other pre-training method and the vectors are sure to capture domain knowledge.

the vectors are more likely to overfit and less likely to generalize well to words that have not been in the (usually smaller) labeled training set.


For the more general setting where p may not be uniform, Foygel and Srebro [4] show that the max norm is still an effective regularizer (in particular, bounds on error for the max norm are not affected by p).

salakhutdinov and Srebro [5] show that the trace norm is not robust to non-uniform sampling-regularizing with the trace norm may yield large error due to over-fitting on the rows and columns with high marginals.


Larochelle and Bengio [12] suggested to couple this generative model P (x, y) with a discriminative model P (y|x), which can help alleviate this issue.

if the objective is to train a deep network, then with ever new layer, the previous V has to be discarded and retrained.


MCMC techniques are a specialized form of local search that only allows moves that maintain detailed balance, thus guaranteeing the right occupation probability once the chain has mixed.

in the context of hard combinatorial spaces with complex internal structure, mixing times are often exponential.


This "Ugliness-in-Averageness" (UiA) effect has previously been explained via a qualitative disfluency account, which posits that the negative affect associated with the difficult race or gender categorization is inadvertently interpreted by the brain as a dislike for the face itself.

we hypothesize that human preference for an object is increased when it incurs lower encoding cost, in particular when its perceived statistical typicality is high, in consonance with Barlow's seminal "efficient coding hypothesis."


In some situations the ability to incorporate the additional information about the input density at test time may be beneficial.

it is also straightforward to effectively 'ignore' this new information and simply compute a set of independent single location predictions.


Using ( 13), (18), and (11), we can further write Since t > 1, it is easy to see that r j (θ) > 0 is a convex function of θ.

since g t is convex and t > 1 it follows that l i (θ) > 0 is also a convex function of θ.


Many planning problems in robotics are best phrased as MDPs, defined over world states or-in case of partial observability-belief states [7].

existing MDP planning techniques generally scale poorly to multirobot systems because of the curse of dimensionality: in general, it is exponentially harder to solve an MDP for N agents than it is to solve a single-agent MDP, because the state and action space for N robots can be exponentially larger than for a single-robot system.


First, we have purposely incorporated the self-attention module into all of our baselines models-indeed having self-attention in the architecture could potentially induce a supervisedly-trained graph, because of which one may argue that this graph could replace its unsupervised counterpart.

as is shown in Table 1, augmenting training with unsupervisedly-learned graphs has further improved performance.


Submodular optimization is an important problem that arises across many settings, including sensor placements [16,15], summarization [26,17,23], inferring latent influence networks [8], diversified recommender systems [5,4,25,21], and multiple solution prediction [1,3,22,19].

the majority of previous work has focused on offline submodular optimization whereby the submodular function to be optimized is fixed a priori (i.e., does not vary depending on feedback).


By Lemma 9, the long-run average payoff to Player 1 from time T onward is within the interval val(G ij ) ± O(κ) ± O(ε).

by Lemma 9 again, the long-run average payoff to Player 1 from time 0 onward is within the interval val(G) ± O(ε).


Although combinatorial methods, which return a provably optimal integral solution of the problem, made a significant progress in the past decade, they are still typically unable to cope with large-scale datasets.

large scale datasets are often defined on sparse graphs and convex relaxation methods, such as linear programming relaxations then provide good approximations to integral solutions.


As pointed out in [52], KDEs seldom do a good job of capturing the underlying density, since they do not scale well with data.

when the underlying data distribution is discrete, count-based non-parametric models such as smoothed n-gram language models [20] are extremely it is therefore quite impossible to separate the various provisions of the single market with regard to quotas .


In Section 3, we have shown that our algorithm SDCB achieves near-optimal regret bounds.

that algorithm might suffer from large running time and memory usage.


Increasing the depth from five layers to eight layers decreases the performance from 65% to 51%, probably because it overfits to the small training set.

when trained with visual transfer from unlabeled video, the eight layer SoundNet achieves a significant gain of around 20% compared to the five layer version.


Figure 1 shows that increasing  always results in less number of iterations (less communication rounds) for COLA.

given a fixed network bandwidth, it leads to a clear trade-off for the overall wall-clock time, showing the cost of both communication and computation.


Since the free set is very sparse and can fit in memory, those W ij only need to be computed once and stored in memory.

the computation of w T i Dw j corresponds to the Hessian computation, and we need two columns for each coordinate update, which has to be computed repeatedly.


Empirical evidence shows that in favorable situations semi-supervised learning (SSL) algorithms can capitalize on the abundance of unlabeled training data to improve the performance of a learning task, in the sense that fewer labeled training data are needed to achieve a target error bound.

in other situations unlabeled data do not seem to help.


Previous analyses of EM only established such results for specific methods of initializing EM (e.g., Dasgupta and Schulman, 2007;Balakrishnan et al., 2014); our results show that they are not really necessary in the large sample limit.

in any real scenario, the large sample limit may not accurately characterize the behavior of EM.


To achieve better numerical efficiency and convergence behavior compared to the dual ascent method, it is favorable to set ρ > 0 in the augmented Lagrangian (2) which we call the method of multipliers.

( 2) is no longer separable and solving entire augmented Lagrangian (2) exactly is computationally expensive.


In order to clearly describe and motivate SFGs, we present them here in the context of image parsing.

sFGs are a general and flexible model class that is applicable anywhere grammars or MRFs are used, including social network modeling and probabilistic knowledge bases.


In a deterministic optimization setting and for general smooth convex functions, these methods enjoy a rate of O(1/n 2 ) (where n is the number of iterations) as opposed to O(1/n) using standard methods.

in a stochastic setting (which is the relevant one for learning problems), the rate of both approaches have an O(1/ √ n) dominant term in general, so the benefit of using accelerated methods for learning problems is not obvious.


There is a series of on-going works on this direction [29,34,32,13,2,11,31,33].

among all these networks designed for image classification, the features of high resolution are extracted by the shallow layers with small receptive field, which lack the high-level semantic meaning that can only be obtained on Design in combining features from different layers.


The first is the insensitivity parameter which defines the loss function as in the realizable case.

in this case we do not assume that there exists w that achieves zero loss over the sequence.


The second step typically makes use of concepts from empirical processes, by pairing up Ledoux-Talagrand contraction type arguments with well established symmetrization results.

in our case, the function is not a contraction like in the symmetric two component case, since it involves the cluster estimates of all M components.


In order to simulate the likely presence of high amplitude artifacts, one way would be to directly simulate the generative model in (3).

this would give us an unfair advantage, since αCSC is specifically designed for such data.


This is because in our scheme the training size is not the number of instances, but rather the number of observed features (See Table 1).

in the next theorem we obtain an upper bound that is independent of m, and hence is tighter for large m. Pr sup {t1,...,tm} where |X j | denotes the alphabet size of X j (i.e.


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

since the true posterior is intractable except a handful of special cases, we must resort to approximation methods.


This is because POLARIS uses a generative network to decide which features to change for drawing tutoring, which leads to one invocation to Algorithm 2 per input.

for mortgage underwriting, POLARIS needs to invoke Algorithm 2 for multiple times per input which searches under a combination of different features.


There have recently been several attempts to construct heuristic approaches to the batch mode active learning problem (e.g., [2]).

theoretical analysis has been largely lacking.


Due to the generality of the distributions, the only tool we could use is Sanov's theorem.

hellinger distance comes out to be the right measure both for lower and upper bounds.


While the sampling based approaches for approximate inference are in general applicable to models with both types of factors, fast mixing is only guaranteed for a subclass of all possible models and these methods may not scale well to large ground sets.

the variational inference techniques were only developed for either log-submodular or log-supermodular models.


Presumably, if given enough training iterations, their accuracies would return to the normal baseline.

for the oversampled condition, Phased LSTM actually increases in accuracy, as it receives more information about the underlying waveform.


This is because the algorithm needs information from outside of the compression set in order to construct its regressors and make predictions.

we can use a VC argument together with a sample compression trick in order to derive a bound for KMP in terms of the level of sparsity achieved, by viewing the sparsity achieved in the feature space as a compression scheme.


Recall that we can estimate θ d t for the unseen web image contexts by generalizing the web-text LDA model using Gibbs sampling.

web topics can be a poor match to image search data (e.g.


In this case, one has the freedom to restructure and sample the background data during the statistical design to gain computational efficiency.

change-point detection problems are related to the statistical two-sample test problems; however, they are usually more difficult in that for change-point detection, we need to search for the unknown change-point location ⌧ .


( 2)) factorizes over a graph, we can, in theory, use local messages to propagate beliefs about statistics t[p ✓ ✓ ✓(x) (y)] along its edges (BP; [20]).

special care must be taken to handle intractable operations caused by non-parametric local potentials and to allow an end-to-end integration.


For general kernels k, these integrals may only be solved numerically.

for at least one specific choice of kernel (square-exponentials) and parametric Ansatz, the required integrals can be solved in closed form.


• Topic+FacultyStudent Distance: Again when two examples, x, y, are from the same topic then they have a small distance between them and a larger distance when they come from different topics.

we add the additional constraint that the distance between a faculty and a student page is smaller than the distance to pages from other topics.


As dictated by our theory, all the MLD curves decay at the O(T − 1 /2 ) rate until they saturate at the dicretization error level.

sGRLD lacks non-asymptotic guarantees, and there is no clear convergence rate we can infer from Figure 1(a).


We then present an algorithm that provably meets these stronger requirements.

we believe that all formal requirements -including our own -are merely baseline guarantees, and any proposed algorithm must be subjected to empirical tests.


This is because the scene classification model is influenced by the latent object modeling through the term ∆L ⋆ d (s), which can improve the decision boundary of a standard linear SVM for those images that have negative scores of ∆L ⋆ d (s), as we have discussed in the online loss-augmented SVM.

object modeling does not improve the classification accuracy and sometimes it can even be harmful when the scene model is learned with the standard MLE.


Hierarchical clustering models aim to fit hierarchies to data, and enjoy the property that clusterings of varying size can be obtained by "pruning" the tree at particular levels.

standard clustering models must specify the number of clusters beforehand, while Nonparametric Bayesian (NPB) clustering models such as the Dirichlet Process Mixture (DPM) [5,13] directly infer the (effective) number of clusters.


The sufficient statistics of the model are the visible activations v, the hidden activations h, and the products vh T . Therefore, γ M A is defined by: For many models of interest, including RBMs, it is infeasible to determine γ M A exactly, as it requires solving two often intractable problems: (1) computing the moments of p b , and (2) solving for model parameters which match the averaged moments s(β).

much work has been devoted to practical approximations [19,20], some of which we use in our experiments with intractable models.


We note that in the dataset, awning and streetlight are not highly co-occuring, thus initially when we create the semantic groups, these two objects do not appear simultaneously in any group.

the semantic groups containing streetlight and the semantic groups containing awning both contain objects like road, building, and car.


For instance, to the best of our knowledge, there is no result explaining how to sample the space so that the corresponding sensing matrix Φ satisfies the nice recovery properties needed by the previous theorems, for a general family of features {ϕ k } k≤K .

it is proven in [12] that under some hypotheses on the functional basis, we are able to recover the strong RIP property for the matrix Φ with high probability.


Much like their psychological counterparts, connectionist networks also show very strong frequency effects.

the ability of a connectionist network to show AoA effects has been doubted (Gerhand & Barry, 1998;Morrison & Ellis, 1995).


An attractive property of these methods is that, unlike ABC, they can be applied to multiple datasets without repeating the training process (i.e., amortized inference).

current practice in population genetics collapses the data to a set of summary statistics before passing it through the machine learning models.


( 8), allows us to create an optimization problem that minimizes an upper bound on the average loss in eq.

( 5) with maximum-margin constraints: ξ iα subject to: Note that if we have a very large number of classes, it might be beneficial to choose P ∈ R r×c with r < c. the convex formulation described in the next paragraph requires P to be square.


In these scenarios, the channels are interpreted as arms and the channel gains as the rewards.

since users are scattered in space, the physical reality dictates that different arms have different expected channel gains for different players.


One possible way of estimating the confidence of a decision maker is to assume that it is equal to the accuracy (or performance) on the task.

the decision maker's belief about the chance of success and accuracy need not be equal because the decision maker may not have access to information that the experimenter has access to [3].


This may be counterintuitive, as one may not expect a model for inhibitory interactions to improve prediction of when spikes do occur.

the GLM predicts almost no spikes (483 spikes of a possible 92,969), possibly due to its inability to capture higher order inhibitory structure.


Here the reason is that the zooming algorithm does not make full use of the fact that the function is locally quadratic (it considers a Lipschitz property only).

in the case α < 1, our rates are worse than algorithms specifically designed for continuum armed bandits.


For practical and computational reasons we choose to work with the space of trigonometric polynomials H nm defined below, where each element of the space is a function in n m variables (n m ∈ N, m = 1, 2, ..., M ).

we note that the results obtained in this paper are not limited to this particular choice of RKHS (see, e.g., [24]).


It is also intuitive to see that since the Hankel matrices Ĥi have been stacked horizontally, the estimation of the right singular subspace might not benefit from performing SVD on Ĥ.

classical results on singular subspace estimation (see e.g.


We verify that the solutions to MF-IIM undergo a shift from focusing on high-degree nodes at low interaction strengths to focusing on low-degree nodes at high interaction strengths.

we also find that for sufficiently high and low interaction strengths, the MF optimal external field achieves the maximum exact magnetization, while admitting performance losses near β c . even at β c , we demonstrate that solutions to MF-IIM significantly outperform common node-selection heuristics based on node degree and centrality.


Theoretically, one would expect to need thousands of Gibbs iterations to achieve convergence.

our experience is that even a single iteration in each of the above B 2 rounds yields good results.


Interestingly, the IBP model infers a greater number of latent factors that did the 2-layer noisy-or model (at the first layer).

the distribution over factors active for each data object is nearly identical.


The rejection thresholds θ(t), t ∈ {1, • • • , T − 1} are critical to the performance and speed of the complete classifier.

it is difficult to set them optimally in practice.


The hierarchical regression parameters are just like topics' regression parameters in SLDA: each topic k (here, a tree node) has a parameter η k , and the model uses the empirical distribution over the nodes that generated a document as the regressors.

the hierarchy in SHLDA makes it possible to discover relationships between topics and the response variable that SLDA's simple latent space obscures.


Learning to accurately classify objects from a single training example is often unfeasible due to overfitting effects.

if the instance representation provides that the distance between each two instances of the same class is smaller than the distance between any two instances from different classes, then a nearest neighbor classifier could achieve perfect performance with a single training example.


Their effort and other related works, first deduce some additional knowledge about the problem [16,20,1], and keep it fixed while learning.

our method learns together the classifier and some additional information.


Recent information-theoretic (IT) policy search algorithms [9] are based on the relative entropy policy search (REPS) algorithm which was proposed in [10] as a step-based policy search algorithm.

in [9] an episode-based version of REPS that is equivalent to stochastic search was presented.


Thus, the habitual system doesn't know what specific action-values should be updated when a novel internal state is being experienced.

it has been argued by some authors [14] that even though habitual responses are insensitive to sensory-specific satiety, they are sensitive to motivational manipulations in a general, outcomeindependent way.


This observation suggests an interesting and useful fact that (3) can be solved by designing tailored alternating minimization type algorithms developed for tackling nonsymmetric NMF.

a theoretical question raised in the regularized form ( 3) is that we are not guaranteed U = V and hence solving (3) is not equivalent to solving (2).


When extended to long-horizon problems, it faces an exponential blowup of variance, and variance-reduction techniques are used to improve the estimator [14,39,10,42].

it can be proved that in the worst case, the mean squared error of any estimator has to depend exponentially on the horizon [20,10].


The pre-image of the projection is the z ∈ X that satisfies ϕ(z) = Pϕ(x); z is also referred to as the KPCA reconstruction of x.

the pre-image of Pϕ(x) usually does not exist, so finding the KPCA reconstruction of x means finding z such that ϕ(z) is as close to Pϕ(x) as possible.


The standard approach to characterizing symmetries in objects is to look not at their images, but at their 3D shape; if the latter is available, then symmetries can be recovered by analysing the intrinsic geometry of the shape.

often only images of the objects are available, and reconstructing an accurate 3D shape from them can be very challenging, especially if the object is deformable.


An MCMC estimator can be based on any ergodic Markov chain with the distribution of interest as its stationary distribution.

the choice of Markov chain greatly affects the performance of the estimator, in particular the accuracy achieved with a pre-specified number of samples [4].


The goal has been to recognize object categories, such as a 'car', 'cow' or 'shirt'.

an object also has many other qualities apart from its category.


Simulation studies have shown very sparse solutions M N and good test performance [1].

starting the RVM learning with as many basis functions as examples, i.e.


Work on online auctions [3] is also related, in that it considers a system with dynamic agent arrivals and departures.

the online auction work considers a much simpler setting (see also [4]), for instance the allocation of a fixed number of identical goods, and places less emphasis on temporal strategies or allocative efficiency.


A general method has been recently proposed for joint inference on the hidden states and the GP dynamics using Particle Gibbs with Ancestor Sampling (PGAS) [20,19].

pGAS is a batch MCMC inference method that is computationally very expensive.


This makes this dataset well suited for Fine-Tuning (FT) to NYUv2.


Unfortunately, it is a computationally hard problem for many interesting applications.

it has been shown that linear programming (LP) relaxations recover the MAP assignment in many cases of interest (e.g., [13,23]).


( 6) and consequently the missing entries are discounted in the learning rules.

it would be useful to obtain Q(x m t |x o t ), i.e., the approximate distribution on the missing entries, which is given by As noted in [6], elements of s t given x o t are dependent.


Supposing that σ is sufficiently small, it is a straightforward argument that even when n = 1, β * is recoverable from Y = X, β * + W by a brute-force method with probability tending to one as p goes to infinity (whp).

for sparse and binary-valued β * , the Basis Pursuit method in the noiseless case Donoho and Tanner (2006) and the Basis Pursuit Denoising Scheme in the noisy case Gamarnik and Zadik (2017b) have been proven to fail to recover a binary β * with n = o(k log p k ) samples.


On the other hand, the affine span of any choices of 3 or more data points in the neighborhood always passes through x 1 .

this requires a linear combination of more than 2 data points.


Clearly there is the strategy of never predicting (by setting confidence 0) all the time that never has a loss but also never has a positive payoff.

if the sequence is very imbalanced and has many more 0's than 1's then this never predict strategy has a high regret with respect to the strategy that predicts the majority bit.


This would not result in a more general model because the effect of this on the marginal distribution over the observed variables is given by: W j ia → k K jk W k ia KK T = Σ.

the extra freedom can be used to define axes in latent space for which the projected data become approximately independent and have the same scale in all directions.


In the standard framework of sparse representation, the objective is to reduce the signal reconstruction error with as few number of atoms as possible.

discriminative analysis methods, such as LDA, are more suitable for the tasks of classification.


The algorithm, called PCA+LDA, is used widely in face recognition.

pCA+LDA has high costs in time and space, due to the need for an eigen-decomposition involving the scatter matrices.


In L-L state, the energy at E rises up, thus ¢ is most strongly stabilized at E ( .

in H-L(L-H) or H-H state, the energy barrier is lower than that of L-L state, thus ¢ can more easily overcome the barrier by using thermal noise.


An alternative approach towards scalability is to restrict the size of the subsets, as done in k-DPP [16] or when using rank-k DPP kernels [9] (where k ≪ N ).

without further assumptions, both approaches still require O(N 3 ) preprocessing for exact sampling; another caveat is that they limit the DPP model by assigning zero probabilities to sets of cardinality greater than k. KRONDPP uses a kernel matrix of the form L = L 1 ⊗ .


. . O i2,i1 O i1,i Q i would be the same.

if some (in many practical cases, the majority) of the O ji 's are incorrect, then different paths from one vertex to another contribute different rotations that need to be averaged out.


As a consequence of this formulation, the algorithms proposed in [11] can be in principle used in order to attain the convex hull of r * γ .

given the implementation difficulties associated with these algorithms, we are motivated to examine more carefully the problem of regret minimization with constraints and provide more practical no-regret algorithms with formal guarantees.


The unsupervised learning computes a vector of scattering coefficients which is typically much larger than the dimension d of x.

only a subset of these invariants are needed for any particular classification task.


This is a reasonable assumption when voltage is recorded directly, via patch-clamp methods.

while voltage-sensitive imaging techniques have seen dramatic improvements over the last few years (and will continue to do so in the near future), currently these methods still suffer from relatively low signalto-noise ratios and spatiotemporal sampling rates.


The earlier models including [26,36,18] are inspired by the recurrent neural networks.

convolution neural networks that learn convolutional filters in the graph Laplacian spectral domain have been demonstrated to perform well.


Both quantities can be much smaller than N despite the fact that empirical risk minimization occurs over the whole N -dimensional convex hull.

the approach to convex aggregation based on minimization of the empirical ℓ-risk over the convex hull does not guarantee that f is sparse even if f 0 is.


In particular, it gives a low probability to the coincidence that, while "dax" meant BALL the entire time, the model happened never to hear dax when there was a ball around.

a lexicon learning no new words scores best on the corpus (because of the prior on smaller lexicons) but has no explanation for why it heard the word "dax" in the new situation.


Recently, the problem has been addressed for conditional generation within an adversarial framework [GLZ + 16] and in various learning to search frameworks [WR16,LAOL17].

by design these models do not perform stochastic state transitions.


This simplification has proved useful for deriving efficient inference techniques and quickly analyzing very large corpora [5].


), which does not follow from the results of [13,10].

our results currently cannot generalize those of [19], which has As discussed below, it is unclear how to extend the work of [19] to the clipped constraints, [g(x t )] + .


In our case, the pair-wise relations between hidden variables are asymmetric and a maximum spanning tree algorithm cannot be used.

as we show below, the Q-term can be maximized by instead using Edmonds's optimal branching algorithm.


This visual similarity is reflected in the rank correlation with absolute value (Figure 3-Top), SSIM, and the HOGs metric (Figure 4).

re-initialization disrupts the sign of the map, so that the Spearman rank correlation without absolute values goes to zero (Figure 3-Bottom) almost as soon as the top layers are randomized.


We will argue that this model proves insufficient to explain human performance on anagram problem solving.

it is a key component of a hybrid symbolic-subsymbolic model we propose, and is thus described in detail.


The classifier resulting from minimising the unhinged loss is not new [Devroye et al., 1996, Chapter 10], [Schölkopf and Smola, 2002, Section 1.2], [Shawe-Taylor and Cristianini, 2004, Section 5.1].

establishing this classifier's (strong) SLN-robustness, uniqueness thereof, and its equivalence to a highly regularised SVM solution, to our knowledge is novel.


This classical view is still the most widely accepted way of reasoning about categories and taxonomies in hard sciences.

as pointed out by Wittgenstein, this is almost certainly not the way most of our everyday concepts work (e.g.


As the table on the right in Figure 4 demonstrates, the adaptive tree algorithm without the diagonal-dominance (DD) check provides convergence over a much broader range of models than the one-tree and two-tree iterations, but not for all valid models.

the modified adaptive tree algorithm with the DD check appears to converge almost up to the validity threshold.


image complexity in terms of the density of intensity, color, and texture features in an image [25].

recent work has pointed out limitations of the feature congestion model [13] [21], leading to the development of alternative approaches to quantifying visual clutter [25][5] [29] [18].


This polynomial lower bound for width is significantly smaller than the exponential lower bound for depth.

it does not rule out the possibility of the existence of an exponential lower bound for width efficiency.


The latter enjoys concentration of measure properties and it can be computed efficiently on any domain where a Reproducing Kernel Hilbert Space (RKHS) can be defined.

the application of HSIC is limited to independent and identically distributed (iid) data, a property that many problems do not share (e.g., BSS on audio data).


For margins γ γ, which are prone to over-fitting, Q n (α(γ), m(γ)) is not a reliable estimate for h S n (γ) since compression may not yet taken place for samples of size n. Nevertheless, these margins are discarded by KSU due to the penalty term in Q.

for γ-nets with margin γ γ, which are prone to under-fitting, the true error is well estimated by As one can see, the assumption that X is finite-dimensional plays a major role in the proof.


Stochastic inverses of graphical models [32] train density estimators to speed up inference.

both approaches have limitations on applicable models and require model-specific training using global information (samples containing all variables).


Indeed, Fisher consistency requires such feature spaces for its guarantees to be meaningful.

naïvely projecting from the original input space, x i , to richer (or possibly infinite) feature spaces ω(x i ), can be computationally burdensome.


GCHK is designed to pick few points, but since it ignores costs, the distance traveled is large.

by incorporating costs, TRUVAR tends to travel small distances, often even staying in the same x 1 location to take measurements at multiple depths x 2 .


The above theorem suggests that ψ-regularized multi-agent inverse reinforcement learning is seeking, for each agent i, a policy whose occupancy measure is close to one where we replace policy π i with expert π Ei , as measured by the convex function ψ i .

we do not assume access to the expert policy π E during training, so it is not possible to obtain ρ π i,E −i .


One obvious way of modeling eye movement selection is to use a reinforcement learning strategy directly.

standard reinforcement learning algorithms are are best suited to handling actions that have direct consequences for a task.


Again a phasic increase over baseline followed by a depression is seen (lower 10).

unlike the case in figure 1 B, there is no persistent reward prediction, since if a reward is subsequently delivered (unexpectedly), the cells become active (not shown) (Schultz, 1998).


In SGD and for the case of convex functions, even a minibatch of size 1 suffices for guaranteed convergence.

for SNGD we require a minibatch of size 1/ 2 .


Robust algorithms could be built by first estimating the undistorted structure and then using this structure as a guideline for constructing solutions for single instances.

hardness of efficient optimization might be linked to the inability to extract meaningful structure.


Label propagation can also be applied to deep learning models [31].

ordinary label propagation requires a predefined distance metric in the input space.


In particular, they showed fine reconstruction for figures consisting of thin lines such as small frames and alphabet letters.

the peripheral reconstruction was poor and often lacked shapes of the presented images.


In this asymptotic setting the local MICL criterion behaves like k-Nearest Neighbor (k-NN).

the finitesample behavior of the local MICL criterion can differ drastically from that of k-NN, especially   , local MICL effectively approximates the local shape of the distribution p j (x) by a (regularized) Gaussian, exploiting structure in the distribution of the nearest neighbors (see figure 3).


In addition, a Dirichlet prior can encourage sparse solutions, a property which is important with probabilistic grammars [11].

in [4], Blei and Lafferty noticed that the Dirichlet distribution is limited in its expressive power when modeling a corpus of documents, since it is less flexible about capturing relationships between possible topics.


We prove that RDP is an FPTAS, returning (1 − )-optimal solutions in polynomial time.

its time complexity, O(n 8 / 6 ), makes it hard to apply it to realistic river networks.


Interior point methods are another tool for solving Problem (1), and have time complexity guarantees of O(n 3 ) when the number of constraints is on the same order as the number of variables (see [10]).

the excessive memory requirements of interior point methods from solving large systems of linear equations typically make them impractical for large data sizes.


It has shown that the bit-width for inference computations can be successfully scaled down to just a few bits (i.e., 2-4 bits) while (mostly) preserving accuracy [3].

reduced precision DNN training has been significantly more challenging due to the need to maintain fidelity of the gradients during the back-propagation step.


We can recover this criterion by setting λ I = 0 in Theorem 3.

the pitfall of AOD is that it does not characterize the quality of predictions on the data, which is essential for classification or regression.


For some simple functions, the proximal map indeed is available in closed-form, see [9] for a nice survey.

for more complicated functions such as the one we consider here, the proximal map itself is expensive to compute and an inner iterative subroutine is required.


As mentioned above, most research has concentrated on the rating prediction problem in CF where the aim is to accurately predict the ratings for the unrated items for each user.

most applications that use CF typically aim to recommend only a small ranked set of items to each user.