It is trivial to observe that these nodes will be be equal to −1 (+1) in the optimal solution and that eliminating them does not affect solving (5) without them.

in practice, this trivial reduction has a computationally minimal affect on large data sets.


Also, (α − γ)/α can go to zero at a suitable rate.

the expected number of common neighbors between nodes tends to zero for sparser graphs, irrespective of whether the nodes are in the same cluster or not.


This coupling is achieved by repeatedly performing inference and updating a set of dual parameters until convegence.

we perform inference independently in each sub-model only once, and reason about individual variables using the sums of max-marginals.


We also tried to run the other approaches with data generated from Gaussian distributions but the results were approximately equal to those shown in Figure 3.

our approach performs similarly but the number of reversed links increases significantly since the model is no longer identified.


In [Zhou et al., 2016], the range of activations is constrained within [0,1], which seems to avoid this situation.

fractional numbers do not solve this problem, severe precision deterioration will appear during the multiplication if there are no extra resources.


When computing Precision T (R, P i ) for a single predicted anomaly range P i , there is no need for an existence reward, since precision by definition emphasizes prediction quality, and existence by itself is too low a bar for judging the quality of a prediction (i.e., α = 0).

the overlap reward is still needed to capture the cardinality, size, and position aspects of a prediction.


For instance, for 37.5% compression, the original squeezed net only achieves 54.7%.

our proposed method lifts it up to 59.4% with a deep teacher (VGG16), which is even better than the uncompressed AlexNet model 57.2%.


[13], who show polynomial sample complexity results for learning influence in the LT and IC models (under partial observation).

their approach uses approximations to influence functions and consequently requires a strong technical condition to hold, which is not necessarily satisfied in general.


In the experts setting we have seen that the learner can distribute a prior amongst the actions and obtain a bound on the regret depending in a natural way on the prior weight of the optimal action.

in the bandit setting the learner pays an enormously higher price to obtain a small regret with respect to even a single arm.


These techniques promote sparsity in determining a small set of codewords from the dictionary that can be used to efficiently represent each visual descriptor of each image [13].

those approaches consider each visual descriptor in the image as a separate coding problem and do not take into account the fact that descriptor coding is just an intermediate step in creating a bag of codewords representation for the whole image.


Moreover, we note that counting the number of possible outputs of ERM also has connections to a counting argument made in [1] in the context of pricing mechanisms.

in essence the argument there is restricted to transductive settings where the sample "features" are known in advance and fixed and thereby the argument is much more straightforward and more similar to standard notions of "effective hypothesis space" used in VC-dimension arguments.


A better one is to handcraft a policy that chooses an action based on the history of actions and observations, a technique used in [18].

it is often difficult to handcraft effective history-based policies.


The reinforcement learning controller is encouraged by the reward structure to accomplish each movement as quickly as possible.

it faces high uncertainty in the plant behavior.


First, continuously projecting at every step helps to reduce overfitting, as can be observed by the slower decline of the blue curve (upper smooth curve) compared to the orange curve (lowest curve).

when projection is performed after many steps, (instead of continuously), performance of the projected model actually outperforms the continuous-projection model (upper jittery curve).


Time series are ubiquitous in many classification/regression applications.

the time series data in real applications may contain many missing values.


In this case, it is rigorously known [21,22,23] that detection is impossible by any algorithm for the SBM with a group structure weaker than where ϵ ≡ ρ out /ρ in .

it is important to note that this is the information-theoretic limit, and the achievable limit for a specific algorithm may not coincide with Eq.


The subsequent use of Lloyd's algorithm to refine the solution only guarantees that the solution quality does not deteriorate and that it converges to a locally optimal solution in finite time.

using naive seeding such as selecting data points uniformly at random followed by Lloyd's algorithm can produce solutions that are arbitrarily bad compared to the optimal solution.


This seems to imply that scaling up these models to large RFs is relatively easy.

these models need to be trained on audio excerpts that are at least as long as their RFs, otherwise they cannot capture any structure at this timescale.


For many nonparametric divergence estimators the large sample consistency has already been established and the mean squared error (MSE) convergence rates are known for some.

there are few results on the asymptotic distribution of non-parametric divergence estimators.


Rather, we maintain a Gaussian approximation of the posterior on the full space, Θ.

when optimizing our stimuli we combine our posterior with our knowledge of M in order to do a better job of maximizing the informativeness of each experiment.


( 1) can be rewritten as the Bellman equation The advantage of using the Bellman equation is that it describes the relationship between the value function at one state s and its immediate follow-up states s ∼ p(s |s, a).


the least squares projection), one can adopt a robust loss such as Huber's loss as the distance, which often gives a better result (robust projection [9]).

a major drawback of these projection approaches is that all pixels are updated by the projection.


After this initial conservative phase, CLUCB has learned enough about the optimal action and its performance starts converging to that of LUCB.

figure 1 shows that per-step regret of CLUCB at the first few periods remains much lower than that of LUCB.


Also, that the localization error of the GPPS system degrades only slowly when the number of calibration measurements is reduced.

the curves for the nearest neighbor based method show a sharper increase of positioning error.


For the variational scale parameters, ln g s , we see that early on the HVP+Local approximation is able to reduce parameter variance by a large factor (≈ 2,000×).

at later iterates the HVP+Local scale parameter variance is on par with the Monte Carlo estimator, while the full Hessian estimator still enjoys huge variance reduction.


Hershey used the power from the spectrogram in his algorithm to detect the visual motion.

our result for spectrogram data is in the noise, indicating that a linear model can not use spectrogram data for fine-grain temporal measurements.


Recently, there has been substantial interest in using large amounts of unlabeled data to learn word representations which can then be used as features in supervised classifiers for NLP tasks.

most current approaches are slow to train, do not model the context of the word, and lack theoretical grounding.


The IBP places a prior distribution over binary matrices where the number of columns (features) K is not bounded, i.e., K → ∞.

given a finite number of data points N , it ensures that the number of non-zero columns K + is finite with probability one.


However, due to the variance of the estimator ŝt , sEM has a slower asymptotic convergence rate than bEM for finite data sets.

specifically, let s * = F (s * ) be a stationary point, Cappe and Monlines [6] showed that Dempster et al.


Autoregressive feedback is considered a necessity for successful unconditional text generation using stochastic sequence models.

such feedback is known to introduce systematic biases into the training process and it obscures a principle of generation: committing to global information and forgetting local nuances.


Many researchers attempted to solve goal-oriented dialog tasks by using the deep supervised learning (deep SL) approach [8] based on seq2seq models [9] or the deep reinforcement learning (deep RL) approach utilizing rewards obtained from the result of the dialog [10,11].

these methods struggle to find a competent RNN model that uses back-propagation, owing to the complexity of learning a series of sentences.


This up-front computation is not needed for any of the MLE algorithms described above.

each of the MLE algorithms requires some initial value for , but no such initialization is needed to find the OLS estimator in Algorithm 1.


Ψ(S) > δ, and its support x S is smaller or equal to min(n 1 , n 2 ), then all children S of S, which satisfy S ⊂ S by construction of the enumeration tree, will also be non-testable and can be pruned from the search space.

such a monotonicity property does not hold for the CMH minimum attainable p-value function Ψ cmh (S), severely complicating the development of an effective pruning criterion.


. . , f4 by minimizing the Kullback-Leibler (KL) divergence between the product of Q \a and f a and the product of Q \a and fa , where Q \a is the ratio between Q and fa .

this does not perform well for refining f2 ; details on this problem can be found in Section 4 of the supplementary material and in [19].


That is, deep learning introduces good function classes that may have a low capacity in the VC sense while being able to represent target functions of interest well.

deep learning requires us to deal with seemingly intractable optimization problems.


Recovering X * from Q * As for linear programming, recovering a primal optimal solution directly from a dual optimal solution is not always possible for SDPs.

at least for the hard-margin problem (no slack) this is possible, and we describe below how an optimal prediction matrix X * can be recovered from a dual optimal solution Q * by calculating a singular value decomposition and solving linear equations.


As shown in Figure 2, when the rank increases from 10 to 300, PMF can achieve RMSEs between 0.86 and 0.88.

the RMSE of MRMA is about 0.84 when mixing all these ranks from 10 to 300.


This proof relies only on commonly applicable, fairly general assumptions, thus rendering a generic result not constraining the design of larger networks.

in which way the timing of the third factor is implemented in networks will be an important issue when constructing such networks.


Specifically in this case, one can obtain small ✏ by increasing k 1 , k 2 in Algorithm 3.

this will mean we select large number of groups, and subsequently increases.


If a strong prior is close to the true values, the Bayesian posterior will be more accurate than the empirical point estimate.

a strong prior peaked on the wrong values will bias the Bayesian model away from the correct probabilities.


Monte-Carlo Tree Search (MCTS) has been successfully applied to very large POMDPs, a standard model for stochastic sequential decision-making problems.

many real-world problems inherently have multiple goals, where multiobjective formulations are more natural.


For short trees, the two perform equally, SSR beating AR slightly for trees with three nodes, which is not surprising since ly performs exact inference in this tiny topology configuration.

as trees get taller, the es more difficult, and only AR manages to maintain good performances.


Obviously, if we knew for each policy which subchains it induces on M (the MDP's ergodic structure), UCRL could choose an MDP Mt and a policy πt that maximizes the reward among all plausible MDPs with the given ergodic structure.

only the empiric ergodic structure (based on the observations so far) is known.


The lower bound ℓ ij is obtained from the extreme case of setting the missing values in a way that the two sets have the fewest features in their intersection while having the most features in their union.

the upper bound µ ij is obtained from the other extreme.


There are well-known lower bounds for multi-armed bandit problems and other online learning with partial-information settings.

they crucially depend on the semantics of the information feedback considered.


Variational autoencoders (VAE) train an inference network jointly with the parameters of the forward model to maximize a variational lower bound [15,5,11].

the use of a parametric variational distribution means they typically have limited capacity to represent complex, potentially multimodal posteriors, such as those incorporating discrete variables or structural uncertainty.


To compare the training cost, if the time cost of the related task (regression or classification) with M features is C(M ), LKRF and EERF simply spend that budget.

running K iterations of our method (with M a multiple integer of K), assuming that repetitive features are not selected, the training cost of MFGA would be P K k=1 C(kM/K), which is more than LKRF and EERF.


In Figure 2(a), the true class only has 10% more correct instances over wrong ones.

the true has 37.5% more correct instances in Figure 2(b).


Similar to [11], Algorithm 1 is also greedy and based on keeping track of the supernodes.

the definition of a supernode and its updating are different.


The point process generalized linear model (GLM) has provided a useful and highly tractable tool for characterizing neural encoding in a variety of sensory, cognitive, and motor brain areas [1][2][3][4][5].

there is a substantial gap between descriptive statistical models like the GLM and more realistic, biophysically interpretable neural models.


⇤ As in the proof of Theorem 1, the main idea is to show that one can design two distributions that are indistinguishable to a learner who can observe no more than d 1 attributes of any sample given by the distribution (i.e., that their marginals over any choice of d 1 attributes are identical), but whose respective sets of "-optimal regressors are disjoint.

in contrast to Theorem 1, both handling general d along with switching to the absolute loss introduce additional complexities to the proof that require different techniques.


Because of the match between the parallelism offered by hardware and the parallelism in machine-learning algorithms, mixed analog-digital VLSI is a promising substrate for machine-learning implementations.

custom VLSI solutions are costly, inflexible, and difficult to design.


Due to the square loss in RPCA, the sparse matrix S can be calculated by subtracting the low-rank matrix L from the observed data matrix.

nevertheless, in LVGGM, there is no closed-form solution for the sparse matrix due to the log-determinant term, and we need to use gradient descent to update S. both the algorithm in [40] and our algorithm have an initialization stage.


functions are not necessarily l.c., as is easily shown (e.g., a mixture of Gaussians with widely-separated means, or the indicator of the union of disjoint convex sets).

a key theorem (10,11) gives: Theorem (Integrating out preserves log-concavity).


In all experiments thus far, our models have been trained to make numeric predictions.

as discussed in the introduction, systematic numeric computation appears to underlie a diverse range of (natural) intelligent behaviors.


Although for certain GLM, e.g., sparse logistic regression, we can choose the step size parameter as ⌘ = 4⇤ 1 max ( 1 n P n i=1 x i x > i ), such a step size often leads to poor empirical performance.

as our theoretical analysis and experiments suggest, the proposed DC proximal Newton algorithm needs very few line search steps, which saves much computational effort.


There have thus been various important suggestions for the functional significance of synaptic depression, including -just to name a few -low-pass filtering of inputs [3], rendering postsynaptic responses insensitive to the absolute intensity of presynaptic activity [4,5], and decorrelating input spike sequences [6].

important though they must be for select neural systems, these suggestions have a piecemeal flavor -for instance, chaining together stages of low-pass filtering would lead to trivial responding.


In some applications, simple models (e.g., linear models) are often preferred for their ease of interpretation, even if they may be less accurate than complex ones.

the growing availability of big data has increased the benefits of using complex models, so bringing to the forefront the trade-off between accuracy and interpretability of a model's output.


Simultaneous-move games can be solved exactly in polynomial time using the backward induction algorithm [7,4], recently improved with alpha-beta pruning [8,9].

the depth-limited search algorithms based on the backward induction require domain knowledge (an evaluation function) and computing the cutoff conditions requires linear programming [8] or using a double-oracle method [9], both of which are computationally expensive.


We model aleatoric uncertainty with MAP inference using loss functions ( 8) and (12 in the appendix), for regression and classification respectively ( §2.2).

we derive the loss function using a Laplacian prior, as opposed to the Gaussian prior used for the derivations in §3.


The most elegant optical implementation of adaptive interconnection is through dynamic volume holography [6,11], but that requires a set of coherent optical signals, not what we have with an array of pulse emitters.

the matrix-vector multiplier architecture allows parallel interconnection of incoherent optical signals, and has been used to demonstrate implementations of the Hopfield model [7] and Boltzman machines [9].


There may be other models we haven't found that could beat the ones we have, and come closer to our proven envelope.

we suspect that the area constraint is not the bottleneck for optimizing memory at times less than O( M r ).


Its decision on labeling is done at once, not separately for each topic.

pMM also has a problem with multi-topic specific features such as "qbit" since it is impossible for texts to have such features given PMM's mixture process.


This massive data access requires an enormous amount of network bandwidth.

bandwidth is one of the scarcest resources in datacenters [6], often 10-100 times smaller than memory bandwidth and shared among all running applications and machines.


This algorithm and its analysis are novel to the best of our knowledge.

we note that a related greedy algorithm (that does not directly optimize the objective (2» called Group-OMP appears in [14,15].


In practice, one finds a single local optimum, projects to the subspace orthogonal to it and continues recursively on a lower-dimensional problem.

a naive implementation of this idea is unstable since approximation errors can accumulate badly, and to the best of our knowledge no rigorous analysis has been given prior to our work.


For both of these sequences, rough tracking (not shown) is possible without occlusion reasoning, since all fingers are the same color and the background is unambiguous.

we find that stability improves when occlusion reasoning is used to properly discount obscured edges and silhouettes.


The cost-average policy π 1 greedily selects the items that maximize the worst-case utility gain per unit cost increment if they are still affordable by the remaining budget.

the cost-insensitive policy π 2 simply ignores the items' costs and greedily selects the affordable items that maximize the worst-case utility gain.


The main difference between our works is the use of a linear scaling of the learning rate 9 , similarly to Krizhevsky (2014), and as suggested by Bottou (2010).

we found that linear scaling works less well on CIFAR10, and later work found that linear scaling rules work less well for other architectures on ImageNet (You et al., 2017).


This is likely possible to improve by tuning the trade-off between relevance and diversity, such as a making a more sophisticated choice of S and σ.


For any δ > 0, the sequence This theorem can be easily generalized to hold for values of ε i that are not all equal (as done in [KOV15]).

this is not as all-encompassing as it would appear at first blush, because this straightforward generalization would not allow for the values of ε i and δ i to be chosen adaptively by the data analyst.


Most commercial LP software thus still relies on exact methods to solve the linear system.

some dual or primal (stochastic) sub-gradient descent methods have cheap cost for each iteration, but require O(1/ 2 ) iterations to find a solution of precision, which in practice can even hardly find a feasible solution satisfying all constraints [14].


Similar to our proposal this work suggests presenting trajectory data to an informed expert.

their queries require the expert to express preferences over approximate state visitation densities and to possess knowledge of the expected performance of demonstrated policies.


Theoretically, the position model should result in three identical peaks that are displaced in disparity.

the measurements show a wide variation in the peak sizes.


As shown in Section 4, ARS V1 can train linear policies, which achieve the reward thresholds previously proposed in the literature, for five MuJoCo benchmarks.

aRS V1 requires a larger number of episodes, and it cannot train policies for the Humanoid-v1 task.


From only positive (P) and unlabeled (U) data, a binary classifier could be trained with PU learning, in which the state of the art is unbiased PU learning.

if its model is very flexible, empirical risks on training data will go negative, and we will suffer from serious overfitting.


[2014]), which also aim to aggregate information over time from multiple parties and make use of proper scoring rules to do it.

prediction markets provide incentives through payments, rather than influence, and lack the feedback mechanism to select among experts.


We choose the step size η to guarantee a descent on the objective.

the gradient of the approximated structured prediction program in Theorem 1 with respect to θ r equals to if either and/or c α equal zero, then the beliefs b x,y,α (ŷ α ) can be taken from the set of probability distributions over support of the max-beliefs, namely b x,y,α (ŷ * α ) > 0 only if ŷ * α ∈ argmax ŷα r:α∈Er,x θ r φ r,α (x, ŷα ) + v∈N (α) λ x,y,v→α (ŷ α ) .


The key insight when proving this theorem is bounding rate of change of f . We can immediately see that f π (θ) := θ log E s,π e J/θ is a convex function since it is the perspective transformation of a convex function, namely, the cumulant generating function of the total cost J. Additionally, Theorem 1 shows that f π is lower bounded by E s,π [J], assumed to be finite, which implies that f π is non-increasing.

by directly differentiating the definition of f π , we get that θf π (θ Since we assumed that the costs, J, are upper bounded, there exist a maximum cost j M such that J ≤ j M almost surely for any starting state s, and any policy π.


Previous results in this setting have been limited to answering a single nonadaptive query repeatedly as the database grows [DNPR10, CSS11].

we provide tools for richer and more adaptive analysis of growing databases.


many functions of interest over graphical models are not Lipschitz with good Lipschitz constants.


First, at an 6 All the code is available at https://github.com/sanghack81/SCMMAB-NIPS2018 7 One may surmise that combinatorial bandit (CB) algorithms can be used to solve SCM-MAB instances by noting that an intervention can be encoded as a binary vector, where each dimension in the vector corresponds to intervening on a single variable with a specific value.

the two settings invoke a very different set of assumptions, which makes their solvers somewhat difficult to compare in some reasonably fair way.


Measures of linear dependence and feedback, based on Granger-Geweke causality (GC) [10] [11]), have been used to estimate instantaneous and lagged functional connectivity in recordings of brain activity made with electroencephalography (EEG, [6]), and electrocorticography (ECoG, [3]).

the application of GC measures to brain recordings made with functional magnetic resonance imaging (fMRI) remains controversial [22][20] [2].


Note that `1 MLE 1 stops prematurely after only 50 iterations, so that training computation time is sometimes comparable to closed-form estimator.

its statistical performance measured by `2 is much inferior to other `1 MLEs with more iterations as well as Elem-GLM estimator.


A straightforward version of this idea would be to perform shape completion in the 3D voxel grid: f 2.5D→3D = c 3D→3D • p 2.5D→3D .

shape completion in 3D is challenging, as the manifold of plausible shapes is sparser in 3D than in 2D, and empirically this fails to reconstruct shapes well.


It is clearly missing the structure of the model filter.

it is possible to obtain a good estimate of it by maximizing information directly, see panel (d).


Our choice of g is motivated by computational considerations: For general functions g, the computation of ( 14) would require O(m) time per function evaluation, where m is the number of documents.

the specific functional form in (14) allows O(1) time per function evaluation as , where the inner term j =i S k (x i , x j ) in the RHS does not depend on w and can be precomputed.


This is to be expected, since mini-batching does not lead to large gains in a serial setting.

using mini-batching in a serial setting might still be beneficial for implementation reasons, resulting in constant-factor improvements in runtime (e.g.


The Bayesian student thus learns the linear features for N = 0 (d).

unlike the GP, it learns all of the remaining nonlinear features for N = O(dK).


[11] introduced parameterized models of indoor environments, constrained by rules inspired by blockworld to guarantee physical validity.

since this approach samples possible spatial layout hypothesis without clutter, it is prone to errors caused by the occlusion and tend to fit rooms in which the walls coincide with the object surfaces.


In classical VB, we optimize the KL divergence between q(•) and a posterior, KL(q(β , z)||p(β , z | x); its objective is a function of a fixed data set x.


Most of the approaches (22; 13) leverage a large set of videos to discriminate or build a foreground model.

we segment and localize the foreground separately on each video, making our approach much more scalable.


SO-DLT in particular is a good example of direct adaptation of standard batch deep learning methodology to online learning, as it uses SGD during tracking to fine-tune an ensemble of deep convolutional networks.

the online adaptation of the model comes at a big computational cost and affects the speed of the method, which runs at 5 frames-persecond (FPS) on a GPU.


The pushforward density p l can then be approximated by the empirical measure given by the particles {x l i } n i=1 , where The first term in (10) corresponds to a weighted average steepest descent direction of the log-target density π with respect to p l . This term is responsible for transporting particles towards highprobability regions of π.

the second term can be viewed as a "repulsion force" that spreads the particles along the support of π, preventing them from collapsing around the mode of π.


Agarwal and Bottou [1] presented a lower bound of ⌦ m + p m log 1 ✏ .

their bound is valid only for deterministic algorithms (thus not including SDCA, SVRG, SAG, etc.


Interestingly, in the case of batch active learning for classification, the random batch selection strategy  has been surprisingly effective and is often difficult to outperform with more sophisticated strategies [8].

as our experiments will show, our approach will dominate random.


Learning uses EM-like algorithms to iteratively localize and refine discriminative image features.

hitherto, the detection accuracy has not be as good as the best methods.


Ideally, the empirical risk of the solution returned by STRSAGA is close to the empirical risk of the ERM over S i .


This is why application of ICA to EEG recently has become popular, yielding new promising results (e.g., [6]).

compared with ICA, the sparse representation has two important advantages: 1) sources are not assumed to be mutually independent as in ICA, even be not stationary; 2) source number can be larger than the number of sensors.


In the case of CS, the `0 norm is relaxed to the `1 norm; for low-rank matrices, the rank operator is relaxed to the nuclear norm.

greedy algorithms [17,20] operate iteratively on the signal measurements, constructing a basis for the signal and attempting signal recovery restricted to that basis.


Today, computer chess programs, built essentially on search techniques and running on a simple PC, can rival or even surpass the best human players.

and in spite of several decades of significant research efforts and of progress in hardware speed, the best Go programs of today are easily defeated by an average human amateur.


They have been extensively analyzed and are the most commonly used methods.

aDP methods typically do not converge and they only provide weak guarantees of approximation quality.


The span of an MDP is the maximum di erence in value of any two states under the optimal policy (M ú ) := max The diameter of an MDP is the maximum number of expected timesteps to get between any two states D(M ú ) = max s" =s Õ min µ T µ saes Õ . PSRL's bounds are tighter since (M ) AE CD(M ) and may be exponentially smaller.

uCRL-Factored has stronger probabilistic guarantees than PSRL since its bounds hold with high probability for any MDP M ú not just in expectation.


Particularly the performance obtained with very small numbers of labels is much better than previous published results which shows that the method is capable of making good use of unsupervised learning.

the same model also achieves state-of-the-art results and a significant improvement over the baseline model with full labels in permutation invariant MNIST classification which suggests that the unsupervised task does not disturb supervised learning.


Concrete dropout layer requires negligible additional compute compared with standard dropout layers with our implementation.

using conventional dropout requires considerable resources to manually tune dropout probabilities.


As expected, the naive method strongly under-estimated correlations in the non-simultaneously recorded blocks, as it can only model stimulus-correlations but not noise-correlations across neurons.

1 our stitching method predicted correlations well, matching those of the fully observed model (correlation 0.84 for stitchLDS, 0.15 for naiveLDS, figure 3d).


This implies f t is difficult to minimize.

if S t is small, then φ i,t is potentially linear for many i.


Our proofs require novel techniques and do not follow from traditional proof progressions.

we first show how we can use these results to arrive at an error bound.


In the BXPCA, we interpret the matrix V as a lower dimensional embedding of the data which can be used for dimensionality reduction.

the corresponding matrix for the BPM model, whose values are restricted to [0,1], is the partial membership of each data point and represents the extent to which each data point belongs to each of the K clusters.


For models with a simple enough graph structure, these algorithms can compute marginal probabilities exponentially faster than direct summation.

these fast exact inference methods apply only to a relatively small class of models-those for which the basic operations of marginalization, conditioning, and multiplication of constituent factors can be done efficiently.


In the deterministic setting, if a term revealing a new v r appeared in half of the components, we could ensure that the algorithm must make m/2 queries to find it.

a randomized algorithm could find it in two queries in expectation, which would eliminate the linear dependence on m in the lower bound!


The regularizers are minimized simultaneously as the network is learned, and thus no pre-training is required.


We can capture such contextual information by using features from all the regions in the image, and then also train a specific classifier of each spatial location for each object category.

the dimensionality of the feature space would become quite large, 1 and training a classifier with limited training data would not be effective.


These models have become very popular and won the recent evaluations of handwriting recognition [9,34,37].

current models still need segmented text lines, and full document processing pipelines should include automatic line segmentation algorithms.


In this general framework, the observations are assumed to follow an exponential family distribution, with natural parameter related to a conditionally Gaussian dynamic model [5], via a nonlinear transformation.

these model specifications may still be too restrictive in practice, for the following reasons: (i) Observations are usually discrete, non-negative and with a massive number of zero values and, unfortunately, far from any standard parametric distributions (e.g., multinomial, Poisson, negative binomial and even their zero-inflated variants).


Given sufficiently small / large constants c T , c H , and , it is easy to see that the linear convergence implied by Theorem 9 directly gives the recovery guarantee and bound on the number of iterations stated in Theorem 5 (see Appendix A.1).

in some cases it might not be possible to design approximation algorithms with constants c T and c H sufficiently close to 1 (in constrast, increasing the sample complexity by a constant factor in order to improve is usually a direct consequence of the RIP guarantee or similar statistical regularity assumptions).


But standard interlacing results can give [19]).

using Mercer's theorem, we have we have K are approximately the same, up to a unitary transformation.


The no-regret algorithm must ensure that the regret vanishes as n → ∞ regardless of the opponent's actions.

in our case, in addition to vanishing regret, we need to satisfy the cost constraints.


ICA is a data driven method which relaxes the strong characteristical frequency structure assumptions.

iCA algorithms perform best when the number of the observed  They generally have more sharpened summits and longer tails than a Gaussian distribution, and would be classified as super-Gaussian.


Li and Li [21] build a cascade classifier where each classifier is implemented as a linear SVM acting on the PCA of inner convolutional layers of the classification network.

these methods all require a large amount of extra computational cost, and some of them also result in loss of accuracy on normal examples.


Unlike [18], we also emphasize on the ability of the methods in recovering the number of motions.

although the methods compared in [18] (except RANSAC) theoretically have the means to do so, their estimation of the number of motions is generally unrealiable and the benchmark results in [18] were obtained by revealing the actual number of motions to the algorithms.


Neural spiking activity is usually analysed by averaging across multiple experimental trials, to obtain a smooth estimate of the underlying firing rates [2,3,4,5].

even under carefully controlled experimental conditions, the animal's behavior may vary from trial-to-trial.


For this approach, we choose the recent spectral mixture kernels of Wilson and Adams [14], which can model a wide range of stationary covariances, and are intended to help automate kernel selection.

we note that our objective function can readily be applied to other parametric forms.


In the figure, as the number of sum nodes goes up, the accuracy of the standard sum-product based estimation (sum) gets better, whereas the accuracy of standard max-product based estimation (max) worsens.

our hybrid messagepassing algorithm (hybrid), on an average, results in the lowest loss compared to the other baselines, with running times similar to the sum/max product algorithms.


These methods have been shown to be very effective in practice.

they do not provide any guarantee on the quality of the results.


In previous work on sample-based tree search, indeed including POMCP [20], a complete sample state is drawn from the posterior at the root of the search tree.

this can be computationally very costly.


On the theoretical side, a different line of work focusing on general hypothesis classes [14] uses martingale-based sequential complexity measures to show that, information-theoretically, one can obtain oracle inequalities in the online setting at a level of generality comparable to that of the batch statistical learning.


We find our method generally performs the best, followed with the parallel SGLD, which is much better than its sequential counterpart; this comparison is of course in favor of parallel SGLD, since each iteration of it requires n = 100 times of likelihood evaluations compared with sequential SGLD.

by leveraging the matrix operation in MATLAB, we find that each iteration of parallel SGLD is only 3 times more expensive than sequential SGLD.


The standard approach for handling such a scenario is to first learn a single-output model and then produce M -Best Maximum a Posteriori (MAP) hypotheses from this model.

we learn to produce multiple outputs by formulating this task as a multiple-output structured-output prediction problem with a loss-function that effectively captures the setup of the problem.


The fraction S/N is critical to determining the scalability of QD-PageRank.

if every document contained vastly different words, S/N would be proportional to the number of search terms, m. this is not the case.


. . , h m (s) which determines the average firing rate of each neuron in response to the stimulus.

the encoding process is affected by neural noise.


We might address this by choosing a more flexible parametric base measure.

since the dimensionality of µ scales only linearly with the number of neurons, the empirical synchrony distribution (ESD), converges quickly even when the sample size is inadequate for estimating the full π.


As a result, even when the teacher network is shallow, the student network usually needs to be deeper, otherwise it will underfit.

both our theorem and our experiment show that if the shallow teacher network is in a pretty large region near identity (Figure 2), SGD always converges to the global minimum by initializing the weights I + W in this region, with equally shallow student network.


Theoretical understanding of the strength of depth starts from analyzing the depth efficiency, by proving the existence of deep neural networks that cannot be realized by any shallow network whose size is exponentially larger.

we argue that even for a comprehensive understanding of the depth itself, one needs to study the dual problem of width efficiency: Because, if we switch the role of depth and width in the depth efficiency theorems and the resulting statements remain true, then width would have the same power as depth for the expressiveness, at least in theory.


Linear and convex aggregation of densities, based on an L 2 criterion, are studied in [9], where the densities are based on a finite dictionary or an independent sample.

our proposed method allows data-adaptive kernels, and does not require and independent (holdout) sample.


If the second condition becomes strict, i.e., r 2 f (x) 0, then we recover the sufficient conditions for a local minimum.

to derive finite time convergence bounds for achieving an SOSP, these conditions should be relaxed.


Indeed, even for discrete problems simple and accurate estimators have proved to be elusive, and MCMC methods do not provide any simple way of computing the partition function.

sMC provides a straightforward estimator of the normalizing constant (i.e.


of ( 2) with respect to the variables w, σ, b.

in this work the focus is only on the data-dependent terms in (2), which include the empirical error term and the weighted norms of σ.


Moreover, the amazing RSs offered by giant e-tailers and e-marketing platforms, such as Amazon and Google, lie at the heart of online commerce and marketing on the web.

current significant challenges faced by personal assistants (e.g.


It requires multiple iterations through the training data, which can become impractical with large models and datasets.

our approach can be adapted to an online implementation.


More sophisticated variational techniques capture multiple modes using substructures  or by leaving part of the original network intact and approximating the remainder .

although these methods increase the number of modes that are captured, they still exclude modes.


Thompson sampling balances exploration with exploitation because actions with large posterior means and actions with high variance are both more likely to appear as the optimal action in the sample r (s) .

the arg max presents difficulties in the reweighting required to perform Bayes empirical Bayes approaches.


The LHS of (10), by the assumption of the theorem, is at most ε 2 implying (9).

note that our anlaysis of the Fujishige-Wolfe algorithm is weaker than the best known method in terms of time complexity (IO method by [11]) on two counts: a) dependence on n, b) dependence on F . we found this algorithm significantly outperforming the IO algorithm empirically -we show two plots here.


For example, if we take n = 100000, L = 100, and µ = 0.01 then the basic FG method has a rate of ((L − µ)/(L + µ)) 2 = 0.9996 and the 'optimal' AFG method has a faster rate of (1 − µ/L) = 0.9900.

running n iterations of SAG has a much faster rate of (1 − 1/8n) n = 0.8825 using the same number of evaluations of f i .


We note that when classifying a new point one does not have to project it to the subspace V , but rather assign a sign according to the classifying hyperplane in R d . In first sight it seems that our result gives a week generalization bound since the margin obtained in the original dimension is low.

the margin of the found solution in the reduced dimension (i.e., within V ) is almost optimal (i.e.


ditioned stimulus (US); the two stimuli are separated by a stimulus-free gap.

in delay conditioning, the CS remains on until presentation of the US.


. . , β k ) and let θ * β be the minimizer of is zero for even a single outlier (x, y), then L(θ * β , ∞) will be infinite.

we can bound θ * β under an alternative loss that is less sensitive to outliers: The key idea in the proof is that replacing S with exp(β ψ) in p θ,β does not change the loss too much, in the sense that When β min 1, Hence, the error increases roughly linearly with β −1 min .


Without convexity or g-convexity, in general at best we might obtain local minima.

as alluded to previously, the set P d of hpd matrices possesses remarkable geometric structure that allows us to extend global optimisation to a rich class beyond just gc functions.


The ID-SP and LF-SP agents both experience two object play slightly more often than the ID-RP baseline, having achieved substantial one object play time.

only the ID-SP agent has discovered how to take advantage of the increased difficulty and therefore "interestingness" of two object configurations (compare blue with green horizontal line in Fig.


A weaker model is the oblivious adversarial model wherein the adversary generates a k-sparse vector in complete ignorance of X and w * (and ).

the adversary is still free to make arbitrary choices for the location and values of corruptions.


One prominent application is their use in modeling conditional independence between random variables via a graphical model.

when the number or random variables is large, and the underlying graph structure is complex, a number of computational issues need to be tackled in order to make inference feasible.


Our specific setup is as follows: for each (s, a) ∈ S×A an uncertainty set U(s, a) is given.


In agreement with theorem 2.1 the measure of these non-informative center points is zero.

if we use as a center point a point on one of the axes, the distribution of the distances will be very different.


The recent success in human action recognition with deep learning methods mostly adopt the supervised learning paradigm, which requires significant amount of manually labeled data to achieve good performance.

label collection is an expensive and time-consuming process.


For example the nearest neighbor classifier in the new distance is equivalent to the Lipschitz regularization (1) weighted with the density proposed in the last section.

implementing such a method requires to compute the geodesic distance in (R d , g), which is non trivial for arbitrary densities p. We suggest the following approximation which is similar in spirit to the approach in [11].


On the one hand, the ultimate goal is to achieve the best possible prediction error.

budgeted computational resources need be factored in, while designing algorithms.


With this property, it is no longer true that all inner distances are smaller than outer distances, and therefore Theorem 6.1 does not apply.

[BBV08] prove the following lemma Lemma 6.3.


This is a Nyquist-type reconstruction formula.

for this theory to be applicable to a real-time setting, as in the case of BMI, we need a causal real-time decoder that estimates the signal at every time t, and an estimate of the time taken for the convergence of the reconstructed signal to the real signal.


Combined with a suitable likelihood function as specified in Equation 2, one can construct a regression or classification model that probabilistically accounts for uncertainties and control over-fitting through Bayesian smoothing.

if the likelihood is non-Gaussian, such as in the case of classification, inferring the posterior process is analytically intractable and requires approximations.


An overview of estimators of the entropy of continuous-valued distributions is given in [30].

to our knowledge, the entropy bias of maximum entropy models in the presence of modelmisspecification has not be characterized or studied numerically.


To address this issue, one may be tempted to use the weak * -topology on 2 , since in this topology the closed balls are both compact and metrizable, thus universal kernels do exist on them.

the Taylor kernels do not belong to them, because -basically-the inner product • , • 2 fails to be continuous with respect to the weak * -topology as the sequence of the standard orthonormal basis vectors show.


From this equation we obtain, Using lemma 1 we have an upper bound on the probability that sup {t1,...,tm} | Îob − Îun | > ǫ over the random selection of features, as a function of m ′ .

the upper bound we need is on the probability that sup {t1,...,tm} |E( Îob ) − E( Îun )| > ǫ 1 .


Experimentally, we found that the trust score better identifies correctly-classified points for low and medium-dimension feature spaces than the model itself.

high-dimensional feature spaces were more challenging, and we demonstrate that the trust score's utility depends on the vector space used to compute the trust score differences.


There is a "ground truth" image G on the bottom of the pool.

overhead, a stationary camera pointing downwards is recording a video stream V . In the absence of any distortion V (x, y, t) = G(x, y) at any time t. the water surface refracts in accordance with Snell's Law.


Its two nested sampling loops can be parallelized in a straightforward way since the variables are independent of each other.

in practice, we use a small number of random labels, and m n. Thus we only need to parallelize the sampling for the set of random transmission times {τ ji }.


The mismatch between this predicted efficiency and animals' actual behaviour has been attributed to the presence of information-limiting correlations between neurons [22,23].

deviation from independence renders most analytical treatments infeasible, necessitating the use of numerical methods (Monte Carlo simulations) for quantifying the performance of such codes [7,15].


[19] proposed a model which jointly infers the true labels and estimate of evaluator's quality by modeling decisions as functions of the expertise levels of decision makers and the difficulty levels of items.

this approach neither models the error properties of decision makers, nor provides any diagnostic insights into the process of decision making.


One of the key benefits of RNNs is their ability to make use of previous context.

for standard RNN architectures, the range of context that can in practice be accessed is limited.


As mentioned before, while Theorem 1 allows for going lower than the standard log n bound on the community size for exact recovery, it requires the number of very small communities to be relatively small.

theorem 2 provides us with the option of having many small communities but requires the smallest community to be of size O(log n) .


To conclude that the animal probably has wings, you might consult a mental representation similar to the graph at the top of Figure 1a that specifies a dependency relationship between flying and having wings.

you might reach the same conclusion by thinking about flying creatures that you have previously encountered (e.g.


It is easy to see that for suitably weighted kNN graphs this is the case: the original density can be estimated from the degrees in the graph.

it is completely unclear whether the same holds true for unweighted kNN graphs.


If an estimated value consists of a large portion of such transitions, then the likelihoods of overestimation and underestimation are both very low.

if backward transition probability p j,j (or any p j,k with k ≤ j) is close to 1, then Var[ Dj ] increases dramatically, resulting a noticeable skewness.


The rate of the code is proportional to the CS budget and we use the rate as a proxy for budget throughout this analysis.

since different types of query have different costs both financially (in crowdsourcing platforms) and from the perspective of time or effort it takes from the user to process it, one needs to be careful in comparing the results of different coding schemes.


Note that when H 2 (f + f − ) is close to 1, e.g., when the side information is perfect, no queries are required.

that is not the case in practice, and we are interested in the region where f + and f − are "close", that is .


If no match is found, we assign the fixation as null.

due to noise, we allow the spatial support to be increased by a factor.


The second intuition is to use the online least squares formulation of the linear equation Ax = b.

since A is not symmetric and positive semi-definite (PSD), A 1 2 does not exist and thus Ax = b cannot be reformulated as Another possible idea is to attempt to find an objective function whose gradient is exactly A t x t − b t and thus the regularized gradient is prox αth(xt) (A t x t − b t ).


First, the Tensor Toolbox [7] uses the method of reducing indices of the tensor for sparse datasets and entrywise multiplication of vectors and matrices for dense datasets.

it is not clear how to store data or how to distribute the tensor factorization computation to multiple machines (see Appendix D).


Our original goal was to develop BO algorithms for aiding this process.

many aspects of this domain complicate the application of BO.


The attention mechanism that we have employed is just one instantiation of a very general idea which can be further exploited.

the incorporation of world knowledge and multi-document queries will also require the development of attention and embedding mechanisms whose complexity to query does not scale linearly with the data set size.


5, but we allow the distribution of the standardized variable to depend (at least weakly) on v. We now generalize the reparameterization idea to distributions that, like the gamma or the beta, do not admit the standard reparameterization trick.

we assume that we can efficiently sample from the variational distribution q.zI v/, and that q.zI v/ is differentiable with respect to z and v. We introduce a random variable defined by an invertible transformation where we can think of D T 1 .zI v/ as a standardization procedure that attempts to make the distribution of weakly dependent on the variational parameters v. "Weakly" means that at least its first moment does not depend on v. For instance, if is defined to have zero mean, then its first moment has become independent of v. we do not assume that the resulting distribution of is completely independent of the variational parameters v, and therefore we write it as q . I v/.


This approach is, as we have discussed, suitable for a standard Bloom filter, where the false positive rate is guaranteed to be close to its expected value for any test set, with high probability.

this methodology requires additional assumptions in the learned Bloom filter setting.


Our results indicate that in finite dimensions, an efficient, compression-based, Bayes-consistent multiclass 1-NN algorithm exists, and hence can be offered as an alternative to k-NN, which is well known to be Bayes-consistent in finite dimensions [12,41].

in infinite dimensions, our results show that the condition characterizing the Bayes-consistency of k-NN does not extend to all NN algorithms.


The variable X 0 may be distributed as X 0 ∼ p(•|θ 1 ) for some true parameter θ 1 .

in order to incorporate under-modeling, the existence of such a true parameter is not required.


The nonparametric online algorithm of [6] is known to have a suboptimal regret bound for Lipschitz classes of functions.

it is a simple and efficient algorithm, well suited to the design of extensions that exhibit different forms of adaptivity to the data sequence.


Due to the exchangeability of the individuals, the case where Friend(A, B) and Friend(A, C) are assigned to True and False respectively has the same WMC as the case where they are assigned to False and True.

the current engines fail to exploit this symmetry as they consider grounded individuals non-exchangeable.


Thus, computing ∂/∂φ j of (19) exactly is mechanical.

using this approximation gives up the usual guarantee that the ELBO lower bounds the marginal likelihood.


On the surface, our network appears similar to AC-GAN [24], where the only difference is the separation of the classifier network from the authenticator network.

this crucial modularisation enables our DA algorithm to replace GANs by other generative models that may become available in the future; likewise, we can use the most sophisticated classification models for C. Furthermore, unlike our model, the classification subnetwork introduced in AC-GAN mainly aims for improving the quality of synthesized samples, rather than for classification tasks.


To solve this problem, Ng & Russell (2000) proposed to first learn a reward function, assuming that the expert is optimal, and then use it to recover the expert's complete policy.

the problem of learning a reward function given an optimal policy is ill-posed (Abbeel & Ng, 2004).


We cannot directly take the large £ limit, since for large word lengths we eventually reach a data sampling limit beyond which we are unable to reliably compute the word distributions.

if there is a range of £ for which the distributions are sufficiently well sampled, the behavior in Eq.


For the evaluation purpose alone, it is enough to use only a query q itself as an example.

we include both one target node (among potentially many other target nodes) and one path from the starting node to this target node (again, among many possible connecting paths) so that they can be exploited when training an agent.


In most previous studies of MAB and linear stochastic bandits, a common assumption is that noises in observed payoffs are sub-Gaussian conditional on historical information (Abbasi-Yadkori et al., 2011;Bubeck et al., 2012), which encompasses cases of all bounded payoffs and many unbounded payoffs, e.g., payoffs of an arm following a Gaussian distribution.

there do exist practical scenarios of non-sub-Gaussian noises in observed payoffs for sequential decisions, such as highprobability extreme returns in investments for financial markets (Cont and Bouchaud, 2000) and fluctuations of neural oscillations (Roberts et al., 2015), which are called heavy-tailed noises.


[17,18] prove that the REC is satisfied when the design matrix is sub-Gaussian.

rEC might not be guaranteed when the row of X follows heavy-tailed distribution.


Binarized Networks, Quantized Networks and the DoReFa-Net.

we believe Flexpoint strikes a desirable balance between aggressive extraction of performance and support for a wide collection of existing models.


When shown a set of M = 36 images consisting mostly of different types of outdoor scenes and a few indoor scenes, it is reasonable for a worker to consider the indoor scenes as a unified category.

if a HIT is composed purely of indoor scenes, a worker might draw finer distinctions between images of offices, kitchens, and living rooms.


In the beginning, Greedy chooses to execute distractors, since they gives positive reward while subtasks A, B, and C do not.

gRProp observes non-zero gradient for subtasks A, B, and C that are propagated from the parent nodes.


SRNN (Fraccaro et al., 2016) addresses the issue by running a posterior backward in the sequence and thus providing future context for the current prediction.

the autoregressive decoder is not informed about the future of the sequence through the latent variables.


Floating point encodes numbers with one exponent per value (Figure 1a), requiring complex hardware structures to manage mantissa alignment and exponent values.

bFP (Figure 1b) shares exponents across blocks of numbers (or tensors), which enables dense fixed point logic for multiply-and-accumulate operations.


This strategy applied to active learning is well known because of its simplicity and its ability to adapt to unknown noise conditions [24].

we mention that when used in this way, this sampling procedure is known to be sub-optimal so in practice, one may want to implement a more efficient approach like that of [21].


In spite of the empirical success in many applications, most of the existing models and the corresponding estimators are based on specific distributions of pairwise measurements, whose correctness hinges on that the models are correctly specified.

in practice, without the knowledge of the true model, applying these methods might incur huge estimation errors.


First, the convolutional layers of DeepSpeech2 contain more phonetic information than those of DeepSpeech2-light (+1% and +4% for cnn1 and cnn2, respectively).

the recurrent layers in DeepSpeech2-light are better, with the best result of 37.77% in DeepSpeech2-light (by lstm3) compared to 33.67% in DeepSpeech2 (by rnn5).


We also anticipate that such analysis is more easily extendable.

the new form of the gradient step due to nonsmoothness of absolute function requires new developments of bounding techniques.


Note that the full Hessian, H, will in general, not be positive definite (in fact rank(H) = rank(H)).

based on its special structure, we can still give convergence guarantees (along with rate of convergence) for our algorithm.


Note that SVP-Newton incurs a RMSE of 0.89 for k = 3.

sVT achieves a RMSE of 0.98 for the same rank.


Using recurrent neural networks to predict sequences of tokens has many useful applications like machine translation and image description.

the current approach to training them, predicting one token at a time, conditioned on the state and the previous correct token, is different from how we actually use them and thus is prone to the accumulation of errors along the decision paths.


When using convolutions as part of a larger network, with multiple parallel filters, max pooling, and non-linear activations, the situation is of course more complex, and we do not expect to get the exact same bias.

we do expect the bias to be at the very least related to the sparsity-infrequency-domain bias that we uncover here, and we hope our work can serve as a basis for further such study.


For example, [2] builds a model that couples this point of view with a representation in terms of deep multi-task Gaussian Processes with vector-valued kernels.

the objective in [2] is to predict fixed time risk (e.g.


Figure 2(b) shows higher ACh ( ¡ ) and NE (© ¡ levels both correspond to fast learning, ie fast shifting of `¡ .

whereas NE is a constant monitor of prediction errors and fluctuates accordingly with every data point, ACh falls smoothly and predictably, and only depends on the observations when global changes in the environment have been detected.


Block Partial Leverage Scores Sampling Recall standard leverage scores of a matrix A are defined as diagonal elements of the "hat" matrix A(A T A) −1 A T [15] which prove to be very useful in matrix approximation algorithms.

in contrast to the standard case, there are two major differences in our task.


As a result, the vertices of the motifs are partitioned with a uniform cost.

this assumption is hardly realistic as in many real networks, only some vertices of higher-order structures may need to be clustered together.


The work [9] proves that the proximal Coordinate Descent method can solve each QPs at a linear rate even when matrix A is not full column rank.

there exists several drawbacks in this approach: (i) the practical solving time of each subproblem is quite long when A is rank-deficient; (ii) the theoretical performance and complexity of using recent accelerated techniques in proximal optimization [14] with the ALM is unknown; (iii) it cannot exploit the specific structure of matrix A when solving each constrained QP.


Previous generative approaches include modeling worlds of painted polyhedra [11] or constructing surfaces from patches taken out of a training set [3].

discriminative approaches attempt to differentiate between changes in the image caused by shading and those caused by a reflectance change.


If at least one point is violated, then the new set (Q, b, s,~) is not feasible for the KKT system (1) with the extended data set.

it is easy to find p such that (Q, b, s, ~) is optimal for (3).


Due to space constraints, we relegate the details of our experiments to the appendix in the supplemental documents.

the results of the experiments are clear-Figures 1(g), 2(g), 3(g), and 4(g) show the mean squared error (MSE) of value estimates when using various methods.


Recently, the convolutional neural networks (CNNs) have been greatly successful for large-scale image classification tasks [17,30,27] and have also demonstrated promising results for structured prediction tasks (e.g., [4,23,22]).

the CNNs are not suitable in modeling a distribution with multiple modes [32].


We show in the supplementary material that if z = (z, 0) and z(i) denotes the ith largest element of z, In particular, if Y ∈ Y = {−1, 1} is binary the dual problem (11) for learning the optimal linear predictor α * given n samples (x i , y i ) n i=1 will be The first term is the empirical risk of a linear classifier over the minimax-hinge loss max{0, 1−z 2 , −z} as shown in Figure 2.

the standard SVM is formulated using the hinge loss max{0, 1 − z}: We therefore call this classification approach the minimax SVM.


We do not have an analytic solution for these equations.

the decomposition they offer allows us to solve them by searching first over b to solve (7), then plugging the result into (8) to get an estimate of a.


Given space considerations, and the fact that the resulting algorithm turns out to reduce to Algorithm 2 from [3] with the squared Euclidean distance replaced by an appropriate Bregman divergence, we will omit the full specification of the algorithm here.

despite the similarity to the existing Gaussian case, we do view the extension to hierarchies as a promising application of our analysis.


when the algorithm can be confident that µ j1 > µ j k . This chaining approach initially seems overly conservative when ruling out arms, as reflected in its regret bound, which is only non-trivial after T k 3 .

the UCB algorithm [5] achieves non-trivial regret after T = O(k) rounds.


. . , u(x n )) T ∈ R n and the covariance or kernel matrix by The Bayesian posterior process for u(•) can be computed in principle using Bayes' formula.

if the noise model P (y|u) is non-Gaussian (as is the case for binary classification), it cannot be handled tractably and is usually approximated by another Gaussian process, which should ideally preserve mean and covariance function of the former.


The coding of information by neural populations depends critically on the statistical dependencies between neuronal responses.

there is no simple model that can simultaneously account for (1) marginal distributions over single-neuron spike counts that are discrete and non-negative; and (2) joint distributions over the responses of multiple neurons that are often strongly dependent.


If the normal to the water surface directly underneath x is pointing straight up, there is no refraction and V (x) = G(x).

if the normal is tilted by angle θ 1 , light will bend by the amount θ 2 = θ 1 − sin −1 ( 1 1.33 sin θ 1 ), so the camera point V (x) will see the light projected from G(x + dx) on the ground plane.


It is important to note here that the GE operators themselves add layers to the architecture (thus this experiment does not control precisely for network depth).

they do so in an extremely lightweight manner in comparison to the standard computational blocks that form the network and we observe that the improvements achieved by GE transfer to the deeper ResNet-101 baseline, suggesting that to a reasonable degree, these gains are complementary to increasing the depth of the underlying backbone network.


In the special case when G h ≡ G ∪ , this gives the graph estimate of the components.

the union graph G ∪ appears to have no direct relationship with the marginalized model P (y).


We also adopt the same prior on E given by ( 7) above and used in [1] and [31], but we need not assume any additional hyperprior on Γ.

for the prior on Z our method diverges, and we define the Gaussian where z vec[Z] is the column-wise vectorization of Z, ⊗ denotes the Kronecker product, and Ψ c ∈R n×n and Ψ r ∈R m×m are positive semi-definite, symmetric matrices.


The resurrection of neural networks in recent years, together with the recent emergence of large scale datasets, has enabled super-human performance on many classification tasks [21,28,30].

supervised DNNs often require a large number of training samples to achieve a high level of performance.


A short derivation (see supplementary material) then shows that the normalized importance weights are defined by a recursion: SIS is elegant as the samples and weights can be computed in sequential fashion using a single forward pass.

naïve implementation suffers from a severe pathology: the distribution of importance weights often become highly skewed as t increases, with many samples attaining very low weight.


2 Then the objective O and gradient ∇O can both be computed in O(nkb) time.

our experience with minimizing O with such an approach using a quasi-Newton L-BFGS algorithm typically resulted in poor local optima; we need an alternative method.


For all the experiments, we use the optimization program ( 5), where we typically set λ = 10.

the clustering and embedding results obtained by SMCE are stable for λ ∈ [1,200].


Our model differs from these in that it uses a global memory, with shared read and write functions.

with layer-wise weight tying our model can be viewed as a form of RNN which only produces an output after a fixed number of time steps (corresponding to the number of hops), with the intermediary steps involving memory input/output operations that update the internal state.


this only holds, if the loss reaches zero, i.e.


The same steps, but with φ(u) = − log u, lead to the bound ) is the so-called lautum information between M and (X n , Y n ) [26], and the second inequality holds whenever N ≥ 2.

it is often more convenient to choose Q as follows.


DRE has also been widely discussed in statistical literatures for adjusting non-parametric density estimation [5], stabilizing the estimation of heavy tailed distribution [7] and fitting multiple distributions at once [8].

as a density ratio function can grow unbounded, DRE can suffer from robustness and stability issues: a few corrupted points may completely mislead the estimator (see Figure 2 in Section 6 for example).


This method reduces the labeling cost to a great degree compared with expert labeling.

the cost still grows quadratically as the dataset size grows, so it is still only suitable for small datasets.


The assumption that the mode of the posterior distribution of the classifier remains unchanged after seeing an additional label is clearly not true at the beginning of the active learning procedure.

we have empirically found it a very good approximation after the active learning procedure has yielded as few as 15 labels.


the fluorescence signal), and, for model comparison, we would like to compute the model evidence, the computation of these quantities is intractable, and this intractability has hindered the application of Bayesian techniques to large-scale data analysis, such as calcium imaging.


Our field of view is reduced by the output lenses.

in principle, it is possible to remove the lenses and expect the neural network to include the free-air propagation operator, from the fibre output to the camera, in its learning process as well.


On one hand, in neuroscience, recent studies point out that there are significant redundant neurons in human brain, and memory may have relation with vanishment of specific synapses [4].

in machine learning, both theoretical analysis and empirical experiments have shown the evidence of redundancy in several deep models [5,6].


Finally, the bandit arms may be indexed by numbers from the real line, implying uncountably infinite bandit arms, but where "nearby" arms (in terms of distance along the real line) have similar payoffs [12,14].

none of these approaches allows for arms to appear then disappear, which as we show later critically affects any regret bounds.


Smoothing We observed that the proposed sharpening methods indeed helped with long utterances.

all of them, and especially selecting the frame with the highest score, negatively affected the model's performance on the standard development set which mostly consists of short utterances.


As indicated by the confusion matrix in Figure 2 (right), our method results in clusters that correspond to reasonable categories.

it is clear that the data often has finer categorical distinctions that go undiscovered.


By choosing relevant tags, users aid in creating a more organized information system.

content owners may have their own individual objective, such as maximizing the exposure of their items to other browsing users.


In other words, if in the m th iteration we move from label f m to f m+1 then it is possible that there exists another labelling .

our analysis in the next section shows that we are still able to reduce the Gibbs energy sufficiently at each iteration so as to obtain the guarantees of the LP relaxation.


The classic GLM is a valuable tool for describing the relationship between stimuli and spike responses.

the GLM describes this map as a mathematically convenient linear-nonlinear cascade, which does not take account of the biophysical properties of neural processing.


A finite convex combination of copulas is a copula, so r (a) is a copula density.

given a set of estimated quantile values A, a suitable parameter values β (edge weight matrix) and θ (parameters for bivariate edge copulas) can be found by maximizing the log-likelihood of A: the parameter optimization of l (β, θ) cannot be done analytically.


The time complexity to answer a transitive query for a discrete CBN is exponential in the maximum number of parents in the worst case.

the sample complexity for queries in discrete and continuous CBNs remains polynomial in n as prescribed in the following theorems.


They are able to predict semantic features even for words for which they have not seen scans and experiment with differentiating between several zero-shot classes.

they do not classify new test instances into both seen and unseen classes.


A second related model is Hofmann's probabilistic latent semantic indexing (pLSI) [3], which posits that a document label d and a word ware conditionally independent given the hidden topic z : ( This model does capture the possibility that a document may contain multiple topics since p(zld) serve as the mixture weights of the topics.

a subtlety of pLSIand the crucial difference between it and LDA-is that d is a dummy index into the list of documents in the training set.


In order to guarantee that the estimation error β (t) − β * in step t of the EM algorithm is well controlled, we would like Q n (•|β (t−1) ) to be strongly concave at β * .

in the setting where n p, there might exist directions along which ) is flat, e.g., as in mixed linear regression and missing covariate regression.


This is due to the fact that the appearance (or descriptors) of keypoints differ considerably for large offset pairs (which is likely when the image set is large), leading to many false matches.

our method improves as the size of the image set increases.


Zero-Shot Learning (ZSL) is generally achieved via aligning the semantic relationships between the visual features and the corresponding class semantic descriptions.

using the global features to represent fine-grained images may lead to sub-optimal results since they neglect the discriminative differences of local regions.


The main challenge in solving such problems is that communication between the different machines is usually slow and constrained, at least compared to the speed of local processing.

the datasets involved in distributed learning are usually large and high-dimensional.


For example, in document data, we can reasonably assume that documents can be clustered based on their relations with different word clusters, while word clusters are formed according to their associations with distinct document clusters.

in the one-sided clustering mechanism, the duality between samples and features is not taken into consideration.


The original formulation of CCCP by Yuille and Rangarajan [30] deals with unconstrained and linearly constrained problems.

the same formulation can be extended to handle any constraints (both convex and non-convex).


Stochastic gradient methods for machine learning and optimization problems are usually analyzed assuming data points are sampled with replacement.

sampling without replacement is far less understood, yet in practice it is very common, often easier to implement, and usually performs better.


The simplest Poisson-based generalised-linear RLM might take as its output distribution where y ti is the spike count of the ith cell in bin t and the function f is non-negative.

comparison with the output distribution derived for the Gaussian RLM suggests that this choice would fail to capture the instantaneous covariance that the LDS formulation transfers to the output distribution (and which appears in the low-rank structure of S above).


where c k=1 kπ k = c. The distribution over the size of the subset a new item joins is then The additional complication however is that, unlike the typical CRP situation, the partitioning itself is unknown, and so we must marginalize over it under the prior when computing the distribution on η x .

we can recognize this as simply using the expected number of subsets of a particular size: where The probability of the partition π is the EPPF [21] multiplied by the unordered multinomial coefficient: where Γ(•) is the gamma function.


Interestingly, it is this same Jeffreys prior that forms the implicit weight prior of SBL (see [6], Section 5.1).

it is worth mentioning that other Jeffreys prior-based techniques, e.g., direct minimization of p(w) = i 1 |wi| subject to t = Φw, do not provide any SBL-like guarantees.


The key motivation behind RCRN is to provide expressive and powerful sequence encoding.

unlike stacked architectures, all RNN layers operate jointly on the same hierarchical level, effectively avoiding the need to go deeper.


Most of these results make specific assumptions on the cascades/graph structure, and assume a full observation setting.

in our problem, the structure of the social graph is assumed to be known, and the goal is to provably learn the underlying influence function.


The probabilistic interpretation opens doors to several extension of the basic setup proposed in [3] which suggested a maximum likelihood approach for parameter estimation.

it still assumes an apriori fixed number of canonical correlation components.


It is important to note that the linear time algorithm in [11,Section 5.5.1] is the key to obtaining a O(nd/ √ ) computational complexity for binary SVMs with bias mentioned in Section 5.1.

this method has been rediscovered independently by many authors (including us), with the earliest known reference to the best of our knowledge being [14] in 1990.


This is because CorrLDA can capture direct dependencies between languages, due to the constraints that topics have to be selected from the topics selected in the pivot language parts.

cI-LDA and SwitchLDA are too poorly constrained to effectively capture the dependencies between languages, as mentioned in Sections 2.1 and 2.2.


Then, K * hom (n) ≤ cK * , where The intuition is that as K increases, we experience diminishing returns with respect to µ because µ is bounded away from 1.

there is a loss due to decreasing L = n/K , the number of representatives.


The variance in the precision decreases as b increases.

for KSHcut the variance is larger and the precision barely increases after b = 80.


But, the problem definition in these works does not specify a target prediction vector or variable; the goal instead is to select diverse features regardless of whether the features are relevant for predicting a particular target variable.

our work requires us to simultaneously optimize for both feature selection and diversity objectives.


1 Equation ( 1) is the standard MLE estimator.

sometimes the unbiased MLE estimation is preferred, where m − 1 replaces m in the denominator.


This allows us to apply our results also to more general forms of regularizers, including squared p norm regularizers, r(w) = λ 2 w 2 p , for p < 1 ≤ 2 (see Corollary 2).

the reader may choose to read the paper always thinking of the norm w , and so also its dual norm w * , as the standard 2 -norm.


As such, there has recently been increased interest towards developing techniques for parallelizing these methods.

these algorithms are inherently sequential and are difficult to parallelize.


This would be quite expensive for large number of items N , since the number of labels scales asymptotically as T ∈ Ω(N 2 ).

we expect a noisy transitive property to hold: if items a and b are likely to be in the same cluster, and items b and c are (not) likely in the same cluster, then items a and c are (not) likely to be in the same cluster as well.


since they include all the constraints from the beginning and the null model is fully connected, their method is only applied to small toy problems.


As the teacher is unaware of the internal workings of the learner, she has no control over which of these two policies the learner will eventually learn by matching feature expectations.

the teacher can ensure that the learner achieves better performance in a worst case sense by providing demonstrations tailored to the problem at hand.


In the convergence proof [7,28], it is assumed that θ i converges to θ * as the number of iterations i increases, then the proof consists of showing that θ * is a critical point of p(θ|y).

in practice, either the E-step or M-step or both can be difficult to compute exactly, especially when working with deep learning models.


Simulation-based search with value function approximation has been investigated in large and also continuous MDPs, in combination with TD-learning [19] or Monte-Carlo control [3].

this has not been in a Bayes-adaptive setting.


Using a 5 component spectral mixture kernel we were able to fully reconstruct the hexagonal lattice structure of the true field despite the size of the observed region covering only about 2 times the length scale of the periodic pattern.

traditional methods (including GP-based inference with standard SE kernels) would fail completely at such extrapolation.


This algorithm recursively computes the moments in a top-down fashion along the tree.

this algorithm breaks down when the graph is a DAG.


The algorithm prefers rare and unusual anchor words that form a poor basis, so topic clusters consist of the same high-frequency terms repeatedly, as shown in the upper third of Table 3.

our algorithm with AP rectification successfully learns themes similar to the probabilistic algorithm.


The currently fastest algorithm for SO, in [MBK + 15], has runtime O(n log 1 δ ) and an expected guarantee of (1 − 1/e) − δ .

the slightly slower, but still nearly linear time O( n δ log n δ ) thresholding algorithm in [BV14], has (the usual) deterministic guarantee of (1 − 1/e) − δ .


If the cascade is already rejecting the negative example, then this term becomes 0 and the classifier ignores its performance on the specific example.

if the cascade is performing poorly, then the term becomes increasingly large and the classifiers put large weights on that example.


With carefully engineered observation features, there does not appear to be very much to be gained from using higher order features.

in some situations, the training data does not come from the same distribution as the test data.


Especially 1 when wi = 0, then Fii is related to subgradient of w w.r.t to wi.

we can not set Fii = 0, otherwise the derived algorithm cannot be guaranteed to converge.


The state-of-the-art approach [12] which utilizes clutter reasoning in the image plane has an error of 21.2%.

our  approach which uses a parametric model of clutter and simple 3D volumetric reasoning outperforms both the approaches and has an error of 16.2%.


If they are defined to match spatially the differences to detect, they can also improve the signal-to-noise ratio by averaging related signals.

the crux of the problem is how to define these ROIs in a principled way.


The ability to tractably simulate MCs along with the generic applicability has made Markov Chain Monte Carlo (MCMC) a method of choice and arguably the top algorithm of the twentieth century [1].

mCMC and its variations suffer from limitations in large state spaces, motivating the development of super-computation capabilities -be it nuclear physics [2,Chapter 8], Google's computation of PageRank [3], or stochastic simulation at-large [4].


Because of the known convergence of spectral projections, we can expect the same behavior asymptotically from the finite sample case.

the convergence speed is the crucial question.


These models appear promising for applications such as language modeling and machine translation.

they scale poorly in both space and time as the amount of memory grows -limiting their applicability to real-world domains.


This ill-conditioning issue of real-number erasure codes has also been recognized in a recent communication problem [20].

our novel way of combining all the partial results including those from the stragglers helps bypass the difficulty of inverting an ill-conditioned matrix.


We find that for x 0 = 1 + ", SGD always escapes and converges to x = 0 instead of staying in the initial basin, as long as " 6 = 0 and ⌘ is relatively large (one trajectory of is shown in Figure 2 in red).

sGD starting from x 0 = " with the same learning rate always converges to x = 0, and we never observe the escape phenomenon.


Solutions to this problem have found applications in many areas of science and engineering.

many real-world applications do not map neatly into this framework.


We see that the improper learning method for the constraint harms the model performance, partially because of the relatively low-quality model samples the constraint is trained to fit.

the proposed algorithm effectively improves the model results.


These bounds on τ lead to a deeper understanding of CoreCut.

they are difficult to implement in practice.


Figure 4 illustrates this transformation.

and where Because we have a matrix-variate t distribution, (H 1 , H 2 ) ∼ t m,d+p (δ − p, 0, αI (m) , I (d+p) ).


We define the biased conductance φ p (S) of a set S ⊂ {1, . . . , n} to be , where Z 0 is chosen according to a fixed distribution p. Just as with the standard definition of conductance, we can interpret biased conductance as an escape probability.

the initial state Z 0 is not chosen following the stationary distribution (as in the standard definition with a reversible chain) but following p instead.


[15] developed a model selection strategy for DPS by reusing the past observed sample sequences through the importance weighted cross-validation (IWCV).

iWCV requires heavy computational costs and includes computational instability when estimating the importance sampling weights.


Since the FCP clusters are unlabelled they do not suffer from label switching problems.

by having labelled clusters HMMs can share statistical strength among clusters across time steps (e.g.


Nevertheless, recently it has been shown to be possible to give a nontrivial certified lower bound of minimum adversarial distortion, and some recent progress has been made towards this direction by exploiting the piece-wise linear nature of ReLU activations.

a generic robustness certification for general activation functions still remains largely unexplored.


They have recently received increasing attention for developing optimization algorithms with fast convergence.

the studies of EBC in statistical learning are hitherto still limited.


Intuitively, this is what one would expect: Q-learning is based on the single estimator and Double Q-learning is based on the double estimator and in Section 2 we argued that the estimates by the single and double estimator both converge to the same answer in the limit.

this argument does not transfer immediately to bootstrapping action values, so we prove this result making use of the following lemma which was also used to prove convergence of Sarsa [20].


As a consequence, different nodes will be frequently exposed to missing data.

most current distributed data analysis methods are algebraic in nature and cannot seamlessly handle such missing data.


the basic conclusions regarding learning with kernel methods and NNs turn out to be valid more generally, e.g.


In the iris problem we obtained excellent clustering results using the first two principal components, whereas in the crabs problem, clustering that depicts correctly the classification necessitates components 2 and 3.

once this is realized, it does not harm to add the 1st component.


When d = 1, the quantile transforms F −1 (α j ) are uniquely defined as the points x j ∈ R satisfying F (X ≤ x j ) ≤ α j , where X is a random variable drawn from F . Equivalently, F −1 (α j ) can be identified with the unique hierarchical intervals [−∞, x j ].

when d > 1, intervals are replaced by sets C 1 ⊂ C 2 . . . ⊂, C q that satisfy F (C j ) = α j but are not uniquely defined.


This shows that even for a single bit, the problem of finding optimal codes is NP hard.

the analogy to graph partitioning suggests a relaxed version of the problem that leads to very efficient eigenvector solutions.


Thus they are difficult to generalize to new circumstances, where the counterparts are unknown or intractable to construct.

unsupervised manifold alignment learns from manifold structures and naturally avoids the above problem.


MP problem is often mapped to a graph, and reduced to a graph search problem.

different from our problem, the MP approaches aim to find an optimal path to the goal in the graph while avoiding obstacles similar to HTN approaches.


On the other hand, if the gradient calculations are stochastic, then a similar claim cannot be made.


All of these patches will be at similar depths, even if there are small discontinuities (such as a window on the wall of a building).

when viewed at the smallest scale, some adjacent patches are difficult to recognize as parts of the same object.


Thus, minimizing the general dynamic regret can automatically adapt to the nature of environments, stationary or dynamic.

the restricted dynamic regret is too pessimistic, and unsuitable for stationary problems.


At first, the lower bound for linear classifiers might suggest that ∞ -robustness requires an inherently larger sample complexity here as well.

in contrast to the Gaussian model, non-linear classifiers can achieve a significantly improved robustness.


If the user can pick any element and suggest that it should precede an entire block of elements it currently follows, then we can instead use an "INSERSION SORT" graph; interestingly, to ensure the property (*), this graph must be weighted.

as we show in Section 3, if the user can propose two arbitrary elements that should be swapped, there is no graph G with the property (*).


For keeping the stimulation waveforms as simple as possible, only postsynaptic adaptation has been included.

it has been shown that presynaptic short-term plasticity also has a strong influence on long-term learning [19,6].


Thus, if the blinding index falls short of the predetermined threshold, the data is effectively thrown away and the trial needs to be repeated.

if the blinding index exceeds the threshold, the analysis of data is performed in the same manner regardless of the actual value of the index, that is, regardless of whether it is just above the threshold or if it indicates perfect blinding.


If q is initially very far from p, Monte Carlo estimates will tend to under-estimate the partition function.

in the context of learning p, we may expect a random initialization of p to be approximately uniform; we may thus fit an initial q to this well-behaved distribution, and as we gradually learn or anneal p, q should be able to track p and produce useful estimates of the gradients of p and of Z(θ).


While neural machine translation (NMT) is making good progress in the past two years, tens of millions of bilingual sentence pairs are needed for its training.


This is perhaps most pronounced in a student/teacher scenario where the teacher provides positive feedback for successful communication and corrections for unsuccessful ones [8,22].

in general any reply from a dialog partner, teacher or not, is likely to contain an informative training signal for learning how to use language in subsequent conversations.


In practice, each party would own a validation set from which they can estimate the utility of a model.

due to the small size of the three datasets, we report the contamination and validation accuracy of a model on the single validation set created during pre-processing of the data.


In this case, the KL divergence is tractably computable (up to a neglectable prefactor).

this form of the KL divergence chooses q(s i |r) to be any one of a very large number of local modes of the posterior distribution p(s i |r).


For a certain layer, a single threshold can be set based on the average absolute value and variance of its connection weights.

to improve the robustness of our method, we use two thresholds a k and b k by importing a small margin t and set b k as a k + t in Equation (3).


This appears to be a key bottleneck and reinforces the view that the use of random features cannot provide computational benefits -it suggests m = Ω(n) random features are required to get a O (1/ √ n) rate.

these rates are conservative when viewed in the sense of excess risk.


It clusters trajectories and assumes that all the trajectories in a cluster are generated by a single reward function.

as a consequence of using EM clustering, we need to specify the number of clusters (i.e.


Their method produces comparable cuts to the ones in [5], while being computationally much more efficient.

they could not provide any convergence guarantee about their method.


The capacity of an LSTM network can be increased by widening and adding layers.

usually the former introduces additional parameters, while the latter increases the runtime.


A generative method builds a flexible probabilistic model for generating the noisy observations conditioned on the unknown true labels and some behavior assumptions, with examples of the Dawid-Skene (DS) estimator [5], the minimax entropy (Entropy) estimator 1 [24,25], and their variants.

a discriminative approach does not model the observations; it directly identifies the true labels via some aggregation rules.


. . , s m ] are scaling factors for the parameter w. To combat overfitting, we assign a Gamma prior Gam(λ v |c 0 , d 0 ) over λ v . Note that this generative model encourages w to align with the major eigenvectors with bigger eigenvalues.

eigenvectors are noisy and not all of them relevant to the classification taskwe need to select relevant eigenvectors (i.e.


[25] developed theoretical tools to recognize and generate G-convex functions as well as cone theoretic fixed point optimization algorithms.

none of these three works provided a global convergence rate analysis for their algorithms.


For general graphs, Problem 1 can only be solved exactly when S contains all n 2 true effective resistances.

given additional constraints on G, recovery is possible with much less information.


The difference between the two components of the GMM-FV is not as startling for lower dimensional SIFT features [13].

for CNN features, the discriminative power of variance statistics is exceptionally low.


One potential issue with having a loss at every step is that it might encourage the network to learn a greedy algorithm that gets stuck in a local minima.

the output function r separates the node hidden states and messages from the output probability distributions.


In other words, both methods are quite good at ranking for classification.

the classification rates of our method are better by about 10% for both 3-object and 4object cases.


On the one hand, short phases allow a high rate of adaptivity, since � X j is recomputed very often.

if a phase is too short, it is very unlikely that the estimate θj may be accurate enough to actually discard any arm.


The matrix exponentiated gradient updates ensure that the estimates for the rotation matrix stay on the manifold associated with the rotation group at each iteration.

with the matrix exponentiation at each step, the updates are computationally intensive and in fact the computational complexity of the updates is comparable to other approaches that would require repeated approximation and projection on to the manifold.


If we assume ideal conditions where both computation resources (CPU, GPU, other accelerators) and communication resources (communication links) are unlimited or abundant in counts/bandwidth, then the total runtime of Pipe-SGD is: where K denotes the iteration dependency or the gradient staleness.

we observe that the end-to-end training time in Pipe-SGD can be shortened by a factor of K. the ideal resource assumption doesn't hold in practice, because both computation and communication resources are strictly limited on each worker node in today's distributed systems.


Graph-like geometric structures arise naturally in many fields, both in modeling natural phenomena, and in understanding abstract procedures and simulations.

there has been only limited work on obtaining a general-purpose algorithm to automatically extract skeleton graph structures [2].


Using only the energy for training should, in principle, gives a good PES model.

the use of forces in the training process significantly reduces the number of snapshots needed to train a good model.


Adam, the first occasional human "driver", often takes control of his car to brake whereas Bob never interrupts his car.

when Bob's car is too close to Adam's car, Adam does not brake for he is afraid of a collision.


The estimate of the corresponding costto-go value inherits this variability.

it also displays a downward bias caused by the minimization over u t . This phenomenon is reminiscent of overfitting effects in statistics.


To some extent, the aforementioned two-layer sampling has relationship with directly sampling from the product space of query and document, and the (n, m)-sampling proposed in [4].

as shown below, they also have significant differences.


Similar Newton-type methods that relied on sub-sampling rather than sketching were also studied by [14].

they are chiefly concerned with the convergence of the iterates to the (stochastic) minimizer of the least squares problem, while we are chiefly concerned with the convergence of the iterates to the unknown regression coefficients β * .


We acknowledge that RANGE-LSH and SIMPLE-LSH are equivalent when all items have the same 2-norm.

mIPS is equivalent to angular similarity search in this case, and thus can be solved directly with sign random projection rather than SIMPLE-LSH.


Recognition involves sampling based on the strength of the associative activation of the list given a specific item and so is independent of the encoding strength of other items.

recall involves sampling from p(item|list) across all items, in which case, having a distribution favoring other items will reduce the probability that the unstrengthened items will be sampled.


A scene graph provides a structured description that captures these properties of an image.

reasoning about the relationships between objects is very challenging and only a few recent works have attempted to solve the problem of generating a scene graph from an image.


Compared with GPR applied to a lattice, lattice regression with a GPR bias again produces a lower RMSE on all five lattice resolutions.

for four of the five lattice resolutions, there is no performance improvement as judged by the statistical significance of the individual test errors.