As seen, even though a low-rank method, 2,1 -RPCA performs reasonably well but not on par with DPCP-PSGM and REAPER, which overall tend to be the most robust methods.

for the same time budget, RANSAC, which is a popular choice in the computer vision community for such outlier detection tasks, is essentially failing due to an insufficient number of iterations.


It turns out that Ω(nk) is also a lower bound, even for randomized algorithms (see, e.g., [13]).

the heuristics developed in practice often ask significantly less queries than nk.


This demonstrates the limited scalability of the interior-point method.

cO-Linear displays excellent scalability.


Besides, in [3], Dang and Lan proposed a randomized algorithm for solving (5).

their algorithm needs to use the full-dimensional gradient in each iteration, so the per-iteration cost is much higher than SPD1.


Previous work has attempted to answer these questions in a variety of ways and has provided encouraging successes [43,10,11,18,36].

many of these methods lack generality, requiring some degree of manual task-specific design, and often require expensive on-policy training that is unable to benefit from advances in off-policy model-free RL, which in recent years has drastically brought down sample complexity requirements [12,15,3].


Their estimator is fairly similar to ours in the identity covariances setting and gives the same error rate.

our result is more general in the following senses: 1) Our estimator and analysis do not rely on Gaussianity assumptions; 2) Our results apply beyond the setting where the label y is a linear function of x plus independent noise, and estimates the fraction of the variance that can be explained via a linear function (the "agnostic" setting); and 3) our approach extends to the unknown non-isotropic covariance setting.


We hypothesized that the human first click would be at a location of high GP variance (to reduce uncertainty about the function), while the second click would be close to the location of highest GP mean (estimated function maximum).

results showed that human 1st clicks were close to the max GP mean and not very close to the max GP std.


BP computes a MAP solution exactly after a sufficient number of iterations, if the factor graph is a tree and the MAP solution is unique.

if the graph contains loops, BP is not guaranteed to converge to a MAP solution in general.


All models described above learn state from pixels.

we also trained two baselines with privileged information: IN from State and LSTM from State models, which have the IN and LSTM dynamics predictors, but make their predictions directly from state to state.


The top-k loss [20] generalizes the maximum loss, as L max (L z (f )) = L top-1 (L z (f )), and can alleviate the sensitivity to outliers of the latter.

unlike the average loss or the maximum loss, the top-k loss in general does not lead to a convex learning objective, as it is not convex of all the individual losses L z (f ).


If the treatment T i has not been applied to unit i (also known as the out-of-sample case [30]), the potential outcome of treatment T i = 1.

if the unit i has already received a treatment T i (i.e., the within-sample case [30]), Y Ti is the factual outcome, and Y 1−Ti is the counterfactual outcome.


. . , x a Na } is a bag of points with N a individuals, and we wish to estimate the regression value η(x a i ) for each individual.

instead of the typical setup where we have a paired sample {(x , y )} of individuals and their outputs to use as a training set, we observe only aggregate outputs y a for each of the bags.


Note that while the weak version of Theorem 1 guarantees only the existence of a saddle point for (7), the strong version further guarantees that any Bayes decision rule of the maximizing distribution results in a robust Bayes decision rule.

the continuity in Bayes decision rules does not hold for the discontinuous 0-1 loss, which requires considering the weak version of Theorem 1 to address this issue.


In prior research, the sample complexity of revenue maximization has been studied primarily in the single-item or the more general single-dimensional settings [Elkind, 2007, Cole and Roughgarden, 2014, Huang et al., 2015, Medina and Mohri, 2014, Morgenstern and Roughgarden, 2015, Roughgarden and Schrijvers, 2016, Devanur et al., 2016, as well as some multi-dimensional settings which are reducible to the single-bidder setting [Morgenstern and Roughgarden, 2016].

the combinatorial settings that we study are much more complex since the revenue functions consist of multi-stage optimization procedures that cannot be reduced to a single-bidder setting.


The LGSSM provides a tractable way to structure p γ (z|a, u) into the variational approximation in (5).

even in the simple case of a ball bouncing against a wall, the dynamics on a t are not linear anymore.


In [15], the authors propose to address the problem by training multiple value functions with bootstrap subsamples.

it requires extra model parameters, causing additional computational overheads.


The two concepts are interchangeable, a contingency table corresponding to the datacube, and a marginal corresponding to its cuboids.

the datasets studied and the metrics applied are different.


Analytical results for posterior median and posterior mean estimators are nontrivial, and beyond the scope of this work.

they are likely tractable, and simulations offer interesting insight into potentially useful functional forms of an equivalent linear bias-discriminability relationship in the high-SNR limit.


A naive form of our model, for representation of sample x i ∈ D, is x i = Ψz i + i .

this is highly restrictive, as it imposes that the coefficients of the dictionary expansion must be binary.


They claim that exploiting few strong annotations substantially improves the accuracy of semantic segmentation while it reduces annotations efforts for supervision significantly.

they rely on iterative training procedures, which are often ad-hoc and heuristic and increase complexity to reproduce results in general.


This is because many participants judged V1 to be grammatical in either S1 or S2 and not both.

participants in the discriminative condition rated occurrences of V1 in S1 and S2 grammatical 100% of the time (see Figure 3a).


Comparison to [1] Our bound (2.4) improves a quadratic dependence on µ 2 to a linear dependence and replaces the dependence on the average squared smoothness EL 2 i with a linear dependence on the smoothness bound sup L. When all Lipschitz constants L i are of similar magnitude, this is a quadratic improvement in the number of required iterations.

when different components f i have widely different scaling, i.e.


In generation tasks, it can sometimes be difficult to incorporate knowledge directly in the generative process (or model architecture), i.e., defining how to generate.

it is often easier to instead specify a evaluation metric that measures the quality of a given sample in terms of the knowledge, i.e., defining what desired generation is.


In a standard setting of regression, the training input points are provided from the environment, i.e., Ü Ò ½ independently follow the distribution with density Ô Ø ´Üµ.

in some cases, the training input points can be designed by users.


For example, fusion (1) requires summing over all configurations of the parents.

for certain types of conditional probability function P(yIXI,' .. ,xJ), this exponential sum reduces to a linear-time computation.


(The example of the Necker cube also invites consideration of Markov Chain Monte Carlo sampling for exploration of multimodal posteriors even in nonsequential inference [1] -such methods are clearly complementary.)

there is very little information available about individual-level behavior to constrain the details of approximate inference.


Since it is unknown, we use its empirical distribution on unlabeled data set D u and the mutual information I pu (x), p θ (y|x) instead.

information rate alone is not enough to characterize good representation since the rate can always be reduced by throwing away many features in the probabilistic mapping.


Gaussian processes (GPs) have found many applications in machine learning and statistics ranging from supervised learning tasks to unsupervised learning and reinforcement learning.

while GP models are advertised as Bayesian models, it is rarely the case that a full Bayesian procedure is considered for training.


The cycle we will apply the red-edge rule to will be composed of e and P . It is clear we only need to compare e with the heaviest edge in P . If e is heavier, we can eliminate it by the red-edge rule.

if it is lighter, then we can eliminate the tree edge by the same rule.


Ideally, the noise-less measurements would consist of the four combinations (with signs) of the columns in the mixing matrix.

due to the noise, the measurement will be scattered around these "prototype" observations.


However, the proposed method still differs in that our attention process is designed to deal with ambiguous expressions in dialogs by dynamically analyzing the dependencies of questions at each time step.

[12] and [14] obtain the attention for a question based on its compositional semantics that is completely given at the time of the network structure prediction.


( 4), with a translation-invariance factor that decays with σ n . The dependence on a notion of depth (the number of layers n here) also appears in [17], with a factor equal to the maximal length of scattering paths, and with the same condition ∇τ ∞ ≤ 1/2.

while the norm of the scattering representation is preserved as the length of these paths goes to infinity, the norm of Φ(x) can decrease with depth due to pooling layers, though this concern may be alleviated by using an additional non-linear prediction layer, as discussed previously (see also [3]).


By using the same argument as for the linear dot-product kernel in R d (see above), the PSS kernel k σ cannot be universal with respect to the metric d k σ , which is induced by the scalar product defining k σ .

it is unclear whether k σ is universal with respect to the metric d W,q .


Therefore, λ is usually learnt from data through cross-validation or through Lepski's method [24] for which guarantees similar to the one presented in Theorem 5 can be provided.

irrespective of the data-dependent/independent choice for λ, checking for the admissibility of Spectral-KMSE (similar to the one in Theorem 1) is very difficult and we intend to consider it in future work.


We see that besides providing a continuous reward, the use of counterexamples (CE) significantly reduces the verification cost, i.e., number of Z3 queries.

the attention mechanism helps to reduce the training cost, i.e., number of parameter updates.


CTC [5] is a popular framework for end-to-end sequence learning tasks, such as speech recognition [6,8,1,2,22], scene text recognition [29,19,7], sign language recognition [4] and video segmentation [10,18].

cTC tends to output highly peaky distribution [5,22], which is a sign for model overconfidence.


The proof closely follows the argument used by Valiant and Vazirani [16] in their complexity theory work on unique satisfiability.

we give a different, non-combinatorial argument for the pairwise independence property of XORs needed in the proof, relying on linear algebra.


[10] developed a three-dimensional NBP person tracker which models the conditional distribution of each linkage's location, given its neighbor, via a Gaussian mixture estimated from training data.

we have shown that an NBP tracker may be built around the local structure of the true kinematic constraints.


Intuitively, we should be able to spend less time updating the strategy for Player 1 following these poor actions, and more time on the actions that proved worthwhile so far.

here, partial pruning will continue to update Player 1's strategy following each action in every iteration.


Thus, v is increased by each presynaptic spike, and in the absence of spikes it decays to its resting value, v 0 , with membrane time constant τ .

the effect of each spike on v is scaled by x which itself is decreased after each spike and increases between spikes back towards one with time constant τ D . Thus, the postsynaptic potential, v, behaves much like the posterior mean of the optimal estimator, µ, while the dynamics of the synaptic resource variable, x, closely resemble that of the posterior variance of the optimal estimator, σ 2 .


Similar to the optimization embedding, Stein variational gradient descent (SVGD) also exploits a nonlinear Fokker-Plank equation.

these two gradient flows follow from different PDEs and correspond to different metric spaces, thus also resulting different deterministic updates.


We then show that when the number m of hidden neurons increases, with a properly decreasing learning rate, the total number of iterations it takes to minimize the loss is roughly not changed.

the total number of iterations that we can couple the true gradient with the pseudo one increases.


(approximate) inverse reinforcement learning [11] aim at estimating a reward function for which an observed policy is (nearly) optimal.


Since h * (x 2 ) is such a function, it should therefore not be surprising that it promotes sparsity to some degree.

when selecting highly sparse subsets of features, the factorial 0 quasi-norm is often invoked as the ideal regularization term given unlimited computational resources.


If the number of don't-know predictions is required to be zero, the model reduces to the well-known mistake-bound model introduced by Littlestone [Lit88].

if no mistakes are allowed, the model reduces to KWIK framework introduced by Li et.


This means as f is allowed to deviate further from F , we must smooth over a larger radius-choose a larger σ-to guarantee the same smoothness as before.

part (2) implies that choosing a large σ increases the upper bound on the gradient and Hessian difference between fσ and F . Smoothing is a form of local averaging, so choosing a too-large radius will erase information about local geometry.


Soft attention is a natural operation which maps variable-dimensional inputs to fixed-dimensional outputs.

by doing so, it may lose information compared to its input.


9: end for 10: end for For the prediction of the label given a new feature vector, our algorithm uses a majority vote over the predictions given by all K trees.


to enable the comparison we modified the UAI instances changing any 0 probability to 0.0001 (and 1 to 0.9999).


For instance, HPN tracks do not move towards macro-goals in unrealistic straight lines, but often take a curved route, indicating that the policy balances moving towards macro-goals with short-term responses to the current state (see also Figure 6b).

the baseline model often generates more constrained behavior, such as moving in straight lines or remaining stationary for long periods of time.


It is not a shrinkage estimator [33,34] so that its mean squared error (MSE) is not necessarily smaller than that of R pu (g).

we can still characterize this reduction in MSE.


In the experiments we discuss in the following, we set the hyperparameters as u The Bayesian method calculates p(θ, Z|X, M ), which is a posterior of unknown parameters and hidden variable set Z = (Y, S) given the data and model structure, M (in our case, this indicates the number of hidden states, and correlation structure).

the calculation of the posterior involves a difficult integral.


This clearly limits its applications to large-scale problems.

vL-BFGS in Algorithm 3 only requires (2m+1) 2 memory storage and is independent on d. For the distributed approach in section 4.2, it requires at least 2m map-reduce step in a two-loop recursion.


By solving the matrix partition problem in (12) using Algorithm 1, an optimal matrix M * is returned.


The essential idea of these variants is to replace the 2 -norm A(M ) 2 with 1 -norm A(M ) 1 then a similar norm inequality can be established for all low rank matrix again.

even using these 1 -norm RIP variants, we are still unable to design an efficient alternating algorithm.


7 to contribute equally during updating.

since the dimension of the data is typically much greater than the number of classes, the dynamics of the conditional herding system will be largely driven by W. To negate this effect, we rescaled the standard deviation of the Gaussian by a factor 1/M with M the total number of elements of the parameter involved (e.g.


Its fulfillment means that our LP relaxation is tight, which is not always the case.

in many practical cases the optimal reparametrization φ corresponds to strict arc consistency of a significant portion of, but not all graph nodes.


This makes them particularly attractive for learning the directed structures among interacting entities.

if the available data is incomplete, one needs to simulate the prohibitively complex CTBN dynamics.


The usage of analytical gradients in physics simulation has been previously investigated in spring-damper systems [Hermans et al., 2014].

due to its limitations, such as instability and unrealistic contact handling, most engines used in practice do not use spring-damper models.


For other matrices such that B¨c £ B § c is a linear function of B¨c (such as the one-against-all matrix), we can prove that loss-based decoding (with L y £ ay) predicts the same class as the non-iterative estimates.

in this case, the non-iterative estimates do not necessarily predict the same class as the iterative ones.


Packing p dense lookup tables would require a dense c × p table.

if the lookup tables are sparse each row of the table could be stored in a sparse data structure.


Neurons tend to fire regularly but without conserving the exact timing of spikes in response to constant or quasi constant input current.

they fire irregularly but reliably in terms of spike timing in response to fluctuating current.


The naive way is to sum the unnormalized posterior p(n, y 1 , .

. . , y K ) over all possible values of n. n has a countably infinite support, so this is not possible.


The fully Bayesian approach to model estimation, in which posterior distributions over model parameters are estimated also provides finite sample gains over ML/MAP [14].

that method is sensitive to the choice of prior when the number of samples is less than the dimension of the space, a situation that poses no difficulty to our proposed classifier.


With the added layers for the classifier, the conjugate-exponential character of the model is retained, sustaining the ability to perform VB or MCMC inference with analytic update equations.

note that the model in (2) may be employed for unlabeled data, and the extension above may be employed for the available labeled data; consequently, all data (labeled and unlabeled) may be processed jointly to infer D. In the above discussion, we implicitly assumed all data D = {x i , y i } i=1,N are used together to infer the dictionary D. in some applications N may be large, and therefore such a "batch" approach is undesirable.


An ideal observer who knows the inertia perfectly will greatly benefit from displays with high inertia in which uncertainty will be low, and will be able to track with the same level of accuracy at greater speeds given a particular spacing.

if inertia is incorrectly assumed to be zero, high-and low-inertia iso-difficulty contours will be quite similar (Figure 3).


Other methods, such as total variation (TV) [23] and learning to diffuse [18] improve the modeling of pairwise relationships by utilizing different objectives, or incorporating more priors into diffusion partial differential equations (PDEs).

due to the lack of an effective learning strategy, it is still challenging to produce learning-based affinity for complex visual analysis problems.


Thus, a lot of burden is placed on the behavioral game-theoretic model to predict agent actions, and the accuracy of such models is still not settled [10].

it does not seem necessary that such prediction is completely accurate, but rather that the behavioral models can pull relevant information from data that would otherwise be inaccessible without game theory, thereby improving over classical methods.


Many systems-such as Factorie [14], OpenBugs [12], PGibbs [5], DimmWitted [28], and others [15,22,25]-use Gibbs sampling for inference because it is fast to run, simple to implement, and often produces high quality empirical results.

theoretical guarantees about Gibbs are lacking.


Landmark results in combinatorial optimization give polynomial-time exact algorithms for SFM.

the highdegree polynomial dependence in the running time is prohibitive for large-scale problem instances.


We consider this distribution to pass the "eye test" -one can not easily distinguish these two distributions by simply glancing at them.

as we will see, our multilinear statistic is able to correctly reject the null a large fraction of the time.


The core idea is to align distributions of points (in the feature space) belonging to same concept class across the two domains (i.e., aligning g#P s (•|y) and g#P t (•|y) where g is a measurable feature generator mapping and g#P denotes the push-forward of a distribution P ), and the prediction performance in target domain directly depends on the correctness of this alignment.

the right alignment of class conditional distributions can be challenging to achieve without access to any labels in the target domain.


For example, in the case of multivariate regression, we can use the Metropolis-Hastings sampler presented above, which lets us sample from all the weights in parallel.

we may be better off generating a Metropolis-Within-Gibbs sampler where the weights are sampled one at a time.


First is the network structure learning for estimating the dependency structure of directed graphical models [7] and probabilistic relational models [7].

these formulations are often intractable and one has to reside to heuristic solutions.


The numerical study showed that the existing method works better than the proposed method if model is correctly specified.

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


Even beyond vision, in most other domains, state-of-the-art classifiers already exist for many sub-tasks.

these carefully engineered models are often tricky to modify, or even to simply re-implement from the available descriptions.


Another closely related problem is learning to hash, which includes BoostSSC [20], Spectral Hashing [26], Restricted Boltzmann Machines [19], Semi-Supervised Hashing [24], Hashing with Graphs [14], etc.

the motivation of hashing problem is fundamentally different from that of the search problem considered in this paper.


[2016]) use "follow the perturbed leader" style algorithms, which invite a natural comparison to our setting.

the phenomenon we are exploiting is quite different.


Lastly, there are some recent works that learn hierarchical graph representations by combining GNNs with deterministic graph clustering algorithms [8,35,13], following a two-stage approach.

unlike these previous approaches, we seek to learn the hierarchical structure in an end-to-end fashion, rather than relying on a deterministic graph clustering subroutine.


Both SVM and RMM have similar asymptotic behavior.

in many cases, warm starting RMM with previous solution significantly helped in reducing the run times.


We refer to the whole model as NYU-Feedback.

dISCO Nets uses a single network whose architecture is similar to NYU-Prior (without constraining on a pose prior).


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

their κ defined as lim ε→0 max(κ 1 , κ 2 ) (in their Theorem 2) is somehow difficult to interpret as a measure of the quantity of near-optimal nodes.


In principle, this amounts to replacing the single observed matching τ ji by an appropriate distribution t ji (τ ) over possible matchings, and concomitantly replacing each σ i with a distribution p i (σ).


Note that this process automatically selects the neighborhood size k to apply for the novel input.

existing local learning approaches typically manually define this parameter and fix it for all test examples [5,8,13,15,29].


The views are similar to criteria in our problem setting.

in our setting, different criteria may be orthogonal and could even give contradictory information; hence there may be severe view disagreement.


For example, the sample complexity required by [7] and [24] is O(d 6 ) and O(d 3 ) respectively.

the computational burden mainly comes from the operation on tensor, which costs at least O(d 3 ) for a very simple tensor evaluation.


The decision to split on the activation of the ReLU non-linearities made by Planet and Reluplex is intuitive as it provides a clear set of decision variables to fix.

it ignores another natural branching strategy, namely, splitting the input domain.


Rather than making updates on each step to improve the estimate, these methods maintain compact summaries of all observed state transitions and rewards and solve for the value function which has zero expected TD error over the observed data.

although LSTD and LSTD(λ) make more efficient use of the data, they require O(n 2 ) computation per time step, which is often impractical for the large feature sets needed in many applications.


The validation error drops as α and β are increased.

for p = 2 61 − 1, the largest value allowed is 1.35 × 10 18 ; this rules out α and β greater than 64, as shown in the table.


We propose to extend classification images to estimate biases from the human visual system.


• We propose a novel trace norm regularizer for low-rank tensor completion problem, which learns a tensor as a non-sparse combination of tensors.

the more popular latent trace norm regularizer [41,42,45] learns a highly sparse combination of tensors.


Many other local search heuristics based on maximum parsimony and maximum likelihood methods can also be found from the phylogenetic community [21].

none of these methods extend easily to the nonparametric case since they require the data to be discrete or to have a parametric form such that statistical tests or likelihoods/EM can be easily computed.


Many machine learning problems have been shown to benefit from the negative dependence properties of Strongly Rayleigh measures: measures based on elementary symmetric polynomials -including (dual) volume sampling -have been applied to experimental design; DPPs have been applied successfully to fields ranging from automatic summarization to minibatch selection and neural network pruning.

tuning the strength of the quality/diversity tradeoff of SR measures requires significant effort.


Convergence rates of the resulting PDEs are not explored in this paper.

in [37], we rigorously analyze stability conditions and time step restrictions for discretizations of accelerated PDEs and show that they are significantly more generous compared to gradient descent.


Most works attempt to process the code directly or use a syntactic tree representation, treating it like sentences written in a natural language.

none of the existing methods are sufficient to comprehend program semantics robustly, due to structural features such as function calls, branching, and interchangeable order of statements.


In particular, the non-zero elements of the optimal sparse factor x are exactly equal to the elements of u * k , the principal eigenvector of A * k . This underscores the inherent combinatorial nature of sparse PCA and the equivalent class of cardinality-constrained optimization problems.

despite providing an exact formulation and revealing necessary conditions for optimality (and in such simple matrix terms), this proposition does not suggest an efficient method for actually finding the principal submatrix A * k -short of an enumerative exhaustive search, which is impractical for n > 30 due to the exponential growth of possible submatrices.


The main challenge in using the curriculum learning strategy is that it requires the identification of easy and hard samples in a given training dataset.

in many real-world applications, such a ranking of training samples may be onerous or conceptually difficult for a human to provide -even if this additional human supervision can be provided, what is intuitively "easy" for a human may not match what is easy for the algorithm in the feature and hypothesis space employed for the given application.


These two quantities are independent for a centered multivariate normal, and therefore if P L µ = 0 then P L Y 2 follows a χ k distribution even if we have conditioned on dir L (Y ).

in the general case where P L µ = 0, we do not have independence between the length and the direction of P L Y , and so while P L Y 2 is marginally distributed as a noncentral χ k , this is no longer true after conditioning on dir L (Y ).


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

in addition to compression it is beneficial to obtain acceleration.


This approach was referred to as transitive assignment kernel in [18] and employed for graph classification.

this does not only lead to non-optimal assignments between individual pairs of graphs, but also suffers from high computational costs.


Attention networks in multimodal learning provide an efficient way to utilize given visual information selectively.

the computational cost to learn attention distributions for every pair of multimodal input channels is prohibitively expensive.


We plot the empirical success probability as a function of k/ √ n for several values of p, with p = n. The empirical success probability was computed by using 100 independent instances of the problem.

a few observations are of interest: (i) Covariance Thresholding appears to have a significantly larger success probability in the 'difficult' regime where Diagonal Thresholding starts to fail; (ii) The curves for Diagonal Thresholding appear to decrease monotonically with p indicating that k proportional to √ n is not the right scaling for this algorithm (as is known from theory); (iii) the curves for Covariance Thresholding become steeper for larger p, and, in particular, the success probability increases with p for k ≤ 1.1 √ n. This indicates a sharp threshold for k = const • √ n, as suggested by our theory.


(2016) later improved this model by simplifying the binarization by simply taking T B = sign(T ) and adding a gradient for this operation, namely the straight-through estimator: The authors showed that the straight-through estimator allowed the binarization of activations as well as weights without collapse of model performance.

they did not attempt to train a model on ImageNet in this work.


DNNs have become ubiquitous in datacenter settings, forcing operators to adopt specialized hardware to execute and train them.

dNN training still depends on floating-point representations for convergence, severely limiting the efficiency of accelerators.


The obtained optimal representation is a noisy linear projection to eigenvectors of the normalized correlation matrix Σ x|y Σ −1 x , which is also the basis obtained in Canonical Correlation Analysis.

in Gaussian IB, the compression tradeoff parameter uniquely determines the dimension, as well as the scale of each eigenvector.


in machine learning, most of the traditional methods are not able to exploit similarities between different learning tasks.


Accordingly, we assume that E F [p j ] > 1/2 and the true labels are defined as Otherwise, we do not impose any condition on the distribution of p j 's.

we assume q i 's are discrete random variables with support at K points.


This method can be applied to most general network architectures.

it requires additional processes after or during training, and therefore, it may further increase the overall amount of time required for preparing the final networks.


Obviously, IWS-LS is impractical in the scenarios we consider since it requires the OLS residuals and full leverage scores.

we use this as a baseline and to simplify the analysis.


Reinforcement learning models have long promised to unify computational, psychological and neural accounts of appetitively conditioned behavior.

the bulk of data on animal conditioning comes from free-operant experiments measuring how fast animals will work for reinforcement.


It has a free parameter σ, the scale of the initial proposal distribution.

careful tuning of this parameter is not required.


Thus one might expect the spectral method to produce cuts with fairly good balance, and this is what does happen for the class of spacelike graphs that inform much of our intuition.

there are now many economically important "power law" [5] graphs whose best quotient cuts have extremely bad balance.


With this setting of RMSPROP and batch size of 320, we obtained a top-1 and top-5 error of 21.63% and 5.79% respectively, under single crop evaluation on the Imagenet validation set comprising of 50K images (slightly lower than the published results).

using YOGI with essentially the default parameters (i.e.


We encode the manifold smoothness into the empirical data distribution used in boosting algorithms for semi-supervised learning, while their implementation adaptively adjusts the edge offset in the marginal Adaboost algorithm for a weight decay used in the linear combination of based learners [19].

our implementation is simpler yet applicable to any boosting algorithms for semi-supervised learning, while theirs needs to be fulfilled via the marginal Adaboost algorithm even though their regularized marginal Adaboost is applicable to both supervised and semi-supervised learning indeed.


More recentely, frameworks such as conditional Generative Adversarial Networks (cGAN) [12], Style and Structure Generative Adversarial Network (S 2 -GAN) [30], and VAE-GAN [17] are proposed to address the problem of supervised imageto-image translation.

in many real-world applications, collecting paired training data is laborious and expensive [37].


[23] concatenate a deep deconvolution CNN and a denoising CNN to perform deblurring and artifact removal.

[23] requires a separate network to be trained for each blur kernel family and kernel parameter.


Benchmark for video tasks There exist benchmarks for several video tasks like online object tracking [29] and video object segmentation [21].

there is no benchmark for the precipitation nowcasting problem, which is also a video task but has its unique properties since radar echo map is a completely different type of data and the data is highly imbalanced (as mentioned in Section 1).


The integral in ( 12) is of the form ( 8), but is intractable since solving it corresponds to a GP prediction at uncertain inputs [14], resulting in non-Gaussian predictive distributions.

the mean and covariance of a Gaussian approximation Z to Z can be computed analytically: either using exact moment matching [14,3], or approximately by expected linearization of the posterior GP [8]; details are given in [4].


While these results are not directly comparable, we have also first results where we ran the original implementation with value iteration and our implementation with Minimax LPA* on a very similar environment and the original implementation expanded one to two orders of magnitude more states than ours even though its number of searches and its final number of states was smaller.

these results are very preliminary since the time per state expansion is different for the different implementations and it is future work to compare the various implementations of the parti-game algorithm in a common testbed.


[7] present a compelling argument that the fly brain is an actor-critic by finding the neurons making up the critic and then artificially activating them to train the actor portions of the brain.

current actorcritic methods in the artificial intelligence community remain biologically implausible because each component of the actor can only be updated with detailed knowledge of the entire actor.


If we use sigmoid as g(z), the new sigmoid-based function satisfies the above properties.

the output of sigmoid is bounded above as [g(z)] i ≤ 1, and this restriction might limit the representational power.


Hence, the scalar product p (γ(t)), γ (t) coincides with the directional derivative of p in direction T , so the right hand side of Equation ( 1) coincides with the left hand side of the equation in the proposition.

it is well known that the line integral over a gradient field only depends on the starting and end point of γ and is given by This coincides with the right hand side of the equation in the proposition.


1(d), we can see that our GenDeR is as good as 'PageRank' in terms of capturing the relevance of the entire top-k ranking list (notice that the two curves almost overlap with each other).

genDeR outperforms 'PageRank' in terms of the diversity by all the three measures (Fig.


A natural consideration for the tree construction is that the tree must be balanced.

we do not need to explicitly enforce this constraint: the balanceness is automatically favored by the term C in (4) as balanced trees give the minimum computational cost.


This penalty function does not appear to be convex in X.

the proposition below (proved in the Supplementary Materials) shows that we can use a (convex) local max norm penalty to compute a solution to any objective function with a penalty function of the form (4): Proposition 1.


This is not the direction pursued here, because the image sequence considered does not have a tensorial structure.

there is a relation to (hierarchical) topic models (e.g.


For convex problems, an alternative to proximal splitting is the subgradient method; similarly, for nonconvex problems one may use a generalized subgradient method [7,12].

as in the convex case, the use of subgradients has drawbacks: it fails to exploit the composite structure, and even when using sparsity promoting regularizers it does not generate intermediate sparse iterates [11].


If the datasets are collected in a clinical setting, they may be subject to many additional constraints.

it may be the case that derivative 32nd Conference on Neural Information Processing Systems (NeurIPS 2018), Montréal, Canada.


All strict local minima are global minima in the sense of points.

x = [a, b] with a ≈ −2.6 and b = −1 is a strict local minimum that is not a global minimum.


Thus, one has to resort to "nonparametric" methods and search for good estimators in a suitably defined class whose complexity grows with n. Some nonparametric methods proposed in the literature, such as kernels [4] and orthogonal expansions [5,6], either have very slow rates of MSE convergence or are computationally prohibitive for large d. For example, the kernel method [4] requires O(n 2 d) operations to compute the estimate at any x ∈ B d , yet its MSE decays as O(n −4/(4+d) ) [7], which is extremely slow when d is large.

orthogonal function methods generally have much better MSE decay rates, but rely on estimating 2 d coefficients in a fixed basis, which requires enormous computational resources for large d. For instance, using the Fast Hadamard Transform to estimate the coefficients in the so-called Walsh basis using n samples requires O(nd2 d ) operations [5].


Mapping the inputs to a high-dimensional feature space, kernel methods compute their inner products without recourse to the explicit form of the feature map (kernel trick).

unfortunately, calculating the kernel matrix for the training stage requires a prohibitive computational cost scaling quadratically with data.


It is obvious that Zinkevich's OGD in (1) requires the full knowledge of set X and low complexity of the projection P X [•].

in practice, the constraint set X , which is often described by many functional inequality constraints, can be time varying and may not be fully disclosed to the decision maker.


assumption, which means that the instances are assumed to be independent and identically distributed (i.i.d.).

the data in many real-world applications, such as web pages and research papers, contain relations or links between (some) instances in the data in addition to the textual content information which is represented in the form of feature vectors.


Corollary 1, which implies the dependency of the threshold for α on L and M , might support this conjecture.

the same applies to the matrix factorization, where VB was shown to give a sparser solution than MAP [17].


In MRMA, the set of ranks decide the performance of the final model.

it is neither efficient nor necessary to choose all the ranks in [1, 2, ..., K].


Like the K-means algorithm, DP-Means alternates between updating the cluster assignment z i for each point x i and recomputing the centroids C = {µ k } K k=1 associated with each clusters.

dP-Means differs in that the number of clusters is not fixed a priori.


Therefore, not all the pursuit methods, such as basis pursuit and LARS/Homotopy methods, that are applicable to the standard sparse representation method can be directly applied to optimize J 2 (X, λ) and J 3 (X, λ 1 , λ 2 ).

the iterative optimization methods employed in the matching pursuit and the orthogonal matching pursuit provide a direct reference to the optimization of J 2 (X, λ) and J 3 (X, λ 1 , λ 2 ).


Some works built classifiers comprised of multi-value rules [1,2,20].

they still rely on greedy methods such as greedy induction to build a model, and they do not consider model complexity or restrict the number of features.


These methods embed the standard RL objective, formulated in terms of rewards, into the framework of probabilistic inference.

we aim specifically to reformulate RL in a way that does not require specifying arbitrary scalar-valued reward functions.


On both the CIFAR datasets, these two mechanisms achieve nearly identical results.

on ImageNet, the simpler SR mechanism is significantly superior.


As before, prior to the change, there is a single bump of activity whose position approximates that of a Kalman filter.

after the changepoint, the network maintains two bumps of activity for several time steps.


Of these, only the LLW method is Fisher consistent and universally consistent [12][13][14].


In particular, the GMM with adjacent breaking and top-k breaking for constant k's are the fastest.

we recall that the GMM with adjacent breaking is not consistent, while the other algorithms are consistent.


For most other layers in the network, DTP [21] computes targets as The second term is the error in the reconstruction, which provides a stabilizing linear correction for imprecise inverse functions.


Since RAI is proved to learn the true underlying graph in the large sample limit (Yehezkel & Lerner, 2009), this single CPDAG will also be the true underlying graph.

we expect that for very small sample sizes, each path in T will be unique.


In fact, one can assume a generalized noise model X T j1 X i1 with probability p P ij with probability 1 − p where X i1 , 1 ≤ i ≤ n are pre-defined underlying permutations from object S i to the first object S 1 .


REINFORCE allows the former to achieve better performances.

even with a large number of trajectories, the approximated errors are still quite large preventing to reach very high performance.


Equivalent budget N = 2 16 GPs (known prior) GPs (known prior) In additional experiments, we observed that optimization of PI and SR behaved like that of EI and UCB, respectively.

overall performance using these acquisition functions was slightly worse, so further results are not reported here.


Thus, given enough training examples, the best performing classification algorithms have typically employed purely discriminative methods.

due to the curse of dimensionality when D is large, the number of data examples may not be sufficient for discriminative methods to approach their asymptotic performance limits.


Since this new stage includes the last stage of the previous cascade, the process mimics the design of an embedded cascade.

there are no restrictions that a new stage should be added at each boosting iteration, or consist of a single weak learner.


In order to compute an (1 + ε) approximation to the k-segment mean of the original signal P , it suffices to compute a (1 + ε) approximation to the k-segment mean of the coreset, where cost is replaced by cost .

since D is not a simple signal, but a more involved data structure, it is not clear how to run existing algorithms on D. In the supplementary material we show how to apply such algorithms on our coresets.


In this context, VNMT and GNMT perform similarly in terms of BLEU scores.

both models are consistently outperformed by GNMT-MULTI (albeit only by a small amount).


For example, in [2], the Laplacian kernel k(x, y) = exp(−γ∥x − y∥ 1 ) can be decomposed through both the Fourier basis and the Random Binning basis, while in [7], the Laplacian kernel can be obtained from the integrating of an infinite number of decision trees.

multiple kernels can be derived from the same set of basis functions via different distribution p(h).


Due to this deterministic dependence between y and h, we can define the classification loss incured by a voting classifier when using the set h as One might want to learn W to minimize training loss i ∆ (y i , h W (x i )).

this fails due to the intractable nature of classification loss ∆.


We prove that there is theoretical identifiability of the rank and the parameters of an FST distribution, using a rank minimization formulation.

this problem is NP-hard, and it remains open whether there exists a polynomial method with identifiability results.


This can be visualized by noting that the label image deforms in the same way as the input image, as show for example in figure 3.

for learning, constraint (1) can be incorporated in a loss function as follows: minimizing this loss has the significant drawback that a global optimum is obtained by simply setting Φ(x, u) = const.


One might be tempted to conclude that the causal relation is non-recoverable because P (w, z, y) is non-recoverable (by theorem 2) and P (y|z, w) is not recoverable (by corollary 2).

p (y|do(z)) is recoverable as demonstrated below: P (y|do(z), w, R ′ y ) = P (y|z, w, R ′ y ) (by Rule-2 of do-calculus (Pearl [2009])) (3) Substituting ( 3) and ( 4) in (2) we get: The recoverability of P (y|do(z)) in the previous example follows from the notion of d*separability and dormant independence [Shpitser and Pearl, 2008].


Third, inference in large label spaces is sometimes possible via exact algorithms or empirically accurate approximations.

with the advent of deep scoring functions s(x, y; w), learning is no longer convex.


In short, these kinds of distributed representations avoid the binding problem in the first place by ensuring that relevant conjunctions are encoded, instead of representing different features using entirely separate, localist units (which is what gives rise to binding problems in the first place).

this form of binding cannot rapidly encode novel bindings required for specific tasksthe phonological loop mechanism can thus complement the basic cortical mechanism by providing flexible, transient bindings on an ad-hoc basis.


by using LfD to find initial policy parameters.

aPID leverages the expert data to shape the policy throughout the planning.


When the model used for learning is correctly specified, the covariate shift does not matter.

for misspecified models, we have to explicitly cope with the covariate shift.


This is a method-of-moments-based estimation process, which, like other spectral methods, provides estimators that are non-iterative, consistent and do not suffer from the problems of multiple optima that dog maximum-likelihood (ML) learning in practice.

they are not as statistically efficient as the true (global) ML estimator.


It is useful to rewrite the matching probabilities as: Adding E(π 1:t−1 , θ) to each item's energy does not change the probabilities because this term cancels out during normalization (but it does change the partition function, denoted by Z * t here).

in this form we see that p(v j |u σ(t) , π 1:t−1 ) is directly related to the change in the partial energy from π 1:t−1 to H(v j , u σ(t) , π 1:t−1 ) -the larger the change the bigger the resulting probability will be.


It would seem that an absolutely integrable kernel would be easier to define and parameterise than a positive definite function.

we require a closed form of C Y ij (d) and this may not be attainable for some non-Gaussian kernels.


In Section 3, we show that two outliers in a dataset are enough to breakdown some centers.

if we restrict our focus on some "well structured" datasets, then (RKM) has some remarkable robustness properties even if there is a considerable amount of contamination.


In fact Kalai and Vempala [2003], address the computational difficulty of handling a large number of experts under certain linear assumptions on the reward functions.

their algorithm is not directly applicable to our setting, due to the fact that in our setting, decisions must be made with respect to the current state of the agent (and the reward could be changing frequently), while in their setting the decisions are only made with respect to a single state.


Estimation of sparse inverse covariance matrices is widely used to identify undirected network structures from observational data.

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


Two common strategies for pooling are max and mean pooling.

when answering a specifical question, it is often the case the correct answer is only related to particular image regions.


However, optimizing these weights freely is not permissible, since this procedure allows us to choose d i = d j even if s (i) = s (j) , which violates the weights in the original LMI.

if we additionally require that s (i) = s (j) ⇒ d i = d j (or more appropriately for continuous features and states, for example that d i − d j → 0 as φ(s (i) ) − φ(s (j) ) → 0 according to some norm) then we are free to optimize over these empirical distribution weights.


Hence, we can employ the available latent tree methods to learn "local" subgraphs consistently, as long as they do not contain any cycles.

merging these estimated local subgraphs (i.e., latent trees) remains a non-trivial challenge.


Many alternative methods (e.g., Topographic ICA) would require some form of distributed optimization algorithm to achieve a similar result, which requires many feed-forward and feed-back passes over the dataset.

the above method is typically less expensive than a single feed-forward pass (to compute the feature values x (i) ) and is thus very fast compared to other conceivable solutions.


However, the success of domain adaptation techniques is often caused by asymmetry between the source and the targetsuch algorithms usually rely on availability of extensive amounts of data from the source and only limited amounts from the target.

in lifelong learning setting all the tasks are assumed to be equipped with limited training data.


One possible approach is to follow a similar approach to that taken in (Rasmussen, 2013); derive a Gibbs sampler using a data augmentation scheme which associates a latent variable to each interaction.

such an algorithm is unlikely to scale well with the number of interactions.


In combination with the waveform input, the inverse effect was observed.

as it was generally harder to find good solutions in this setting, it could be that testing more configurations eventually would lead to the same result as for the spectrum.


Segmenting a sample trajectory should be performed using a lower-order function approximator than that used for policy learning, since we see merely a single trajectory sample rather than a dense sample over the state space.

merging should be performed using the same function approximator used for learning.


Current likelihood-free methods in population genetics leverage scientific simulators to perform inference, handling the exchangeable-structured data by reducing it to a suite of low-dimensional, permutation-invariant summary statistics [2,3].

these hand-engineered statistics typically are not statistically sufficient for the parameter of interest.


Thus one of the principal advantages of using the weakly-informative informative prior, obtained as a limit of Gaussians, considered in this paper is that the worst-case error can be reinterpreted as a posterior standard deviation.

to ensure this variance provides meaningful quantification of uncertainty can be challenging.


They derive several primal and dual reformulations for the problem, and propose corresponding first-order methods such as ADMM, proximal-point, and accelerated projected gradient.

each iteration of these algorithms involves a full SVD of complexity O(min(M 2 N, N 2 M )), making it hard to scale them to large problems.


This means that the state vector h t can be reset to 0 after a sufficient time in the absence of an input; i.e., the GRU can forget the past information entirely.

when |λ 1 (J )| becomes greater than one, the fixed point at 0 becomes unstable.


3.9, through P (y|W ij,l ) = P (v L = y|W ij,l ).

this computation is still generally intractable, since all of the above summations (Eqs.


Common to most approaches is that they deal with the insufficient state information by maintaining a model of the traffic situation, derived from available sensor counts.

imperfections in the model is a further source of errors and performance may consequently suffer.


Considering d as the target dimension and d i × d i as the convolutional filter size of the i-th layer, the weight matrix would be inaccurately reshaped in the case of A more reasonable approach would be to resize the DCT coefficient matrices of convolutional filters in the frequency domain, because high-frequency coefficients are generally small and discarding them only has a small impact on the result (d i > d).

the introduced zeros will be immediately compressed by CSR since we do not need to encode or store them (d i < d).


The results in this study are in line with such notions: a dynamic and bi-directional network can refine its representations across time, leading to convergent representations to support object recognition.

pCN is not contradictory to existing feedforward models, because the PCN block itself is integrated with a Inception-type CNN module.


Both types of interference degrade the harmonic structure in the log power spectra and extracted partials.

nonnegative deconvolution is still able to recover the pitch of the original speaker, as well as the pitch of the second speaker.


4 This theorem, which can be viewed as the tail bound version of the expected bound in [11], implies that the risk of the average hypothesis is close to 3 $ ¡ 8£ for "most" samples 3 .

note that it is unlikely that ¤ 3 fe F6 P @Q gi 6 $ ¡ 8£ concentrates around T vV h e ¡ ¤£ , at least without taking strong assumptions on the underlying on-line algorithm.


Although gradient descent (GD) almost always escapes saddle points asymptotically , this paper shows that even with fairly natural random initialization schemes and non-pathological functions, GD can be significantly slowed down by saddle points, taking exponential time to escape.

gradient descent with perturbations [Ge et al., 2015 is not slowed down by saddle points-it can find an approximate local minimizer in polynomial time.


The results in this section were based on middle layer neurons in the GoogLeNet CNN predicting middle layer neurons in the ResNet CNN.

it is possible that CNN neurons in other layers may be better predictors than those in a middle layer.


It can be observed that majority of the unknown samples D a , from the Devanagari dataset, fall within the region of the background class.

there are still many samples from D a overlapping the samples from D c , mostly at the origin where low probabilities are to be expected.


The multi-view fisher discriminant analysis (FDA) [13] provides a supervised approach to finding such a projected subspace.

this deterministic approach cannot provide viewlevel predictions, such as image annotation; and it would also need a density estimator in order to apply the information criterion [9] to detect view disagreement.


The most natural metric for evaluating disaggregation performance is the disaggregation error in (4).

average disaggregation error is not a particularly intuitive metric, and so we also evaluate a total-week accuracy of the prediction system, defined formally as  Despite the complex definition, this quantity simply captures the average amount of energy predicted correctly over the week (i.e., the overlap between the true and predicted energy pie charts).


To be specific, we would like to minimize under some state distribution d(s).

this method makes no distinction between "good" and "bad" actions.


In the fog, the agent can then do no better than to estimate the average number of steps from a foggy state until the next hill top.

the true value, shown in red, can be achieved exactly with natural value estimates.


The authors use 60-frame as the network input and demonstrate its advantage over 16-frame.

it is still an ad hoc manner and difficult to favor all the action classes.


Apprenticeship learning is based on the insight that often it is easier for an "expert" to demonstrate the desired behavior than it is to specify a reward function that induces this behavior.

when attempting to apply apprenticeship learning to large domains, several challenges arise.


Most of the successes of RL have been in single agent domains, where modelling or predicting the behaviour of other actors in the environment is largely unnecessary.

there are a number of important applications that involve interaction between multiple agents, where emergent behavior and complexity arise from agents co-evolving together.


Although they have experimented on applying their model on image collections with mixed sport categories, their method seems to work better with single sport category training.

the input to our learning problem is a set of images from several sport categories, together with their associated textual annotations.


It is known that a good binary CPE model can be used to obtain a good binary classification model (by thresholding at 0.5), and also to obtain a good bipartite ranking model (by using the CPE model directly as a ranking model); it is also known that a binary classification model does not necessarily yield a CPE model.

not much is known about other directions.


Indeed, for a stable FBM environment (α = 1), G t = 1 a+b+t , which is clearly not constant.

fitting EXP's parameters freely still performs close to DBM (Fig.


In particular, even though the optimization problem has an exponentially large number of constraints (one constraint per policy), the optimum can be found efficiently (i.e., in polynomial time) using, for example, the ellipsoid method, since we can efficiently identify a constraint that is violated.

5 in practice we found the following constraint generation method more efficient:  1.


Principally, we have been assuming that each individual signatory of the petition exposes her petition copy independently with probability δ.

the assumption of independence of nodes' exposure events -while useful as an analytical abstraction -appears to be too simple to capture all the properties we see in the exposure events for the real data.


(7) is reduced to If φ is a quadratic function, the constrained problem (10) requires the projection onto the constraint set X .

in some cases, by choosing a proper Bregman divergence, (10) can be solved efficiently or has a closed-form solution.


Part of the problem is that the local SIFT features are relatively low-dimensional (128D), and might not be powerful enough to capture anything of higher complexity.

switching to a more descriptive feature (e.g.


Our analysis for k-AS is inspired by [8,10,11] (in particular the median elimination technique in [8]).

the details are very different and more involved than the previous ones (the application of median elimination of [8] was in a much simpler context where the analysis was considerably easier).


It consists of building a strong classifier as a linear combination of weaklearners, by adding them one after another in a greedy manner.

while textbook AdaBoost repeatedly selects each of them using all the training examples and all the features for a predetermined number of rounds, one is not obligated to do so and can instead choose only to look at a subset of examples and features.


For categories with small ground sets (safety, furniture, carseats), there is no advantage of using the higher-order attractive potentials but the repulsive higher-order potentials improve performance significantly.

in combination with repulsive potentials the attractive potentials enable the model to improve performance over models with only repulsive higher-order potentials.


In CartPole, it is not immediately clear that Φ guess is better than Φ net , since both should be very close to V * .

φ net is both a biased estimate of V * and noisy (due the inexactness of gradient descent), whereas the simple expert Φ guess is highly related to the goal (keeping the pole centered).


3D-PIM incorporates a simulator with the aid of a 3DMM to obtain prior information to accelerate the training process and reduce the amount of required training data.

we do not employ 3DMM to present shape or texture information.


We note that the orthogonality is critical to their argument.

the observation operator, in our case, turns out to be non-orthogonal, which becomes a major challenge in our proof.


natural images in the case of the retina, therefore this type of stimulus should be relatively quickly cancelled out.

non-natural stimuli, like white noise patterns, will be less well captured by interneuron receptive fields and their activation will occur after a longer Accordingly, it will take longer to cancel out nonnatural stimuli, leading to longer principal neuron transients.


In many real-world applications, collection of labeled data is both time-consuming and expensive.

a large amount of unlabeled data are often readily available.


Their techniques obtained similar speed-ups as ours over Viterbi inference.

their algorithms do not provide extensions to inference in trees, a margin-violation oracle, and approximate inference using a duality gap.


One widely adopted method is multitask Gaussian process (MTGP) [4], which assumes a Gaussian process prior over latent functions to directly induce correlations between tasks.

for a cokriging task with M variables of P locations for T time stamps, the time complexity of MTGP is O(M 3 P 3 T ) [4].


Compared to GD, NGD exemplifies faster convergence, especially in the neighborhood of stationary points [25].

nGD has been less popular due to its requirement of accessing the full gradient and its norm at each update.


It received the outputs of the cells in the first and second subsets during the second stage of training, and received the outputs of all complex cells during the third stage.

the training period of the non-developmental system, or model ND, was not divided into separate stages; its neural network received the outputs of all complex cells throughout the entire training period.


Thus, minimizing A B 2 minimizes the strength of the strongest linear trend of A not captured by B.

measuring the difference using an entry-wise norm, e.g., the Frobenius norm, can be completely uninformative.


For instance, the shape of the action potential is intimately related to the dynamics of sodium and potassium channels in the Hodgkin-Huxley model.

the space of possible features is immense, and given the highly non-linear nature of many of the neural models in question, it can sometimes be of interest to simply perform statistical inference without having to hand-design features.


Traditional code optimisation strategies used in compilers are based on applying pre-specified set of transformations that make the code faster to execute without changing its semantics.

our work involves adapting programs to make them more efficient while considering correctness only on a target input distribution.


Except in some special cases [12], it is not known whether any of the approaches used within the Learning community lead to optimality in either of the above senses of the word.

it is known that under certain regularity conditions, Bayesian estimators lead to either minimax or admissible estimators, and thus to well-defined optimality in the classical (frequentist) sense.


Both algorithms are much more efficient than Laplacian Eigenmaps.

lMDS permits an accuracy/speed trade-off that makes it preferable.


[22] and Bach and Jordan [3] in their approaches to construct a low-rank kernel matrix.

these approaches are not selecting features from a set of ridge functions, but find a subspace of a preselected kernel feature space with a good set of hypothesis.


Most hierarchical classification learning algorithms treat the taxonomy as an indisputable definitive model of the world, never questioning its accuracy.

most taxonomies are authored by human editors and subjective matters of style and taste play a major role in their design.


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

the noise N a and bias B a are difficult to estimate when X is high-dimensional or continuous.


Their model outperformed classical RL methods in simple games, such as tic-tac-toe and rock-paper-scissors.

aQM applied opponent modeling to a cooperative multi-agent setting.


On the one hand, a small value of L led to over-generalization, because of insufficient uniformity of ECs associated with short SPs (not enough context sensitivity).

using large values of L in conjunction with the ADIOS1 statistical learning algorithm did not lead to the emergence of well-supported SPs.


To this end, various classes of models such as decision lists [11], decision sets [9], prototype (case) based models [1], and generalized additive models [13] were proposed.

none of these approaches can be readily applied to determine error properties of decision makers.


This has the potential to automate a range of applications, such as autonomous vehicles and interactive conversational agents.

current model-free reinforcement learning algorithms are quite data-expensive to train, which often limits their application to simulated domains [Mnih et al., 2015, with a few exceptions [Kober andPeters, 2009, Levine et al., 2016].


This model is related to latent-variable GP models (GP-LVM) [21], in that we infer the latent {w i } that reside within a GP kernel.

here {w i } are also factor scores in a factor model, and the GP is used within the context of a Bayesian SVM classifier; neither of latter two have been considered previously.


[11] used a similar set up on Atari games.

their results showed that the performance of the learned neural network fell well short of the MCTS expert, even with a large dataset of 800,000 MCTS moves.


(2015) develops a primal-dual gradient method solving (1-2), which achieves a convergence time of O(1/" 1+⌫ 1+3⌫ ), where ⌫ is the modulus of Hölder continuity on the gradient of the dual function of the formulation (1-2).

2 the work Yu and Neely (2018) shows that when the dual function has Lipschitz continuous gradient and satisfies a locally quadratic property (i.e.


We see that on average for "ON" genes, the attention profiles near the TSS region are well defined for H prom , H enhc , and H struct .

the weights are low and close to uniform for H reprA and H reprB .


Ongoing research efforts seek to further increase that performance density by replacing floating-point with fixedpoint arithmetic.

a significant roadblock for these attempts has been fixed point's narrow dynamic range, which is insufficient for DNN training convergence.


For small p, collecting additional data is more valuable than decontaminating the existing data, but once we have roughly p = 4 samples, the benefit of decontamination is comparable to the benefit obtained from collecting an additional round of ratings.

the cost of collecting additional ratings can be quite high if you consider large data sets, e.g., music and movies.


Some recent approaches give strong performance guarantees by training the policy iteratively.

it is important to note that these guarantees depend on how well the policy we found can imitate the oracle on the training data.


The result of Lemma 2 is for Gaussian random matrices.

it would be possible to extend this result using non-asymptotic bounds for the extreme singular values of more general random matrices [19].


This introduces K new free variational parameters, which is similar to a refinement step in chunky EM.

chunky EM refines the same data block across all components, which is not the case in CS-EM.


So in the computation of nearest neighbor distances, each of the p 1 dimensions of {x 1i } receive the same weight, as shown in (1).

inspired by the recently proposed ideas in metric learning [22], we use a more general distance metric by applying a linear transformation T 1 of size p 1 × p 1 in the space, and then perform MCU using the transformed points, T 1 x i .


In such large datasets, it is difficult to predict convergence times; after 28 hours, it seems as though no algorithms have converged.

the Sub-Clusters method seems to be approaching a solution, whereas FSD has yet to prune topics and DA has yet to to achieve a good cross-validation score.


[23] utilized a dropout technique to reduce overfitting by dropping out some neuron activations from the previous layer, which can be seen as an ensemble of networks sharing the same weights.

the dropout process is random regardless the discriminative power of individual neurons.


As before, we will use the EM-algorithm to maximize the model evidence p(Y) with respect to the parameters Λ, W, σ.

we additionally impose that each column Λ i of Λ shall be sparse, thereby ensuring that the diversity of parameter dependencies of the latent variables z i = φ z φ,i is reduced.


Even our approach requires a similar optimization process.

unlike [19], we perform meta-learning only on the task network.


These algorithms can be called global learning algorithms as the whole training dataset is used for training.

in local learning algorithms [1], for a given test data point, a model is built only with its neighboring training data, and then the label of the given test point is predicted by this locally learned model.


Application of viscous flow to dendrites has been discussed in [10].

it is hard to see how dendrites could be conduits to viscous fluid if their ends are sealed.


The DDP value function V d t inherits this variability.

it also displays a significant optimistic bias.


In a traditional convolutional layer, the learned filters stay fixed after training.

we introduce a new framework, the Dynamic Filter Network, where filters are generated dynamically conditioned on an input.


The drop in TD NSS scores likely reflects the players' shift of attention away from the usual relevant locations (horizon line, focus of expansion) and toward other regions relevant to the crash-recovery task.

the lack of change in BU NSS scores indicates that the locations attended during crash recovery where neither more nor less salient than locations attended in general; together, these results suggest that during crash recovery players' attention is more strongly driven by some influence that is not captured well by either of the current BU and TD models.


Consequently, their functional properties and connectivity can be inferred from data [11][12][13][14][15][16][17][18].

the idea is not to simply build a more powerful statistical model, but to develop a model that can help us learn something about the underlying structure of networks deep in the brain.


The Poisson MRF is developed by assuming that every conditional distribution is 1D Poisson.

the original formulation in [1] only allowed for negative dependencies.


We also examined the scaled latent convex regularization method [34].

it did not perform well and was omitted.


By sampling π j ∼ DP(α, β), the HDP prior encourages modes to have similar transition distributions (E[π jk | β] = β k ).

it does not differentiate self-transitions from moves between modes.


In the problem of scene understanding (as in many others), state-of-the-art models already exist for many of the tasks of interest.

these carefully engineered models are often tricky to modify, or even simply to re-implement from available descriptions.


In summary then, the general methods of [4,8,11] and [12,13,17] as well as the variational method of [15] are all identical with respect to their ARD-based cost functions; they differ only in which covariance components (and possibly hyperpriors) are used and in how optimization is performed as will be discussed below.

the variational model from [14] introduces an additional hierarchy to the ARD framework to explicitly model temporal correlations between sources which may be spatially separated.


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

classification problems simulated using random splits of video frames are rare in real-world applications.


For general loss functions, the DC-programming approach only guarantees convergence to a stationary point.

for the squared loss, our problem can be cast as an instance of the trust region problem, which can be solved globally using the DCA algorithm of Tao and An [1998].


2 (a) respectively, beyond which the L → ∞ scenario outperforms the L = R scenario, while the R = 1 case does not have such a threshold.

if the bandwidth is wide enough, the difference of the expected bit error probabilities in decibel, P (p, R), is proved to have similar qualitative characteristics as shown in Fig.


Our analysis can be modified to establish similar positive results for other formulations of the large-margin learning problem, including ones (see [28]) that have been tied closely to weak learnability (these modifications are not presented due to space constraints).

our main negative result is an information-theoretic argument that suggests that such positive parallel learning results cannot be obtained by boosting alone.


Our QK framework can also be seen as an efficient and robust MKL on a specific family of binary base kernels.

our binary base kernels originate from more general quantizations: they correspond to their regions of constantness.


For instance, it requires a one-time O(2 k ) effort to generate the vocabulary of size ≤ k graphlets for graphlet kernel.

one needs to build the vocabulary dynamically in Weisfeiler-Lehman and Shortest-Path kernels since the sub-structures depend on the node labels obtained from the datasets.


This clarifies the relation between CCA and our method: Both methods aim to minimize the average distance between X and Y embeddings.

cCA forces both embeddings to be centered and with a unity covariance matrix, whereas our method introduces a global regularization term related to the partition function.


The deteriorating performance of NVIL is most likely due to overfitting.

fABIA is robust to the change of the initial model size.


As showed in Table 2, the baseline can only acquire 0.01 positive symptoms on average in the case of 400 diseases.

our proposed REFUEL algorithm can acquire 1.31 positive symptoms.


Finally, as in [5], an application of nonlinear radial-basis kernels did not produce significan t improvement in the number of correct classifications when compared to linear kernels and this was the case for type Rt classifiers for which the improvement never exceeded 2% (results not shown).

the performance of type R int classifiers increased considerably (~8 % ) when they were trai ned with nonli near as opposed to linear kernels (time interval t = [150, 450] ms, res ults not shown).


Although polynomial, it is not clear whether the algorithm given in Lovasz and Vempala [2006], based on random walks, is of practical interest (e.g., the running time bound has a constant of 10 30 ).

we believe our observation provides insight into the complexity of sampling when ↵ is not too small, and may be a starting point towards explaining the empirical success of using Markov chain Monte Carlo to do inference in LDA.


The greedy approach has been widely studied in the context of learning sparse predictors for linear regression.

in multiclass problems, one needs sparsity of groups of variables (columns of W ).


In this paper, we propose a new model that takes the player-interaction effects into consideration.

under certain circumstances, the total number of individuals can be very large, and number of player interactions grows quadratically, which makes learning intractable.


Note that these algorithms give a different result from the basic least-squares system identification algorithm only in situations where the least-squares model is unstable.

least-squares LDSs trained in scarce-data scenarios are unstable for almost any domain, and some domains lead to unstable models up to the limit of available data (e.g.


As expected, the L1-linear model tends outperforms the others on the linear data set.

surprisingly, on a few folds, the MMIT-L and Interval-CART models were able to achieve low test errors.


Our algorithm retains the crucial property of the original method [LRT14] that the decision trees can be updated incrementally.

contrary to the original approach, our algorithm uses an increasing sequence of lifetime parameters (λ n ) n 1 , so that the corresponding trees are increasingly complex, and involves an alternative online updating algorithm.


Initial ideas to multi-task learning exploited supervised data from related tasks to define a form of regularization in the target problem [2,12].

in this setting, related tasks, also sometimes referred to our DA approach learns a single linear boundary β in a common feature space Z, and task-specific mappings φ 1 (x), φ 2 (x) : X → Z.


The basic form of the nonparametric tree developed here is based on the the nested Chinese restaurant process (nCRP) topic model [4,5].

to achieve the goals of the unique problem considered, we make the following new modeling contributions.


The SICS problem where f (X) = − log det(X) + ⟨ Σ, X⟩ and g(X) = ρ∥X∥ 1 , is of the same form as (4).

in this case neither f (X) nor g(X) have Lipschitz continuous gradients.


They also provide guarantees on the global minimum of a generative network with certain structure.

their work does not analyze how to find the global minimum.


Some recent works attempt to first infer the geometric layout from 2D images for improving the object detection [12,14,28].

such a geometric layout is not accurate enough to give significant improvement.


If 0 ∈ ∂ q(λ) then the direction d * = argmin d subject to d ∈ ∂ q(λ) is a descent direction and inf α>0 q(λ − αd) < q(λ) − .

if 0 ∈ ∂ q(λ) then q(λ) ≤ inf λ q(λ) + .


Often this issue is partially alleviated by an encoder such as e.g.

a BiRNN [2] or a deep convolutional network [3] that encode contextual information into every element of h . capacity of h elements is always limited, and thus disambiguation by context is only possible to a limited extent.


This can be problematic since the chance of producing an assignment of values to Y that has high probability under the likelihood can be quite low, in effect wasting many particles.

if we can analytically marginalize out the new rows of Y, we can avoid sampling those values from the prior and instead sample them from the posterior, in end for 7: normalize particle weights 8: resample particles according to weight CDF 9: for ℓ = 1, . . . , L do 10: sample end for 12: end for Figure 4: Infinite binary matrix factorization results.


A similar technique can be adopted to derive a fast version of Algorithm 2 that has an improved complexity bound of O(1/ √ ϵ), while keeping the computational effort in each iteration almost unchanged.

we do not present this method here, since when applied to the SICS problem, it did not work as well as Algorithm 2.


The above fact implies that model selection of importance estimation algorithms should be performed within the importance estimation step in an unsupervised manner.

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


Note, that computing the first expectation term is trivial for the fully observed case.

partially observed cases requires exact inference.


The HTP-style methods have been shown to have strong approximation guarantee and impressive numerical performance in high dimensional statistical learning applications.

the current theoretical treatment of these methods has traditionally been restricted to the analysis of parameter estimation consistency.


However, we do not have any assumptions on the form of the expected reward function other than the Lipschitz continuity and that it depends on a single type for each action.

in [12] graphical bandits are proposed where the learner takes an action vector a which includes actions from several types that consitute a type set T . The expected reward of a for context vector x can be decomposed into sum of reward functions each of which only depends on a subset of D ∪ T . it is assumed that the form of decomposition is known but the functions are not known.


Fundamentally, the problem of identifying a good local explanation is a causal question, which is typically very difficult to answer since most models are not causal.

the local explanation is not trying to find causal structure in the data, but in the model's response.


For each of these models, we select the best tuning parameter through log likelihood on held out data.

this criteria resulted in complete graphs for Nonparanormal and GGM (325 edges) and a relatively sparser graph for Expxorcist (168 edges).


A scale invariant local measure of curvature is the cosine distance between the two vectors formed by three temporally adjacent samples.

minimizing the curvature directly can result in the trivial solutions: z t = ct ∀ t and z t = c ∀ t. These solutions are trivial because they are virtually uninformative with respect to the input x t and therefore cannot be a meaningful representation of the input.


As in [7], we handle cost functions that are multivariate, in the sense that the number of documents returned for a given query can itself vary, but the key challenge we address in this paper is how to work with costs that are everywhere either flat or non-differentiable.

we emphasize that the method also handles the case of multivariate costs that cannot be represented as a sum of terms, each depending on the output for a single feature vector and its label.


On the power of gradient vs prox oracles For non-smooth functions, we show that having access to prox oracles for the components can reduce the polynomial dependence on ✏ from 1/✏ 2 to 1/✏, or from 1/( ✏) to 1/ p ✏ for -strongly convex functions.

all of the optimal complexities for smooth functions can be attained with only component gradient access using accelerated gradient descent (AGD) or accelerated SVRG.


This approach does not require the rank of the decomposition to be specified beforehand, and due to the low-rank inducing property of the Schatten 1-norm, the rank of the decomposition is automatically determined.

it has been noticed that the above overlapped approach has a limitation that it performs poorly for a tensor that is only low-rank in a certain mode.


With the recent advances of convolutional neural networks (CNN), two-stream architectures [25] and ranking losses [21] have shown great improvements.

to achieve their performance gain, CNN architectures require millions of samples of supervised training data or at least the fine-tuning [3] on large datasets such as PASCAL VOC.


We also performed experiments on small synthetic data (2-tier and 3-tier), where we were able to show that our algorithm converges to exact solution given by an LP solver (Appendix C).

since LP solvers are very slow, it is not feasible for web-scale problems.


While conventional hidden Markov models (HMMs) have been used to model disease progression, they are not suitable in general because they assume that measurement data is sampled regularly at discrete intervals.

in reality patient visits are irregular in time, as a consequence of scheduling issues, missed visits, and changes in symptomatology.


Applied to (1), RCD performs the iteration 1 Many of our results can be extended to convex functions of the form f (x) = φ(Ax) − b x, where φ is a smooth and strongly convex function.

due to space limitations, and the fact that we already have a lot to say in the special case φ(y) = 1 2 y 2 , we leave these more general developments to a follow-up paper.


Comparison with [16] on combinatorial cascading bandits By Lemma 1, we can apply Theorem 1 to combinatorial conjunctive and disjunctive cascading bandits with bounded smoothness constant B = 1, achieving O( √ mKT log T ) distribution-independent regret.

besides having exactly these terms, the results in [16] have an extra factor of 1/f * , where f * = i∈S * p(i) for conjunctive cascades, and f * = i∈S * (1 − p(i)) for disjunctive cascades, with S * being the optimal solution and p(i) being the probability of success for item (arm) i.


Other methods take a classification perspective and use tools from cost-sensitive classification [6][7][8].

since the absolute error of a predictor on training data is typically a non-convex (and non-continuous) function of the predictor's parameters for each of these formulations, surrogate losses that approximate the absolute error must be optimized instead.


On the face of things at least, feature vectors for overlapping frames are treated as independent and feature vectors must be augmented with derivative information in order to enable successful modeling with mixtures of diagonal-covariance Gaussians (see [2,3] for a more in-depth discussion of the exact consequences of the delta features).

perhaps even more disturbing than the frame-independence assumption are the compromises required to deal with two competing pressures in Gaussian mixture model training: the need for expressive models capable of representing the variability present in real speech data and the need to combat the resulting data sparsity and statistical efficiency issues.


While this is initially true due to the initialization algorithm, our intermediate centers might escape these balls during our update.

we show using a delicate martingale based argument that with high probability, our estimates stay within slightly larger balls around the true means, which turns out to be sufficient for us.


Among the literature surveyed here, this paper is the closest to the present work in terms of its intended application: roughly speaking, achieving mutually desirable outcomes via sequential decision-making.

the work is concerned with an ongoing interaction between the principals, rather than selecting a policy for a single agent to follow as in this paper.


In the standard multi-armed bandits setting, we assume that we have no information whatsoever on whether undisplayed ads would have been clicked on.

in many cases, we do have some side-information.


The development of our approach is inspired by DA using latent variables proposed by the statistical learning community [29], where the motivation is to introduce latent variables to facilitate the computation of posterior distributions.

directly applying this idea to deep learning is challenging because sampling millions of network parameters is computationally difficult.


We present the pseudo-code of our MCSSPs method using the full search on S in Algorithm 1.

if c is a bit large, we may adopt a similar approach as proposed in [10], which is based on a greedy search, to find the suboptimal solution.


Clearly if the algorithm is asked (as above) to output the full partition of the network, it will require a memory scaling linearly with n, the size of the output.

in the streaming model, we can remove this requirement and the algorithm can output the full partition sequentially similarly to an online algorithm (however our algorithm is not required to take an irrevocable action after the arrival of each column but will classify nodes after a group of columns arrives).


On one hand, we want to use the hierarchy to define the problem.

we don't want arbitrary choices and unbalanced splits in the taxonomy to have a significant effect on the outcome.


If indeed P 2 were to always play Rock, Paper, and Scissors with probability 0.4, 0.4, 0.2 , then P 1 could choose any arbitrary strategy and receive an expected value of 0.

by assuming P 2 is playing a fixed strategy, P 1 may not find a strategy that is robust to P 2 adapting.


We show that for a natural data distribution (the Gaussian model), the model class we train does not matter and a standard linear classifier achieves optimal robustness.

robustness also strongly depends on properties of the underlying data distribution.


As shown in recent literature [7,9], for the MKL formulation, different types of norm constraints fit different data sets.

rKL outperforms MKL (as well as KL-C) under both L 1 and L 2 norm constraints on most sets.


This dataset is particularly simple, and we chose this comparison because the two most important features that both LDA and BCM learn are identical for each cluster.

lDA does not learn prototypes, and represents information differently.


Quasi RNN (QRNN) and simple recurrent unit (SRU) are a kind of linear RNNs.

when applied to acoustic modeling, the accuracy with linear RNN was not as good as that of LSTM RNN.


We acknowledge that improved results could potentially be obtained by using more than one neighbour or with more sophisticated techniques such as locally weighted regression [36].

we focus on learning a good metric for performing this task rather than the regression problem.


Thus, a common method is to learn human-defined (or semi-human-defined) semantic concepts as mid-level representations to help video classification [4].

those human defined concepts are hardly generalized to a larger or new dataset.


For example, when distributing an advertisement by email, we can easily record to whom the advertisement has been sent.

for technical or privacy reasons, it is difficult to keep track of those people until we observe the outcomes on whether they buy the product or not.


Prior work on 3D urban scene analysis is mostly limited to simple ground plane estimation [4,29] or models for which the objects and the scene are inferred separately [6,7].

in this paper we propose a novel generative model that is able to reason jointly about the 3D scene layout as well as the 3D location and orientation of objects in the scene.


We currently have preliminary results on this issue, using an approach similar to (Ferns et al, 2005), which assumes lower-semi-continuity of the reward function.

the details are not yet fully worked out.


Under suitable assumptions like strongly convex functions or a sufficiently small step size for the dual variable update, ADMM can achieve a linear convergence rate [8,19].

as pointed out by [4], "There is currently no proof of convergence known for ADMM with nonquadratic penalty terms."


Some algorithms for noisy non-square instantaneous mixing have been developed [1], as well as algorithms for convolutive square noise-free, mixing [9].

the full problem including noise and convolution has so far remained open.


In practice, we typically discard the value of V * 0 once the optimization is converged since we are only interested in the fitted variational parameters λ * .

during the optimization process, V 0 is an important auxiliary quantity and the inference algorithm would be inconsistent without an optimization over V 0 : if we were to extend the model p(x, z) by an additional observed variable x which is statistically independent of the latent variables z, then the log joint (as a function of z alone) changes by a constant positive prefactor.


When the combined error of the ideal hypothesis is large, there is no classifier that performs well on both the source and target domains, so we cannot hope to find a good target hypothesis by training only on the source domain.

for small λ (the most relevant case for domain adaptation), Theorem 1 shows that source error and unlabeled H∆H-distance are important quantities for computing target error.


The logistic upper bound is obtained using 100 logistic samples: the logistic upper-bound A logistic is close to the superdifferential lower bound from [5] and is indeed significantly lower than the bound A L-field .

the tree-reweighted belief propagation bound behaves a bit better in the second case, but its calculation takes more time, and it cannot be applied for general submodular functions.


We also notice that similar problem was studied for graphs [13].

their method cannot be applied to our setting, because their input is restricted to the adjacency matrix of a graph.


Generative Adversarial Networks (GANs) excel at creating realistic images with complex models for which maximum likelihood is infeasible.

the convergence of GAN training has still not been proved.


Note that the algorithm of [24] optimizes the first order approximation of the objective function (21).

as seen previously, for our problem this results in an undesirable solution.


Electronic health records provide a rich source of data for machine learning methods to learn dynamic treatment responses over time.

any direct estimation is hampered by the presence of time-dependent confounding, where actions taken are dependent on time-varying variables related to the outcome of interest.


As to be expected, underestimating the temporal smoothness results in increased variance due to the lack of regularization.

overestimating the smoothness results in a highly biased estimate as well as anti-causal information leakage.


An important difference between Imax and the IB setting, is that in the Imax setting, I(Y a ; Y b ) is invariant to scaling and translation of the Y 's since the compression achieved in the mapping X a → Y a is not modeled explicitly.

the IB framework aims to characterize the dependence of the solution on the explicit compression term I(T ; X), which is a scale sensitive measure when the transformation is noisy.


During evaluation, all networks achieve greater than 98% accuracy on audio-only and combined audio-video inputs.

video-only evaluation with an audio-video capable network proved the most challenging, so the results in Fig.


Most CRF models use a linear potential function to represent the relationship between input features and output.

in many real-world applications such as protein structure prediction and handwriting recognition, the relationship between input features and output is highly complex and nonlinear, which cannot be accurately modeled by a linear function.


These results appear to be competitive with recently proposed randomized algorithms in terms of pass efficiency and run time.

the randomized algorithms may produce more accurate features, at the cost of small probability of failure.


This condition entails the following: first, for any i ∈ U, adding a single individual to any dataset D can either keep f (i, D) constant, or increase it by 1/n; and second, f (i, D) can only increase in this case for at most items i ∈ U.

the utility of this algorithm depends only on log , rather than log K. our algorithm does not require the first condition.


Both agents quickly learned to master the training episodes.

as shown in Figure 5, the agent with the NAC performed well on the task for T ≤ 19, whereas performance of the standard A3C agent deteriorated for T > 13.


Modeling studies have shown that a small number of samples are sufficient to perform well on low-dimensional tasks (intuitively, this is because taking a lowdimensional marginal of the posterior accumulates samples over all dimensions) [14,15].

most sensory data is inherently very high-dimensional.


This is a big improvement over the two previous models as it incorporates the interaction of two entity vectors in a simple and efficient way.

the model is now restricted in terms of expressive power and number of parameters by the word vectors.


The sublinear O(1/k 2 ) convergence rate is known to be optimal if f is simply given by a first-order oracle [12].

if f is strongly convex, then the convergence rate can be improved to O(c k ) for some c ∈ (0, 1) (i.e., a linear convergence rate) [16].


In particular, at (w, v) = (0, −1/ ), the gradient is 0 and the Hessian equals 0 − − 0 , which is arbitrarily close to 0 if is small enough.

the objective value at that point equals Remark 3.


Since we can replay an execution trace with the interpreter to obtain detailed information about the program state at each step, a trace-based synthesis model can rely upon the interpreter to handle the semantics of the DSL's operations, and focus more on how to infer control flow constructs by reconciling different paths taken in different inputs.

execution traces are difficult to obtain as they are much more challenging for the end user to specify, so it is hard to reap their benefits.


By sharing the f k t (•) across all steps, g k (•) receives the same feature from a given output state, which encourages the feature reusage and thus reduces the feature redundancy.

such an information sharing strategy makes it difficult for residual networks to explore new features.


Together with the transformation U , this implies that there exists a weight matrix Although A k a is indeed sparse, any attempt to learn W k a using GL would fail, since W k a may have a very low level of sparsity.

an algorithm able to learn a suitable transformation U , it may be able to recover the representation Φ * (and the corresponding space F * ) and exploit the high level of sparsity of A k a .


The ability to better transmit images over multimode fibre (MMF) has applications in medicine, cryptography and communications in general.

as pointed out by Stasio [2017], MMFs are not normally utilised for imaging because they do not act as a relay optical element.