Compared with GD, which achieves -stationarity using O( N i=1 L i / ) gradient evaluations in the worse case (in the sense that N i=1 L i /N = L), the rate in [21] is O(N 1/3 ) times better.

the algorithm in [21] is different from NESTT-G in two aspects: 1) it does not generalize to the nonsmooth constrained problem (1.1); 2) it samples two component functions at each iteration, while NESTT-G only samples once.


Unfortunately, if the assumption of the independence of features is not satisfied, e.g., if we have almost same features, then ws does not converge to w * .

if we introduce an 1 -regularization to the minimization problem in the definition of w s and change the definition of ws to a weighted average of the modified vectors w 1 , .


Deep neural networks (DNNs) have outperformed traditional methods at several supervised learning tasks.

they have a large number of parameters that need to be estimated from data, which makes them especially vulnerable to learning relationships between target variables and nuisance factors and, thus, overfitting.


For slow-moving variables that represent a "level" (as opposed to a "difference" or a "return"), one can conceivably keep their value constant to the last known realization across the forecasting period.

this solution is restrictive, problem-dependent, and precludes the incorporation of short-term dynamics variables (e.g.


This is likely due to the fact that these algorithms optimize the generalized KL divergence directly, while multi-layer NMF is a greedy algorithm with sub-optimal solutions.

our mfNMF algorithm consistently outperforms the method of [9] by a significant margin, with on average 40% less iterations.


One advantage of the mixPLDS model is that it not only returns cluster assignments for neurons but also provides a measure of uncertainty over these assignments.

variational inference tends to return over-confident posteriors in general and the factorization approximation (5) might yield posterior uncertainty that is uninformative.


There are many existing methods, such as pitch perception model based methods, and probabilistic approaches [4,15,16,17].

multi-pitch estimation is a very difficult problem and remains unsolved.


This map moves N points of mass 1/N each a distance at most 2✏ n (K), so we may bound Combining these two bounds, we see that For each n, we choose to set N = n, which yields W 2 (⌫ n,n , ⌫ ⇤ )  2✏ n (K) + Cn 1/d .

applying Lemma 4.1, and recalling that ⌫ ⇤ is the minimizer of J, we have we must have , because both are measures on the same n point 2✏ n (K)cover, but ⌫ ⇤ n has weights chosen to minimize J.


It can be noted that increasing the sparsity of signal shifts the phase transitions to the right.

the phase transition for Block CoPRAM has a less apparent shift (suggesting that sample complexity of m has sub-quadratic dependence on s).


For the combined sources, MDAN always perform better than the source-only baseline (MDAN vs. Combine-Source).

a naive combination of different training datasets can sometimes even decrease the performance of the baseline methods.


The diagonal set would work well with the exact constraints but badly with pseudo-max, and the difference can be arbitrarily large.

the input distribution on the right, populating the J * + x 2 = 0 decision line, would permit pseudo-max to identify J * .


In the first, non-stochastic setting [7,11], the reward is generated by an adversary instead of a stationary, stochastic process.

the reward observed by the learner is still a real reward, in that the learner is still interested in maximizing it, or more precisely, minimizing some notion of regret in reference to some reference policy [8].


SLEEC also significantly outperforms methods such as WSABIE [13] which also use kNN classification in the embedding space but learn their embeddings using the traditional low-rank assumption.

clustering based speedup: kNN classifiers are known to be slow at prediction.


[15] are another gradient based approach which uses the same architecture and relaxation as SPENs.

the training objective is inspired by value based reinforcement learning.


( 4) gives us a concrete expression for evaluating the risk of p(O).

to evaluate a potential query, we also need its expected posterior risk.


In general, an RKHS is usually smaller than the L 2 space defined on the same input domain.

so, it is not always true that fλ,G * achieves f . one can choose to use universal kernels K uj so that their corresponding RKHSs are dense in the L 2 spaces (see [3], [15]).


Our second contribution is another algorithm, PEGE2, which combines gap estimation with a PEGE algorithm, to achieve an O(log T ) regret bound, matching the GCB guarantee but removing the dependence on size of the learner's action space.

like GCB, PEGE2 requires access to both offline oracles and the existence of a unique optimal action.


For large graphs, it simply has the effect of normalizing all hitting times to ≈ 1, leading to C LN K ≈ 2.

we believe that the ranking introduced by this distance function still contains useful information about the data.


If either of these are too large, then it will affect the accuracy of our final estimator.

if p is uniform on a domain of size Θ(n), it must be the case that ).


In particular, the joint peristimulus time histogram (JPSTH) and its integral, the shuffle-corrected correlogram [1,2,3] have become widely used tools to analyze such data.

the JPSTH and correlogram cannot distinguish correlations induced by connections between the two measured neurons (direct connection correlations) from correlations induced by common connections from a third, unmeasured neuron (common input correlations).


Such a conditional independence property is essential for the guarantees that we will present in this work to extend to a BAYES-CCE and hence do not seem to extend to the notion given in [4].

as we will show in Section 5, the no-regret dynamics that we analyze, which are mathematically equivalent to the dynamics in [4], do converge to this smaller set of BAYES-CCE that we define and for which our efficiency guarantees will extend.


The mutual information rate measures the rate at which the spike train removes uncertainty about the stimulus.

the mutual information estimate does not depend on identifying either the relevant features of the stimulus or the relevant features of the response, which is crucial in analyzing the response to such complex stimuli.


1 can be computed in parallel for each node i, because they depend only on the parameters from the previous iteration.

mPLP follows a block coordinate descent strategy in which optimization is performed over a subset of variables, keeping all the other variables fixed [5].


This is indeed the case, as state-of-the-art recognition algorithms may still significantly underperform human.

note that for a system to work in a real-world scenario such as aid-giving robots, it is crucial that the agent be able to take direct perceptual inputs.


Of many inference problems one can formulate using a GM, computing the partition function (normalization), or equivalently computing marginal probability distributions, is the most important and universal inference task of interest.

this paradigmatic problem is known to be computationally intractable in general, i.e., it is #P-hard even to approximate [11].


Secondly, for different values of α, MST and TSP need to be recomputed since the distance between two points is the p-th power of their Euclidean distance where p = d(1 − α).

the k-NN graph does not change for different values of p, since p-th power is a monotone transformation, and hence the estimates for multiple values of α can be calculated without the extra penalty incurred by the recomputation of the graph.


This phenomenon is closely linked to the graph connectivity issues associated with SSC, mentioned before.

in particular, under a random-sample model, the true positive rate for SSC will go to zero as N t /d t grows, where N t is the number of samples from S t with dim(S t ) = d t . the true positive behavior for CSC has several favorable characteristics.


We remark that the same multi-stage scheme (especially the setting of m and n 0 ) Algorithm 1 is due to [8], which was also used in several stochastic optimization algorithms for solving different problems [11,12].

the difference from these studies is that ∂ Q t (θ) is not an unbiased stochastic gradient of Q(θ).


Figure 4 (Right) shows that AQM nearly always chooses the true target image from 10K candidates in six turns if the PropAcc λ is 1.0.

aQM also chooses correctly with a probability of 51% and 39% (accuracy of goal-oriented dialog) in six turns, when the PropAcc λ is 0.95 and 0.90, respectively.


At the very least, RCRN provides comparable efficiency to using stacked BiLSTM and empirically we show that there is nothing to lose in this aspect.

we note that CUDA-level optimizations have to be performed.


Another related body of work lies in the field of competitive analysis -see [5], which also deals with loss functions that depend on the player's past actions, and the adversary's memory may even be unbounded.

obtaining sublinear regret is generally impossible in this case.


However, this scales poorly as mentioned earlier.

one may replace µ with µ K , yielding the finite-dimensional NRMM (FNRMM), for which efficient variational Bayes can be developed provided that the finite-dimensional process is ideal.


This form of coding was loosely inspired by the idea of "energy landscape" coding proposed by Hinton and Brown [2].

contrary to [2] and other theories using rate-based representation of probabilities, this model is self-consistent and does not require different models for encoding and decoding: As output spikes provide new, unpredictable, temporally independent evidence, they can be used directly as an input to other Bayesian neurons.


FHMMs are widely used in energy disaggregation.

the resulting model has a huge (factored) state space, making standard inference FHMM algorithms infeasible even for only a handful of appliances.


In the extreme case where all of the top-k eigenvalues of B are identical and equal to m − 1, the expression for c is : and thus the approximation is less meaningful.

in contrast to the MAP objective, this degradation of approximation is gradual, and catastrophic failure such as that seen in Figure 1 is completely avoided.


For the analysis described herein, we assume the balanced N-ary tree to simplify discussions of computational complexity.

arbitrary state space trees do not change the substance of what follows.


More importantly, in BayesSCDC the variational posterior gathers information from L through message passing in the relational model.

the amortized form q(z|o)q(x, z|o) used in SCDC ignores the effect of observed annotations L. Another advantage of the inference algorithm in BayesSCDC is in the computational cost.


In words, this theorem says that intra-dipole correlations do not disrupt the estimation process by creating local minima, and that the global minimum is always unbiased.

inter-dipole correlations can potentially create local minima, but they do not affect the global minimum.


For large values of ρ the following holds: where Setting the derivatives ( 9) and ( 10) to zero and inserting equations (8) yields the following necessary conditions for a maximum of the free energy that hold in the limit ρ → ∞: Note that equations (11) are not straight-forward update rules.

we can use them in the fixed-point sense and approximate the parameters which appear on the right-hand-side of the equations using the values from the previous iteration.


Averaging of the green points which are close with respect to the geodesic distance is still reasonable.

the blue points which are close with respect to the Euclidean distance are not necessarily close in geodesic distance and therefore averaging can fail.


The motion of a simulated whisker in reaction to external forces from a collision is constrained only by the fixed spatial location of the follicle, and by the damped dynamics of the springs at each node of the whisker.

although the spring equilibrium displacements are determined by static measurements as described above, the damping factors and spring stiffnesses cannot be fully determined from these data.


Over the last decade multiple authors have introduced explicit reductions showing how stochastic planning can be solved using probabilistic inference (for example, [4,25,5,17,23,12,8,19,26,10,18]) with applications in robotics, scheduling and environmental problems.

heuristic methods and search are still the best performing approaches for planning in large combinatorial state and action spaces [9,7,2].


As our next step in this direction, we will begin exploring this mapping with Neurogrid, a hardware platform with sixteen programmable neuromorphic chips that can simulate up to a million spiking neurons in real-time [9].

bandwidth limitations prevent Neurogrid from realizing random connectivity patterns.


Lastly, it is important to notice that MFA performs slightly better than LRMC, demonstrating the importance of the union of low-dimensional subspaces model for the problem.

getting trapped in local optima does not allow MFA to take full advantage of such a model, as opposed to SSC-Lifting.


That is, an optimal design (one that minimizes the final posterior entropy) can be planned out entirely in advance of the experiment.

this does not hold for linear-Gaussian models with non-Gaussian priors, such as those considered here.


In particular, it has been shown that a slow-and-smooth prior, and related models, can qualitatively account for a range of experimental results [17,15,16] and can quantitatively account for others [7,12].

the integration strategy modeled by the slow-and-smooth prior may not generalize to more complex motion types, such as circular and radial motion, which are critically important for estimating ego motion.


On one hand, Skew-Top100 simulates the case that at the startup phase of a service, popular recipes are first published, while less frequently used recipes are introduced later.

skewNonTop100 captures the opposite situation.


In [7,5,19] a more general case of Legendre-type cost functions is considered.

note that additive loss functions are commonly used, if one considers i.i.d.-drawn examples.


We can see that SqueezeNet [7] has the smallest size.

the speed is even slower than AlexNet and the accuracy is not competitive to other compact CNNs.


Each time interval provides evidence as to the value ρ it .

given prior distribution ρ it ∼ Beta(α it , β it ), the posterior is to limit the evidence provided from each item, we scale it by a factor of n. When all locations are considered, the resulting posterior is: where F i is feature map i and χ t is the set of locations containing elements of type t. With the approach we've described, evidence concerning the value of ρ it accumulates over a sequence of trials.


Given the relative success of previous studies with low resolution faces it is reassuring that 21-by-12 faces can, in fact, be used for reliable sex classification.

most of the previous studies used datasets of relatively few faces, consequently with little statistical significance in the reported results.


This network was designed to have limited parameters, requiring 2200 for their smallest model.

the SyncNet filters are simple to interpret and require learning only a few hundred parameters.


Unfortunately, any discontinuous reward function will usually lead to discontious values functions so that this assumption is violated in many settings of interest.

we only require that the future value is Lipschitz in the sense of equation ( 3).


In other words, using longer sequences helps to learn a communication protocol faster.

this is not at all the case for the REINFORCE estimator: it usually takes five-fold more updates to converge compared to GS-ST, and also there is no clear dependency between the number of updates needed to converge and the maximum possible length of a message.


[12] analyzed a single-loop algorithm based on Nesterov's AG method for deterministic non-convex optimization.

none of these studies provide an explicit complexity guarantee on extracting NC from the Hessian matrix for a general non-convex problem.


2    The large margin principle has played a key role in the course of machine learning history, producing remarkable theoretical and empirical results for classification (Vapnik, 1995) and regression problems (Drucker et al., 1997).

exact large margin algorithms are only suitable for shallow models.


Note that the proof can be easily extended to column equilibration, and row and column equilibration.

we can not prove that the Jacobi preconditioner improves the upper bound, which provides another justification for using the equilibration preconditioner.


In addition, recent dynamic Poisson-based models such as [24,47,40,1] analyze sequential count vectors.

mGDMF has the conjugate Gamma-Markov chains and aggregates the static portions with the dynamic portions at each time slice and prevents the instability of the chains.


Consequently, many researchers are now working on developing semi-supervised learning techniques for a variety of approaches, including generative models [14], self-learning [5], co-training [3], information-theoretic regularization [6,8], and graph-based transduction [22,23,24].

most of these techniques have been developed for univariate classification problems, or class label classification with a structured input [22,23,24].


For the experiments presented in this paper, we will assume that the operator U that is utilized in MAML and E-MAML is stochastic gradient descent.


Some other researchers explored different types of multilingual topic models that are based on the premise of using multilingual dictionaries or WordNet [9,10,11].

cI-LDA and SwitchLDA only require multilingual comparable documents that can be easily obtained, such as from Wikipedia, when we use those models for multilingual text analysis.


The methods relying on a whitening step [2][3][4], will perform the whitening using the matrix E † l obtained from the low-rank SVD truncated at rank l: TPM will use E l to whiten the tensor M 3 to a tensor T l 2 R l⇥l⇥l .

when k > l, T l may not admit a symmetric orthogonal decomposition 4 .


The experimental design consists of randomized stimuli, thus all runs of repetitions or alternations are spurious, and any behavioral tendencies driven by such patterns are useless.

compared to artificial experimental settings, truly random sequential events may be rare in the natural environment, where the laws of physics and biology dictate that both external entities and the observer's viewpoint undergo continuous transformations for the most part, leading to statistical regularities that persist over time on characteristic timescales.


The quality of f is measured by its excess risk, which is the expectation of its loss `(Y, f (X)) minus the expected loss of the best prediction function f ⇤ in a given class of functions F. Analysis in this setting usually involves giving guarantees about the performance of f in the worst case over the choice of the distribution of the data.

the setting of sequential prediction (also called online learning) [2] makes no probabilistic assumptions about the source of the data.


It is worth noting that, since the gain function g(v i ) defined in Eq (1) has no upper saturation, recurrent interactions can easily result in runaway excitation and firing rates growing unbounded.

our optimization algorithm will naturally seek stable solutions, in which firing rates are kept within a limited range due to a fine dynamic balance of excitation and inhibition [14].


Hence, the circuit model can be used to describe short-term synaptic depression in a network simulation.

the nonlinear recovery dynamics of the circuit model leads a different functional dependence of the average steady-state EPSP on the frequency of a regular input spike train.


We first show that an algorithm that naively uses the predicted number of days to decide whether or not to buy is 1-consistent, i.e., its competitive ratio is 1 when η = 0.

this algorithm is not robust, as the competitive ratio can be arbitrarily large in case of incorrect predictions.


Following this road may lead to designing efficient selection criteria for BO methods (for example new ways to augment gradient information with BO).

it remains to be addressed how our findings scale up to higher dimensions and benchmark optimization problems.


Now from all x ∈ D which result in the same truncated representation, we select a single representative to be included in D This results in a set D of size at most (4nT ) n/2 which is a 1/ √ T -net for D. That is, every x ∈ D is at distance at most 1/ √ T from its nearest neighbor in D. Since an admissible loss vector has norm at most √ n, summing over the T rounds of the game, we see that the optimal loss for D is within an additive √ nT of the optimal loss for D. For implementation purposes, it may be impractical to store the decision set (or the covering net of the decision set) explicitly as a list of points.

our algorithms only require the ability to sample from a specific distribution over the decision set.


The main idea is to use distributions of gradient orientations in order to be insensitve to color, brightness and contrast changes and, to some extent, local deformations.

to account for more macroscopic variations, due for example to changes in pose, a more complex statistical model is warranted.


Empirically, it is shown that the proposed GHN benefits from a fast and robust learning process that is on par with that of the batch-normalization approach, yet without resorting to sophisticated learning process of additional parameters (see Section 4 for experimental results).

gHN also benefits from the rapid developments of neural computing techniques, in particular, those employing parallel computing on GPUs.


Let C ⊂ R D be a convex set and let x ∈ C. Then for all z, we have where y ≡ argmin y∈C d f (y, z) is the projection of z onto C. At first glance, the Pythagorean theorem may appear to be a triangle inequality for Bregman divergences.

the inequality is actually the reverse of the standard triangle inequality and only applies to the very special case when y is the projection of z onto a convex set containing x.


Hence, to improve our results in the situation where d Q is closed to 1/2, one will have to consider higher moments.

it is not clear that this will lead to a better bound of R(B Q ) because, even if Theorem 5 generalizes to higher moments, its tightness is then degrading.


One major issue that complicates the direct use of their approach for the VRP is that it assumes the system is static over time.

in the VRP, the demands change over time in the sense that once a node has been visited its demand becomes, effectively, zero.


Existing ALP methods for factored finite-state MDPs search for this subset more efficiently by taking advantage of local constraint decompositions and various heuristics.

at the end these methods always rely on the fact the decompositions are defined on a finite state subspace.


The conditional draw of p(x t+1 |y t ) encourages taking samples with smaller density value (inefficient moves), within the domain of the slice interval X.

when a > 1, draws of y t tend to take smaller values, while draws of x t+1 encourage sampling from those with large density function values (efficient moves).


Furthermore, given any point x = (x 1 , ..., x d ) generated from the distribution Λ, calculating ŷ the regression model output (5), involves finding a ŷ that solves equation ( 12), where z = (ŷ, x 1 , ..., x d ), and, recalling from above, for ŷ is in general a nonlinear single variable optimization problem, which can be solved using a root finding algorithm (for example the Newton-Raphson Method outlined in [4]).

below we present a specific form of nonlinear K c (z i , z) that allows (12) to be solved analytically.


When using unidirectional RNNs as generative models, it is straightforward to draw samples from the model in sequential order.

inference is not trivial in smoothing tasks, where we want to evaluate probabilities for missing values in the middle of a time series.


Such a dependency may potentially be useful in a multi-group setting.

when all data are contained in a single group as in the current study sharing the same mixture component across multiple cluster distributions leads to shared mixture components being statistically unidentifiable.


Functional MRI: Neural activity signals are composed of brief spikes and are considered sparse.

observations via functional magnetic resonance imaging (fMRI) are distorted by convolving with the hemodynamic response function.


To date, almost all techniques of text classification are based on words, in which simple statistics of some ordered word combinations (such as n-grams) usually perform the best [12].

many researchers have found convolutional networks (ConvNets) [17] [18] are useful in extracting information from raw signals, ranging from computer vision applications to speech recognition and others.


It is straightforward to create deeper variants of the model by augmenting SyncNet with additional standard convolutional layers.

in our experiments, adding more layers typically resulted in over-fitting due to the limited numbers of training samples, but will likely be beneficial in larger datasets.


Moreover, their estimate of the fODF is useful for tracking the fascicles through the white matter for estimates of connectivity.

these estimation techniques either use different variants of NNLS, with a discrete set of candidate directions [2], or with a spherical harmonic basis set [1], or use stochastic algorithms [9].


Until recently, limitations in experimental methods have made it challenging to test hypotheses about synaptic plasticity on a large scale.

as such data become available and these barriers are lifted, it becomes necessary to develop analysis techniques to validate plasticity models.


Notice that since f de (S) is not monotone in general [13], we cannot use Theorem 3.

in the case when δ ≥ 1, a simple application of Lemma 13 shows that f de (S) becomes monotonically increasing and we can then use Theorem 3 to obtain a tighter approximation bound.


By Chebyshev's inequality, an estimator with finite variance enjoys the tail bound P( At the expense of working with slightly more conservative step-size policies (see below), much of our analysis goes through with this weaker requirement for the tails of ξ.

the extra control provided by the O(1/z q ) tail bound simplifies the presentation considerably, so we do not consider this relaxation here.


With a fixed hidden dimension of 2,048, the required preview window width does not change significantly, which is consistent with the observations in Section 4.1.

the number of full-view vectors N should increase as the vocabulary size grows.


In classification, one seeks a binary-valued function h : X →Y that predicts the class of a new instance in X .

in ranking, one seeks a real-valued function f : X → R that induces a ranking over X ; an instance that is assigned a higher value by f is ranked higher than one that is assigned a lower value by f . The area under the ROC curve (AUC) has recently gained some attention as an evaluation criterion for the bipartite ranking [3].


One active research topic is to reach a stationary point for unconstrained optimization [35; 32; 1] or constrained optimization [18; 27].

without proper assumptions, a stationary point may not lead to any global approximation guarantee.


[12,Theorem 3.1] have shown that in smooth Banach spaces -and in particular in the Hilbert space L 2 ρ (X) -an -greedy incremental sequence of functions can always be constructed.

not every such sequence of functions converges to the function with respect to which it was constructed.


The computational complexity of LQDEXP3 is exponential in the dimension d due to the discretization step, hence quickly becomes impractical when the number of features is large.

one can easily modify the algorithm to run without discretization by replacing EXP3 with its continuous version.


The recent resurgence of interest in this task has been driven in part by the development of new and larger benchmark datasets such as Flickr 8K [4], Flickr 30K [5] and COCO Captions [6].

even the largest of these datasets, COCO Captions, is still based on a relatively small set of 91 underlying object classes.


This energy functional looks quite abstract.

in a special coordinate system on M , the so called normal coordinates, one can evaluate it quite easily.


Removing a rule will yield a simpler model but may lower the likelihood.

we can prove that the loss in likelihood is bounded as a function of the support.


However, it is impractical to expect an end user specifying the desired program to also provide the correct execution trace for the program, since devising the trace is almost as much work as writing the actual program itself.

if neural networks can learn to synthesize programs from input/output examples as shown by Bunel et al.


In other words, as the quality of social network increases, the minimum sample complexity decreases.

the gain of side-information is characterized as diminishing returns: When Is is larger than a certain threshold, the minimum sample complexity stops decreasing.


More concretely, for sufficiently small we argued that δ 3k [Φ] > 1/ √ 32 for all k, and consequently convergence to the optimal solution may fail.

it can be shown that δ * 3k [Φ] will remain quite small, satisfying implying that performance will nearly match that of an equivalent recovery problem using A (and as we discussed above, δ 3k [A] is likely to be relatively small per its unique, randomized design).


In any case, if we define µ ij = k w k f ik f jk to be the similarity predicted by a particular choice of F and w, then: where σ 2 is the variance of the Gaussian error distribution.

self-similarities s ii are not modeled in additive clustering, and are generally fixed to (the same) arbitrary values for both the model and data.


The results show that the solution is insensitive to neither the population size N nor the choice of the matching algorithm, which implies that we can use the cheap approximated matching and relatively small population size for speed.

decreasing the mini-batch size |B| improves the final PMD significantly, supporting our claim in Sec.


• Empirical evidence of the viability of our approach on real-world datasets.

in general, even to represent a probability distribution P (V ) over discrete variables 1 V we need space exponential in the size n of V . junction trees of limited treewidth allow compact representation and tractable exact inference.


Historically, models and variational families for which expectations were simple enough to allow closed-form updates of w were used [2,3,32].

for more complex models, closed form expressions are usually not available, which has led to widespread use of stochastic optimization methods [8,18,19,20,26].


Evidence for both directions has been reported previously (17; 18).

details of the dynamic information flow during scene processing, such as when and how significant the feedback effect is, is not well understood.


To evaluate diversity, we follow [5] to use Dist-1 and Dist-2, which is characterized by the proportion between the number of unique n-grams and total number of n-grams of tested sentence.

this metric neglects the frequency difference of n-grams.


The practical need to avoid state enumeration is a key motivation for POMDP compression.

the complexity of the search for a good compression must also be independent of the state space size.


To solve (9), we first take the convex surrogate of the objective function, which corresponds to an 1 / p -norm [29,30], where we drop the indicator function and, for p ∈ {2, ∞}, solve The nonnegative parameter λ is a regularization parameter and the function ρ(•) ∈ {ρ e (•), ρ a (•)} enforces whether the reconstruction of each point should be exact or approximate, where More specifically, when dealing with missing entries from noise-free data, which perfectly lie in multiple subspaces, we enforce exact reconstruction by selecting ρ(•) = ρ e (•).

when dealing with real data where observed entries are corrupted by noise, exact reconstruction is infeasible or comes at the price of losing the sparsity of the solution, which is undesired.


[2016] also develop a differentiable physics engine, with motivations similar to our own.

in this case they made their engine differentiable by simply implementing it in its entirety in the Theano framework [Al-Rfou et al., 2016].


The non robustness of k-means has led to the development of many formulations of robust clustering, see a review by [14].

we show that our joint loss yields an estimator that has a non-zero breakdown point, and is hence robust.


It is also widely accepted that the function f (•) (or the functionf (•)) is a nuisance function as we do not observe its value and its sole purpose is for a convenient formulation of the model [14].

in this paper, we show that by using privileged information as the noise term, the latent function f now plays a crucial role.


Note that the majority of false positive errors are confusion with background and localization errors.

after adapting the network using LSDA we find that the errors found in the top false positives are far less due to localization and background confusion (see Figure 5(c)).


Recently, support vector machines (SVMs) [4] have been used for phoneme (or phone) recognition [5] and have shown encouraging results.

use of a standard SVM classifier by itself implicitly assumes i.i.d.


Some of these heuristics -such as average-linkage -implicitly try to create clusters of small "radius" throughout the hierarchy.

to the best of our knowledge, there is so far no procedure which specifically hillclimbs the space of hierarchical clusterings according to a precise objective function.


Another straightforward approach is to employ a majority vote among the players: let each player independently identify an arm, and choose the arm having most of the votes (alternatively, at least half of the votes).

this approach does not lead to any improvement in performance: for this vote to work, each player has to solve the problem correctly with reasonable probability, which already require Ω(H ε ) pulls of each.


Of course, multi-category text may sometimes be weighted more toward one category than to the rest of the categories among multiple categories.

being averaged over all biases, they could be canceled and therefore PMM1 would be reasonable.


It is worth noting that the regret bound of the UCB algorithm π F1:∞ depends on the specific confidence sets {F t : t ∈ N} used by the algorithm whereas the bound of π TS applies for any sequence of confidence sets.

the decomposition (3) holds only in expectation under the prior distribution.


Since the cutting plane model is usually inaccurate when p is far away from {p j } i j=1 , the updated solution p could be significantly off target [3].

a regularization term p − p i 2 2 /2 is introduced in SD to prevent the new solution being far from the current one, p i .


at iteration i + 1, and n,t,r ✓ i ,s,r ✓i , P (R ✓ n t 1 = r ✓ , S n t = s, R ✓ n t = r✓|s n , a n , ⇤ i ) can be computed efficiently by exploiting the intermediate results from evaluating P (R ✓ n t = r ✓ |s n , a n , ⇤ i ) described previously, as detailed in Appendix B.

if the feature measurements of ' s can be observed by the agent during the expert's demonstration, then recall that we use a generalized linear model to represent ⌧ !


Inverse Reinforcement Learning (IRL) approaches attempt to learn the objective function that the demonstrations are optimizing and show better generalization capabilities.

iRL approaches often require a model of the domain, can be limited by the representation of the reward function and are learning a policy indirectly.


Performing this task at the state-of-the-art level requires an intertwined meld of probability theory, computational mathematics, and software engineering.

a number of factors unite to allow us to solve the algorithm design problem computationally: 1.


Machine learning models are vulnerable to adversarial examples: small changes to images can cause computer vision models to make mistakes such as identifying a school bus as an ostrich.

it is still an open question whether humans are prone to similar mistakes.


Let N 2 N µ,⌫ (n, d) be a random network as in Definition 1.

for any fixed input to N , we have the fourth moment of Z p,q (x) is exponential in Moreover, there exists a constant C K,µ > 0 depending only on K and the first 2K moments of the measures {µ Remark 2.


Looking at alternative models (in which phase transitions are known), we have found that this rapid degradation co-incides with the appearance of multiple fixed points.

the behavior of the TRW method is extremely stable, consistent with our theory.


In the binary classification setup, learning with complementary labels is equivalent to learning with ordinary labels, because complementary label 1 (i.e., not class 1) immediately means ordinary label 2.

in K-class classification for K > 2, complementary labels are less informative than ordinary labels because complementary label 1 only means either of the ordinary labels 2, 3, . . . , K. The complementary classification problem may be solved by the method of learning from partial labels [5], where multiple candidate class labels are provided to each training pattern-complementary label y can be regarded as an extreme case of partial labels given to all K 1 classes other than class y.


Then we randomly select point (x, y, z) to sample a video clip of fixed size 80 × 80 × t. A common alternative is to pre-process data by using a sliding window approach to have pre-segmented clips.

this approach limits the amount of data when the windows are not overlapped as in [28].


Our deployment of sensors throughout the estuary has resulted in an actual reduction of the error loss from 68% to 35%.

this figure does not adequately reflect the efficacy of the detectors.


The regret for this choice is O(ln T ), which is better than O(T 2/3 ) of Section 4.1.

the constant depends on the gap ∆ which can be small.


This equivalent formulation suggests a naive sampling (NS) algorithm for approximating σ(A, T ): draw n samples of {τ ji } (j,i)∈E , run a shortest path algorithm for each sample, and finally average the results (see Appendix C for more details).

this naive sampling approach has a computational complexity of O(nC|V||E| + nC|V| 2 log |V|) due to the repeated calling of the shortest path algorithm.


This coefficient can be arbitrarily large: consider the case where µ concentrates on a single starting state (that is µ(s 0 ) = 1 for a given state s 0 ) and such that the optimal policy leads to other states (that is, d µ,π * (s 0 ) < 1), the coefficient is then infinite.

it is also the best concentrability coefficient according to [21], that provides a theoretical and empirical comparison of Approximate Policy Iteration (API) schemes.


Alternatively, nonsmooth SDPs can be solved by ALM.

the augmented primal and dual objective functions are still complex SDPs, which are equally expensive to solve in each iteration.


Implications for Portfolio Selection: By comparing Propositions 1 and 2, the first interesting conclusion one can reach about portfolio selection is that, without considering any additional information, the worst-case CVaR criterion yields the same optimal portfolio weighting x as the worst-case VaR criterion (recall that VaR minimizes α in Proposition 1 by adjusting x while CVaR minimizes f by adjusting x in Proposition 2).

the worst-case distributions for the two approaches are not the same, which can be seen from the relation ( 16) between VaR and CVaR and observing that α in ( 4) is not the same as in (19).


Then our theorem indicate that as long as m = poly(N, 1/δ ), where δ is the minimal distance between each examples, we can actually fit arbitrary labels of the input data.

since the total iteration only depends on log m, when m = poly(N, 1/δ ) but the input data is actually structured (with small k, l and large δ), then SGD can actually achieve a small generalization error, even when the network has enough capacity to fit arbitrary labels of the training examples (and can also be done by SGD).


Ensuring consistency requires frequent translations between moment and canonical parameterizations, which is the origin of potentially severe numerical instability [10].

eC works largely with moment parameterizations of Gaussians, for which relatively few numerical difficulties arise.


Technically our technique is related to the random walk approach [16].

we note that our algorithms aggregate full rankings under PL, while the RC algorithm aggregates pairwise comparisons.


In the standard semi-supervised learning framework, given only a small number of training images with strong annotations, one needs to infer the full segmentation labels for the rest of the data.

it is not plausible to learn a huge number of parameters in deep networks reliably in this scenario.


By Theorem 1 and 2, f 1 B and f 2 B do not satisfy as many desired normative properties as the Kemeny rule for winners.

they minimize Bayesian risk under F 1 ϕ and F 2 ϕ , respectively, for which Kemeny does neither.


This algorithm updates the policy differently from κ-API.

similarly to κ-API, it uses hard updates.


A more general approach is to adapt both marginal feature and conditional distributions by minimizing a global divergence between them.

this task is usually hard since no label is available in the target domain and therefore no empirical version P t (Y |X) can be used.


. . is introduced such that x t and x ′ t are independent and identically distributed given "the past".

"the past" is itself an interleaving choice of the original sequence and the tangent sequence.


This observation is justified in the following sense: the upper bound of β grows proportionally to √ m π .

the classical exponential mechanism does not have that kind of prior-dependency.


These policies manage to achieve expected returns with less than © loss.

the average loss of a random policy is about ' § (or ).


Its instantiation in PR is the GCPRL algorithm.

the key benefit of developing the SDP solution for PR in this paper is that the global convergence can be guaranteed.


By following these steps, one can find the WFOMC of many theories in polynomial time.

if we reach a point where none of the above rules are applicable, we ground one of the populations which makes the process exponential in the number of individuals.


Our HSCRF is related to the conditional probabilistic context-free grammar (C-PCFG) [9] in the same way that the HHMM is to the PCFG.

the context-free grammar does not limit the depth of semantic hierarchy, thus making unnecessarily difficult to map many hierarchical problems into its form.


There is more detail in the appendix about the joint action expansion.

the key point is that if the current cost and partial derivatives can be calculated for each parameter, one can construct the affine function for each agent.


From an application point of view, previous segmentation systems for extracting basic movements employed considerable human intervention [16].

automatic probabilistic methods for modeling movement templates assumed that the time-series data was pre-segmented into basic movements [5,17].


This algorithm, and thus each step in the numerical optimization, has exponential time complexity O(E t N Ct t ) where C t is the size of the maximal clique in G t [18].

the learning subroutine for an DCNN requires only one forward and backward pass for each instance in the training data.


1/↵) multiplied by the inverse KL divergence between the null and anomalous distributions.

when the two distributions are not well separated then the necessary sample complexity explodes to this latter quantity squared.


• We show that determining whether there is a PSNE in (3) is NP-complete.

there is a polynomial-time algorithm to compute a PSNE for (1).


The relative density ratio is always upper-bounded by 1 α , which can give a more robust estimator.

it is not clear how to de-bias such an estimator to recover the true density ratio function.


4 Since � K k=1 π k = 1, using K sufficient statistics involves one redundant parameter.

this does not violate any of the necessary assumptions for Eq.


since pAUC discriminates between positives and negatives, our previous analysis cannot be applied directly.


As is standard, the boosting algorithm can be viewed as minimizing a convex potential function.

the proof is significantly different than the analysis of AdaBoost [7], where they simply use the fact that the potential is an upper-bound on the error rate.


Magnetoencephalography (MEG) and electroencephalography (EEG) are well-suited tools for such purposes, in that they measure changes of magnetic fields or scalp voltages, which are almost instantaneously induced by electric activity of neurons.

spatially localizing the source activity in MEG/EEG is challenging.


Uniform perforation mask is just N points chosen randomly without replacement from the set Ω.


Unsurprisingly, the PCA face reconstructions are extremely faithful reproductions of the original images.

pCA accurately reconstructs also visual effects, such as lighting variations and changes in facial expressions, that are unimportant for the task of face verification and that might potentially hamper recognition.


It is worth noting that achieving either notion of non-discrimination requires some cost to at least one of the groups.

maintaining calibration further increases the difference in F.P.


Previous studies have focused on reducing the dimensionality of this chemical feature space [1], or on identifying dimensions of olfactory perceptual space using psychophysical measurements in humans [2,3].

the dimensions of olfactory space underlying neural representations in the brain remain largely unknown.


[2017]) require joint measurements of an exponential number of copies of the quantum state, and assume the ability to perform noiseless, universal quantum computation.

the algorithms implicit in Theorems 1 and 2 involve only single-copy measurements, allow for noisy measurements, and capture ground reality more closely.


[2] showed that it is possible to learn the structure of these models with a sample complexity that scales sublinearly with the number of possible binary dependencies.

the sample complexity scales exponentially for higher degree dependencies, limiting its ability to learn complex dependency structures.


One common approach is to build a Markov decision process (MDP) with parameters (i.e., rewards and transition probabilities) learned from data, and then find an optimal policy: a sequence of actions that would maximize expected cumulative reward in that MDP.

optimal policies are sensitive to the estimated reward and transition parameters.


In this paper, we assumed that the subtask graph (e.g., subtask dependencies and rewards) is given to the agent.

it will be very interesting future work to investigate how to extend to more challenging scenarios where the subtask graph is unknown (or partially known) and thus need to be estimated through experience.


Last but not least, the interpolation kernels in the layer is learned from data rather than hand-crafted, therefore it is more flexible and could be more powerful than pre-designed kernels.

it is end-to-end trainable so that the learned interpolation operators are embedded in the overall optimization objective of the model.


With this assumption, although one needs to balance between exploration and exploitation in the beginning, after some trials, one can be confident about which action is the best and rest assured that there are no more surprises.

the world around us may not be stationary, in which existing learning algorithms for the stationary case may no longer work.


In the traditional BN, the normalization step seeks to eliminate the change in the distributions of its internal layers, by reducing their internal covariant shifts.

prior to normalizing the distribution of a layer, BN first estimates its BN has a limitation, which is limited by the memory capacity of computing platforms (e.g.GPUs), especially when the network size and image size are large.


Given diverse object appearances and correlations in each image, personalized edge connections with respect to each knowledge form should be adaptive for different regions.

our work aims to develop in-place knowledge modules which can not only explicitly incorporate any kinds of commonsense knowledge (both explicit or implicit) for better semantic reasoning but also link external knowledge with visual observations in each image in an adaptive way.


In general, the inference step in sparse coding can be slower than the membership assignment in GMM model.

the computational efficiency can be greatly improved by using an approximated sparse coding algorithm such as learned FISTA [23] or orthogonal matching pursuit [10].


Existing efficient algorithms employ random sampling to learn game G before coordination.

these approaches are thin for the goal: Even when the game structure estimated from samples is within of G, its PO conventions might still be away from these of G. Here we present a new algorithm to identify -PO conventions efficiently.


We obtain the best recovery for small graphs, learning over half of the true edges in FB SMALL A and FB SMALL C. Typically, the number of edges learned increases as we increase the number of constraints and decrease the noise variance.

occasionally, considering fewer effective resistances in fact improves learning, possibly because we more effectively solve the underlying optimization problem.


if some numbers depend on K K , we will explicitly present it in the big O notation.


We show that this enables it to attain generality and compactness at least equal to that of the generative-model approach.

the PSR approach is also like the history-based approach in that its representations are grounded in data.


RRL has not yet demonstrated scalability to problems as complex as those considered here-previous RRL blocks-world experiments include relatively simple goals 13 , which lead to cost functions that are much less complex than the ones here.

unlike RRL, our API assumes an unconstrained simulator and (for the FF heuristic) a world model, which must be provided or learned by additional techniques.


Recently a generic acceleration algorithm called Catalyst [Lin et al., 2015], based on the proximal point method improved this rate of convergence, but the practical performances highly depends on the input parameters.

recent papers, for example [Shalev-Shwartz and Zhang, 2014] (Accelerated SDCA) and 31st Conference on Neural Information Processing Systems (NIPS 2017), Long Beach, CA, USA.


The following two tables summarize the situation (again, ignoring constants): From the tables, we see that for both methods, there is an initial linear speedup as a function of the minibatch size b.

in the AG algorithm, this linear speedup regime holds for much larger minibatch sizes 1 .


In our current study, we fitted a global time of day curve at 5 minute resolution to data obtained from randomized serving scheme through a periodic (weekly) adaptive regression spline.

there are still interactions that occur at an article level which were difficult to estimate offline through article features.


In fact, a natural greedy algorithm gives a factor 1/2 approximation for min-min, while local search gives a constant factor approximation for sum-sum, even with matroid constraints [6,2,4].

for the sum-min objective, the best known algorithm had an approximation factor of O(1/ log n) [6] and no inapproximability results were known.


Many features compress well using RLE: sparse features, continuous features with few distinct values, and categorical features with low arity.

to train directly on compressed data without decompressing, we must maintain the feature in sorted order throughout the duration of training, a prerequisite for RLE.


One approach would be to reduce the problem to a tractable one, e.g., by constraining the model to a low tree-width graph.

empirically, using more complex interactions together with approximate inference methods is often advantageous.


Our practical implementation computes a small number of CG steps relative to n, K = O(1), and as a result the search direction is not an accurate approximation of the true Newton step.

such inexact Newton steps achieve a good balance between the computational cost and the quality of the direction.


Therefore, we have (N, δ) = Eφ(x N +1 )−φ(x * ) for strongly convex f (x).


Instead of using (t, m, n)-nets and mapping to S n , we could have also used spherical t-designs, the existence of which was proved in [9].

construction of such sets is still a tough problem in high dimensions.


Building on the UCB algorithm [2], a regret minimizing algorithm, variants of the UCT algorithm [17] have been used for MCTS in growing trees, leading to successful AIs for games.

there are only very weak theoretical guarantees for UCT.


For nodes with τ i = 0 (or i ∈ A in marginal MAP), there is no closedform solution for {δ α i (x i )} and {w i , w α i } to minimize the upper bound.

because of the fully decomposed form, the gradient w.r.t.


Now construct h 2 , also with sparsity r 2 = 5 + 5/ε.

the loss for H our batch algorithm uses sparsity r = 10 + 10/ε in each encoder h 1 , h 2 and achieves reconstruction error (1 + ε) X − X 2 2 F . The iterative algorithm uses sparser features, but pays for it a little in reconstruction error.


The reinforcement learning problem in Markov decision processes (MDPs) involves an agent using its observed rewards to learn an optimal policy that maximizes its expected total reward for a given task.

such observed rewards or the reward function defining them are often not available nor known in many real-world tasks.


Note that the most expensive step in the above approach is the inversion of the Hessian matrix.

it is easy to verify that in our case all the off-diagonal elements of the Hessian are equal to each other.


They rely on the density structure of the data itself to propagate known labels to areas lacking annotations, and provide a natural way to incorporate labeling uncertainty.

to model the density of the data, each point must measure its proximity to every other.


To be able to use SMC for inference in PGMs we have to define a sequence of target distributions.

these target distributions do not have to be marginal distributions under p(X V ).


HDPs [23] partially address this modeling aspect by providing a way to construct multiple DPs implicitly depending on each other via a common parent.

their hierarchical structure may not be appropriate in some problems (e.g.


More importantly, one can encode structural information through the cost function F , which selects and establishes preferences over the set of atoms S F . As pointed out in [6], when F is submodular, (4) can be evaluated by a secant method with submodular minimizations ([21, §8.4], see also Appendix B).

as we will show, it is possible to do significantly better by completely avoiding submodular optimization.


A number of recent work have used EA as an alternative to DRL with some success [8,22,44,53].

eAs typically suffer with high sample complexity and often struggle to solve high dimensional problems that require optimization of a large number of parameters.


In using all of the eigenvectors, the dimensionality of the feature embedding is not reduced.

in scaling the eigenvectors by the inverse square-roots of their eigenvalues, the directions of least cost in the network regularized problem become the directions of maximum variance in the associated ridge regularized problem, and hence are the directions of least cost in the ridge problem.


Since media such as movies and music are nondurable goods, most users are quite receptive to buying or renting them in rapid succession.

users only purchase durable goods when the time is right.


The main difference between ( 13) and ( 6) is that all ANOVA kernels in the sum share the same parameters.

to increase modeling power, we allow each kernel to have different weights θ 1 , .


Proposition 5 follows from the Whitney-Glaeser extension theorem for smooth functions [14,15] and implies that the complete graph Stein discrepancy inherits all of the desirable convergence properties of the classical discrepancy.

the complete graph also introduces order n 2 constraints, rendering computation infeasible for large samples.


Action Response Layers The feature layers described above are sufficient to meet our objective of mapping from the input payoff matrices to a distribution over the row player's actions.

this architecture is not capable of explicitly representing iterative strategic reasoning, which the behavioral game theory literature has identified as an important modeling ingredient.


Note that both the temporal convolution layers and the dense layers do not observe the environment rewards directly.

in cases where the reward cannot be fully inferred from the environment, such as the DirectionalHopper environment we will examine in Section 4.1, we add rewards r i to the set of inputs in Eqs.


We would ideally like to represent a given observation x by the unknown θ (or the corresponding a related to θ by θ = aV + b) that generated it, since the conditional distribution P (x|θ) is used to model random effects.

the actual value of a is not known to us and all of our knowledge of a is contained in the posterior distribution P (a|x) = P (a)P (x|a)/P (x).


Several state-of-the-art implementations, such as Spark based wordcount() + sort() use this method.

our experiments (sec 6 of Supplementary document) reveal that O(M ) storage and communication, even with the best possible distributed implementation can be orders of magnitude slower compared to approximate solutions in a distributed setting.


However, these two approaches differ in an important point: Sherali-Adams hierarchy uses beliefs over all subsets of |R|  d variables, where d is the degree in the hierarchy; this leads to an LP of size ).

gBP only retains regions that are contiguous in G. If G has maximum degree k, this produces an LP of size O(nk d ), a reduction which is significant for large-scale problems.


If the size of the parameter space (|S|) is finite, such an approach may be feasible.

if |S| is large or infinite, testing all points may be impractical.


As can be seen, our reimplementation of DeepCoder is slower than the original implementation (discarding hardware differences).

the new method (PCCoder) is considerably faster than the original DeepCoder method, even though our implementation is less optimized.


The best known such constant is due to the work of [17] that requires a bound on the RIP constant δ 2k ≤ 0.5 (or equivalently a bound 1+δ 2k 1−δ 2k ≤ 3 on the condition number).

real-life high dimensional statistical settings, wherein pairs of variables can be arbitrarily correlated, routinely require estimation methods to perform under arbitrarily large condition numbers.


This is reminiscent of the difficulties that arise in matrix completion.

in our case, these pathological cases turn out to be rare, since it is unlikely that a random subset of Pauli matrices will all commute.


From Proposition 4, we know that the two inequalities are strict.

if φ is top-2 subgroup order sensitive, the following inequalities hold with at least one of them being strict: φ(g, (1, 2, 3)) ≥ φ(g, (2, 1, 3)), φ(g, (1, 3, 2)) ≥ φ(g, (2, 3, 1)), and φ(g, (3, 1, 2)) ≥ φ(g, (3, 2, 1)).


We then use the plugin estimator How well does this plugin estimator work, that is, what is its relative risk We cannot simply write L n ( λn ) and apply Theorem 1 because L(•) can only be applied to nonrandom arguments.

we can still leverage existing machinery by defining a new plugin regularizer R Henceforth, the superscript • will denote quantities concerning the plugin regularizer.


We can consider this algorithm to be an approximation to the single-processor Gibbs sampler in the following sense: at the start of each iteration, all of the processors have the same set of counts.

as each processor starts sampling, the global count matrix is changing in a way that is unknown to each processor.


Their method can exploit correlations between labels, and take classification decisions.

their approach is purely heuristic, and no theoretical guarantee is given.


Unfortunately, it is more challenging to give a simple estimate of the optimal k as in Theorem 3.4, even when A t is a random bipartite graph, because the spectral properties of the random matrix are complicated by blockwise structure, and may depend on the prior distribution Q(ν).

experimentally the optimal k follows the trend a n t , where the constant a depends on both the model assumption and the choice of Q(ν), and can be numerically estimated by simulation.


the distance between the graphs completed by linear segments at jump points) would also be a pertinent choice.

providing a theoretical basis in the case of the Hausdorff distance is very challenging and will not be addressed in this paper, owing to space limitations.


More precisely, we consider prior distribution P with probability density P (z i , σ) to be facotorizable in its compression set dependent component and message string component (conditioned on a given compression set) such that: The above choice of the form for P I (i) is appropriate since we do not have any a priori information to distinguish one compression set from other.

as we will see later, we should choose p(d) such that we give more weight to smaller compression sets.


If we sample batches of size 30000 from the replay buffer, the performance further improves.

as seen in the "IPG-β-last30000" curve, if we instead use the 30000 most recent samples, the performance degrades.


One of the key advantages of a standard Bloom filter is that it is easy to insert an element (possibly slightly changing the false positive probability), although one cannot delete an element without using a more complex structure, such as a counting Bloom filter.

there are more recent alternatives to the standard Bloom filter, such as the cuckoo filter [6], which can achieve the same or better space performance as a standard Bloom filter while allowing insertions and deletions.


We could just add all the armchair examples to the sofa training set.

not all instances of armchairs will look close enough to sofa examples to train an effective detector.


Note that the schizophrenia patients studied here have been selected for their prominent, persistent, and pharmaco-resistant auditory hallucinations [14], which might have increased their clinical homogeneity.

the patient group is not representative of the full spectrum of the disease, and thus our conclusions may not necessarily apply to all schizophrenia patients, due to the clinical characteristics and size of the studied samples.


One common solution to this problem is to perform validation on fewer number of samples, where the downside is that the learner would obtain a much more noisy and sometimes completely unstable estimate of the out-of-sample performance compared to the case where the entire LOOCV vector is at the learner's disposal.

aLOOCV described next will provide the benefits of LOOCV with negligible additional computational cost.


The results are shown in Figure 2 (c) where the performance of RLS significantly drops as the number of missing data is increased.

both GLAS and GLAS+ are not affected that much.


This means that classical algorithms such as kd-trees are no longer suitable [25] and new algorithms have to be designed to handle high dimensionality.

existing approaches for large scale search in high dimension relied mainly on algorithmic constructions that are either data independent or weakly dependent.


We observe this phenomenon for both OMPR and nIT-Newton method which is consistent with their respective theoretical goarantees (see Theorem 4).

as expected, the phase transition diagram of OMP has a negligible fraction of the plot that shows high recovery probability.


The notion of margin, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically successful results for both classification and regression tasks.

most large margin algorithms are applicable only to shallow models with a preset feature representation; and conventional margin methods for neural networks only enforce margin at the output layer.


The main challenge is to evaluate p(✓ d |w d,1:N , , ↵), i.e., infer the topic proportion given each document, which is also the important inference problem in the unsupervised LDA model.

it is well known that the exact evaluation of the posterior probability p(✓ d |w d,1:N , , ↵) is intractable [4,5,9,15,26,27].


The above lasso optimization problem can be solved efficiently with the shooting algorithm [3].

the main challenge in optimizing Equation (1) arises from ensuring that the β j 's satisfy the DAG constraint.


On this aspect the two distributions lead to very similar results, with a mean sticking closely to F (σ ij ), except for low values of σ ij where the slight bias, previously mentionned, is observed in both cases.

the two distributions lead to very different results in term of their spectra (Panel B).


In many domains such as document classification, image histogram classification and gene microarray experiments, fixed monotonic transformations can be useful as a preprocessing step.

most classifiers only explore these transformations through manual trial and error or via prior domain knowledge.


It can be argued that the knowledge of an upper bound on γ is required, whereas this is not needed for the monotone algorithm.

if γ > 1 − 1/ √ T , the regret bound on monotone is super-linear, and therefore uninformative.


The regression datasets tend to be quite small in terms of both number of random variables and number of datapoints, so it is harder to amortize the costs of GPU execution.

the results are very different for models where the number of inferred parameters grows with the data set.


For phonetic reduction, choices about word duration can directly modulate information density.

it is less clear how the effects of UID at higher levels of language production observed by Genzel and Charniak (2002) and Keller (2004) come about.


These models treat the relations as static information.

a large amount of relational data in the real world is time-varying.


Coherence is considered well-aligned to human judgment when evaluating a single topic -a higher coherence score means better quality of a mined topic.

coherence does not evaluate the relationship between different mined topics; e.g., if the mined F topics are identical, the coherence score can still be high but meaningless.


However, such similarities in numerical implementations are only tangential to the more fundamental relationship among the objective functions of different non-ML learning methods.

the energy based learning [22] presents a general framework that subsume most non-ML learning objectives, but its broad generality also obscures their specific statistical interpretations.


This is because the input graph does not necessarily minimize the objective -there can be graphs with smaller total edge weight and lower effective resistances.

the learned graphs do capture information about edges in the original: their heaviest edges typically align with true edges in the target graph.


The loss in statistical efficiency is moderate for b = 2, in particular for ρ close to 1.

as b increases that loss becomes more and more substantial; cf.


Such linear transformations seem to suggest linear dendritic operations and, in combination with a single global 'somatic' nonlinearity, they are often assumed in neural network models and descriptive models of neuronal signal processing [10].

as we will show below, estimation from the spike trains of multiple correlated presynaptic neurons requires a non-linear integration of inputs even in this case.


However, the goal there is to learn a better stand-alone student model.

we make use of both the lowcost (student) and high-accuracy (teacher) model during prediction via a gating function, which learns the limitation of the low-cost (student) model and consult the high-accuracy (teacher) model if necessary, thereby avoiding accuracy loss.


It is straightforward to generalise the model by substituting other noise models for Equation 3, for example using a logistic link for binary data y dn ∈ {0, 1}.

in the following we will focus on the Gaussian case.


The matrix H is a non-expansion by construction.

unlike the OLS hat matrix H = X(X T X) −1 X T , the matrix H depends on the targets y.


This simple change allows us to prove that OMPR has the best known guarantees for sparse recovery in terms of the Restricted Isometry Property (a condition on the measurement matrix).

oMP is known to have very weak performance guarantees under RIP.


A standard Bayesian treatment of the GPLVM requires the computation of the log marginal likelihood associated with the joint distribution (Eq.6).

both F and X must be marginalized out, propagating the prior density p(X) through the nonlinear mapping makes this inference difficult.


One common effect of this kind is that people judge stimuli that cross boundaries of two different categories to be further apart than those within the same category, although the distances between the stimuli are the same in the two situations [6].

biases need not reflect suboptimal performance.


an update move that perturbs existing kernel centres.

we found that the simple moves presented yield satisfactory results while keeping the computational complexity acceptable.


Simultaneous changes in both copulas and marginals can occur.

there is no limitation in updating each of the modified components separately.


The key difference between the frameworks is the order in which the marginalisation and variational approximation are applied.

for CEGs this order turns out to be irrelevant.


Since the size of datasets for unsupervised subspace clustering is usually limited (e.g., in the order of thousands of images), our networks remain of a tractable size.

for the same reason, it also remains difficult to directly train a network with millions of parameters from scratch.


Recently, there have been a few attempts to define and solve different forms of task descriptions such as natural language [1,2] or formal language [3,4].

most of the prior works have focused on task descriptions which explicitly specify what the agent should do at a high level, which may not be readily available in real-world applications.


The Clebsch-Gordan decomposition has recently appeared in two preprints discussing neural networks for learning physical systems [21,22].

to the best of our knowledge, in the present context of a general purpose nonlinearity, it has never been proposed before.


The first part of the regret (i.e., the regret coming from pulling the suboptimal arms) suggests that the exploration phase τ should be long enough for the algorithm to select the empirically best arm î * at τ equivalent to the actual optimal arm i * with high probability; and at the same time, as short as possible to reduce the number of times the suboptimal arms are explored.

the second part of the regret (i.e., the variance of pulling arms with different means) is minimized by taking τ as small as possible (e.g., τ = 0 would guarantee a zero regret).


The monoid action also divides the U r d into several subsets.

these subsets are not necessarily disjoint after mapping.


One possibility would be to train the sofa detector using only the sofa instances.

this would result in somewhat poor performance due to the limited size of the training set.


An informal explanation to this interesting phenomenon is that as the degree of orthogonality of the random projections gets higher, the code becomes more and more informative, and thus provides better estimate.

it can be observed that the performances on the mean-centered datasets are similar as on the original datasets.


For small amounts of poisoned data ( 5%) we can still certify the resilience of MNIST-1-7 and Dogfish (Section 5).

with more (30%) poisoned data, the attacker can subvert the outlier removal to obtain stronger attacks, increasing test error on MNIST-1-7 to 40%-much higher than the upper bound of 7% for the oracle defense.


If the repeats are longer than the k-mers, the C1P assumption is violated and the order given by the Fiedler vector is not reliable anymore.

handling the repeats is possible using the information given by mate reads, i.e.


Here, it would be natural to regard these dynamical systems are "different" each other even with almost zero ✏.

if we compute the kernel defined via the exponential discounting, these dynamical systems are judged to be similar or almost the same.


Since the generalization error is not known, it is tempting to try to estimate the optimal convex aggregate classifier by minimizing the training error P n {(x, y) : yf (x) ≤ 0} over the convex hull conv(H).

this minimization problem is not computationally feasible and, moreover, the accuracy of empirical approximation (approximation of P by P n ) over the class of sets {{(x, y) : yf (x) ≤ 0} : f ∈ conv(H)} is not good enough when H is a large class.


Even worse, Baik, Ben-Arous and Péché [BBAP05] and Paul [Pau07] demonstrate a phase transition phenomenon: if β < √ α the estimate is asymptotically orthogonal to the signal v PC , v → 0.

for β > √ α, v PC , v remains strictly positive as n, p → ∞.


On unweighted Let C H(i t ) be the set of the connection nodes i of H(i t ) for which ∆(i) = 0 if C H(i t ) ≡ ∅ Let j be the node of C H(i t ) closest to i t Set y it = sgn ∆(j) else Set y it = −1 (default value) trees, computing ∆(i) for a connection node i reduces to the Fork Label Estimation Procedure in [5, Lemma 13].

predicting with the label of the connection node closest to i t in resistance distance is reminiscent of the nearest-neighbor prediction of WTA on weighted line graphs [6].


The model is therefore quite general: in particular, it is met if we simply randomize the order in which we upload our task batches, since this will have the effect of randomizing which workers perform which batches, yielding a distribution that meets our requirements.

it is not realistic to assume that we know what the prior is.


In the discriminative optimization problem formulated in Section 4.1, the µ variables are used to optimistically select both instances and their labels, with the goal of achieving the best classification model according to the objective (5).

when the labeled set is small and the discriminative partition (clustering) information contained in the large unlabeled set is inconsistent with the true classification, the labels optimistically guessed for the selected instances through µ might not match the underlying true labels.


A similar result has been proven independently by [10].

the results in [4] and [10] only concern model (5).


[5] give another bound on window size which requires τ = O(n/m).

with a output alphabet of size m, specifying all moments in a N length continuous time interval requires m N time and samples, and therefore all of these approaches lead to exponential runtimes when m is constant with respect to n. Also relevant is the work by Anandkumar et al.


Minimizing the L ∞ approximation error is theoretically preferable, since it is compatible with the existing bounds on policy loss [10].

few practical bounds exist for API with the L 2 norm minimization [14], such as LSPI [12].


They show the general problem of maximizing influence to be NP-hard and give approximation algorithms for several classes of instances.

it appears that for most reasonable random graph models, the highest degree vertices have large influence with high probability.


In particular, S. Shalev-Shwartz and T. Zhang [16] have derived new bounds on the duality gap, which have been shown to be superior to earlier results.

there still lacks of efforts in extending these types of methods to a distributed fashion and comparing them with SGD-based algorithms and ADMM-based distributed algorithms.


More positive results can be obtained in the class of potential games where, in a recent paper, the authors of [15] established the convergence of multiplicative weights and other regularized strategies in potential games with only payoff-based, bandit feedback.

moving beyond mixed extensions of finite games, much less is known, and only a moderate amount of literature exists.


Note that true coupling terms are unavailable here.

of greater interest is how well our model can recover pairwise correlations between nonsimultaneously measured neuron pairs.


The most famous approach is spectral clustering [7], which corresponds to the spectral relaxation of the ratio/normalized cut and uses k-means in the embedding of the vertices found by the first k eigenvectors of the graph Laplacian in order to obtain the clustering.

the spectral relaxation has been shown to be loose for k = 2 [8] and for k > 2 no guarantees are known of the quality of the obtained k-cut with respect to the optimal one.


The last four Figures have illustrated some aspects of learning with 'wrong' priors.

all of our results may be considered as belonging to the 'wrong prior' class.


The parameter λ controls a tradeoff between the ability to hold information over time and the ability to update when new relevant information arrives.

many neural network models have two distinct parameters that control these aspects of memory.


These predilections are encoded in the observational distribution P (y|x).

the experimental distribution P (y|do(x)) encodes the process in which the natural predilections are overridden, or ceased by external policies.


factor of 1 κg (1 − ( In the worst case, k f = 1 and K f = n, in which case the guarantee is 1/n.

the bound above follows from a simple observation that the constraint {f (X) ≤ b} is down-monotone for a monotone function f . in this variant, we do not use any specific information about f . In particular it holds for maximizing a submodular function g over any down monotone constraint [2].


With the additional conditions of zero noise and isotropic Gaussian inputs, [1] propose an initialization for the EM algorithm to guarantee exact recovery of the true parameters.

in addition to the stringent statistical assumptions, these methods and results are specialized to the case of two components, and seem non-trivial to generalize.


The resulting complete-information game has i∈N |Θ i | players and |A i,θi | actions for each player (i, θ i ); a Nash equilibrium can be represented using just i θi |A i,θi | numbers.

the normal form representation of the agent form has size j∈N |Θ j | i,θi |A i,θi |, which grows exponentially in n and |Θ i |.


However, this requires us to evaluate the intractable normalization constant during training as well as in the inference, making the model not tractable anymore.

we may consider using the log-probability of a sample under the mixture-ofexperts model as the training criterion (18) This criterion resembles clustering, where individual models may specialize in only a fraction of the data.


Our proof is inspired by recent results from [16], who proposed an online dictionary learning method and provided the convergence guarantee of the proposed online dictionary learning method.

[16] can only guarantee that the solution converges to a stationary point of the optimization problem.


Later, [8] proposed dynamic neural module network, which learns to optimize the layout structure by predicting a list of layout candidates.

the layout candidates are still generated by dependency parses.


We are operating in a non-Bayesian setting, so we are not given a measure (prior) on the space H. In the absence of a measure, there is no natural notion of the "volume" of the current version space.

the distribution P does induce a natural distance function on H, a pseudometric: We can likewise define the notion of neighborhood: We will be dealing with a separable learning scenario, in which all labels correspond perfectly to some concept h * ∈ H, and the goal is to find h ∈ H such that d(h * , h) ≤ ǫ.


[3] proposed an efficient sparse coding algorithm for auditory signals and demonstrated its usefulness in audio classification tasks.

the proposed methods have been applied to learn relatively shallow, one-layer representations.


Unlike the binary or Gaussian dropout, in the truncated log-normal model there is no "dropout rate" variable.

we can use the signal-to-noise ratio E✓/ p Var(✓) (SNR) for thresholding.


The analysis presented here does not directly address the neural implementation of the solution to the localization problem.

our abstract analysis of the sound localization problem has implications for neural processing.


Suppose first that neither endpoint of P is a leaf of T e (t).

then, from parts 1 and 3 of Lemma 1 it follows that from part 2 of Lemma 1 it follows that Now by construction the root e ∈ P ∩ S, and hence w(P ∩ M * T ) > w(P ∩ M ).


Typically, all of the weights (↵ s,t ) are set to a constant value ⌘, called the learning rate parameter.

since we are not in the full information setting and the decision maker does not observe g t , the algorithms mentioned above cannot be used directly.


In contrast, larger clusters will emerge when c is small, increasing the time to compute the top-r eigendecomposition for each A ii .

k k is likely to decrease in this case, resulting in faster convergence of Algorithm 1.


So far we have assumed a fixed kernel function.

humans can adapt to a wide variety of structural forms [13,8], suggesting that they have the flexibility to learn the kernel function from experience.


Given our hidden variable problem of determining correct name-face assignments, from a statistics point of view EM seems like the most favorable choice.

many computer vision problems have observed better results by choosing maximum over expected values.


We note that using the decomposed u j and v j as the weight initialization in CNNs would lead to a more expressive network for image deconvolution [31].

the model in ( 4) is only applicable to a single kernel, and the network needs to be retrained when the blur kernel changes.


There has been significant work on infinitely nested beliefs in game theory, where Brandenburger and Dekel [2] introduced the notion of an infinite sequence of finitely nested beliefs.

they do not describe any method for computing these beliefs from a world model or updating them over time.


Other methods, like BEBFs, can be interpreted in this way in the case of policy evaluation; however, the "traditional" BEBF approach in the case of control does not exactly fit this framework.

we suspect that it could be adapted to exactly follow this blueprint (something we leave for future work).


If τ is too small, signal measurements decay too quickly, thereby preventing large memory capacity.

if τ is too large, signals from the distant past do not decay away, thereby interfering with the measurements of more recent signals, and again degrading memory.


Moreover, we are able to make collapsed predictions in which we compute the predictive distribution test ψ's given ω, integrating out the training ψ.

the LNM GP must condition on the training GP values in order to make predictions, and effectively integrate over training samples using MCMC.


This performance degradation of discriminative methods on corrupted signals is evident in the examples shown in [17].

reconstructive methods have shown successful performance in addressing these problems.


The problem is harder because of tighter constraints.

the important benefit of using such enforcements is that instead of comparing features of two different spatio-temporal paths y and ȳ, one can compare the features of individual box pairs (b i , bi ) of those two paths.


In image analysis, the transformed mixture of Gaussians (TMG) model uses a probabilistic framework and an EM algorithm to jointly learn clustering and alignment of image patches subject to various forms of linear transformations [4].

this model only considers sets of transformations in discrete pixel space, whereas we are focused on curve modelling that allows for arbitrary continuous alignment in time and space.


Much of the work in this area has focused on determining whether a treatment has a significant effect on the population as a whole.

a growing body of work has focused on learning optimal, personalized treatments from observational data.


If no noise is present, our warping function y = g(f ) maps latent space f to output space y.

in [1] the inverse mapping f = w(y) is defined due to analytical tractability reasons.


earlier we agreed that our aim is to reach the modest goal ( 6) and next we show that this is indeed possible.Corollaries 1 and 2 provide sufficient conditions for strict improvements when we use the upper bounds ( 8) and ( 7) respectively.


The above sequence of inequalities give us that inf Since this holds for all p ∈ Δ n , we have that We note that Ramaswamy and Agarwal [16] showed a similar least-squares type surrogate calibrated for any loss � : Y × T →R + ; indeed our proof technique above draws inspiration from the proof technique there.

the surrogate they gave was defined on a surrogate space of dimension n − 1, where n is the number of class labels in Y.


Note that, the remaining hidden neurons (excluding the bias unit) act as three different logic gates and altogether make up the XOR classifier.

if the pruning operations are conducted only on the initial parameter magnitude (as in [9]), then probably four hidden neurons will be finally kept, which is obviously not the optimal compression result.


The stochastic process model for the mapping functions also makes it straightforward to estimate the function at previously unobserved points, thus generalising out-of-sample with ease.

the GP-LVM gives up on the intuitive preservation of local neighbourhood properties that underpin the non-probabilistic methods reviewed above.


The relatedness of the EP representation of related patterns is clear in the rich structure of this matrix -this shows the extent of the explicit code learnt by the RBM.

this code does not make indexing perfect.


There have been a few studies on group invariant kernels [4,10].

[4] does not examine whether the unitary group structure is actually preserved in the RKHS, which is critical.


As another interesting phenomenon, local coordinate coding seems to encourage coefficients to be nonnegative, which is intuitively understandable -if we use several bases close to a data point to linearly approximate the point, each basis should have a positive contribution.

whether there is any merit by explicitly enforcing nonnegativity will remain an interesting future work.


While these methods are iterative, they have strong theoretical guarantees on structure recovery when the true distance matrix forms an additive tree metric.

most previously known tree metrics are defined for discrete and Gaussian variables.


One possible way is to generate N random samples {S (n) } N n=1 from the prior p S (S) which is a HMM, and then p * τ can be modelled by using kernel density estimation.


For a given problem, it is in general not easy to come up with a useful conditional prior.

once such a prior is specified, we can in principle use the same powerful techniques for approximate Bayesian inference that have been developed for supervised discriminative settings.


As a consequence, the recovery algorithm for p and M is identical to theirs.

insofar as the asymmetric part of the kernel is concerned, everything, starting from the definition and the introduction of the vector field r as a way to model the asymmetry, through the derivation of the asymptotic expression for the symmetric plus asymmetric kernel, is new.


Multiple studies support that the decision threshold is set to maximize reward [7,8,9].

the mechanism by which subjects learn the optimal thresholds has not been addressed.


CYCLADES fails to get much speedup when nearly all the features are used.

as more dense features are removed, CYCLADES obtains a better speedup, almost equalling HOGWILD!


For both models, A i (t) and σ i (t) are unobserved.

we have a data set of M noisy observations Y ≡ {y 1 , .


This may explain why DBMs with three hidden layers typically perform worse than the DBMs with two hidden layers [7,8].

the disadvantage of the pretraining procedure for Deep Belief Networks is that the top-layer RBM is forced to do most of the modelling work.


Sun and Zhang [18] apply it to conversational recommendations: a simulated user allows to train the dialogue agent to extract the facet values needed to make an appropriate recommendation.

we propose a conditional generative model of (natural language) recommendation conversations and our contributed dataset allows one to both train sub-modules as well as explore end-to-end trainable models.


It also obtains nearly the best VI metric score.

g-means and X-means find many more classes than the truth, which do not help them score well on the VI metric, and BKM takes over twice as long as PG-means.


Optimization (2) shares the same underlying insight with Self-Paced Learning (SPL) [14,15] where the algorithm automatically learns the weights over data points during training.

the process and scope in the two methods differ fundamentally: SPL minimizes the weighted loss over datapoints within a single domain, while optimization (2) minimizes the weighted loss over multiple tasks across possibly heterogeneous domains.


This is usually done by introducing convex relaxations of the problem and minimising them.

the computed upper bound should be as small as possible, so as to allow pruning out other regions of the space or discovering counterexamples.


All three samplers capture the evolving structure of the distribution.

the finite sampler seems unable to discard unneeded components.


This is expected, given that the large number of outliers can easily introduce wrong solutions of high score.

increasing the quadratic score, does increase the matching rate as can be seen by comparing the results between the Tables 2 and 1.


These rare events result in poor training data for the generator.

the DeepGenMSMs approximates the kinetics well within the uncertainty that is mostly due to estimator variance (Fig.


There is no guarantee that the change to the transform and to the ¦ C © is so small that simple re-estimation based on previous GMMs would suffice.

this depends on the optimization method used.


In general, our method aims to identify motif pairs that have high affinity, potentially leading to interaction between protein pairs that contain them.

a sequence motif might be used for a different purpose, and not give rise to an active binding site; it might also be buried inside the protein, and thus be inaccessible for interaction.


The accuracy of a single segment classifier is too low to make our approach practical.

if the source of sound does not move for a period of time, we can accumulate evidence from multiple segments in order to increase the accuracy.


Indeed, the matrix A 0 contains more information than the stationary distribution of the above process (1), and only the latter can be learned from independent samples.

(iv) letting η → 0, one can produce an arbitrarily large number of distinct samples.


The benefits of the GAMP method for neural mapping are that it is computationally tractable with large sums of data, can incorporate very general graphical model descriptions of the neuron and provides a method for simultaneously estimating the parameters in the linear and nonlinear stages.

methods such as the common spike-triggered average (STA) perform separate estimation of the linear and nonlinear components.


When spikes overlap, although the result can accurately be modeled as a linear sum in voltage space, the resulting waveform often does not appear in any cluster in PC space (see [1]).

our online approach can readily find such overlapping spikes.


We know from [19] that this structure obtains provably sub-linear query time and provably subquadratic space, where the exponent depends on the probability of hash collisions for "similar" and "not-similar" sets.

we also know that implementing MinHash with a poorly chosen hash function leads to constant bias in the estimation [28], and this constant then appears in the exponent of both the space and the query time of the search structure leading to worse theoretical guarantees.


Interestingly, BOUCHARD gives the best classification error, even better than the exact softmax training, but at the same time it always gives the worst nlpd which suggests sensitivity to overfitting.

recall that the regularization parameter λ was fixed to the value one and it was not optimized separately for each method using cross validation.


When the constraints of (4) are relaxed using various convex norms, ||c − E Psrc(x) P (y|x) [f (X, Y )]|| ≤ �, the RBA classifier is obtained by � 1 -or � 2 -regularized maximum conditional likelihood estimation (Theorem 2) of the dual optimization problem [23,24], The regularization parameters in this approach can be chosen using straight-forward bounds on finite sampling error [24].

the sample reweighted approach to learning under sample selection bias [1,7] also makes use of regularization [9], but appropriate regularization parameters for it must be haphazardly chosen based on how well the source samples represent the target data.


Nonlinear methods have been shown to find embeddings that nicely reflect the variability in the data caused by variation in face identity, pose, position, or lighting effects.

it is not possible to tell these methods to extract a particular single factor for the purpose of, say intelligent image manipulation or pose identification, because the extracted factors are intermingled and may be represented simultaneously across all latent space dimensions.


Under the assumption of independent and identically distributed (iid) Gaussian noise, the SFS problem can be formulated as a least squares problem in a space over three types of variables: the locations of the microphones, the locations of the acoustic events, and their emission times.

this least squares problem is plagued by local minima, and the number of constraints is quite large.


News articles are edited to a higher standard, so learned topics are often fairly interpretable when one models, say, thousands of articles.

our experiments use 23-29 articles, limiting the data for topic learning.


To learn these parameters, one way is to fix the matrix rank and update each matrix using gradient based methods.

it is easily trapped in local optima and one needs to tune the rank for the best performance.


These forms of plasticity, generally termed Spike Timing Dependent Plasticity (STDP), increase the synaptic efficacy of a synapse when a presynaptic spike reaches the neuron a few milliseconds before the postsynaptic action potential.

when the postsynaptic neuron fires immediately before the presynaptic neuron the strength of the synapse diminishes.


Hence, the candidate set S returned by thresholding the common neighbors has a non-vanishing fraction of nodes from outside q's community.

this fraction is relatively small, which is what we would exploit in the cleaning step.


For RRSVM, it is hard to combine the uses of multiple types of relation.

c-CRF can easily do it by incorportating the relations in different edge feature functions.


[8] introduced a weight for each slot that corresponds to the reward obtained by clicking on that slot.

no principled way of defining the weight has been described.


Such topic models with max-margin posterior constraints have shown superior performance in various settings [16,14,13,9].

their constrained formulations, especially when using soft margin constraints for inseparable practical problems, make it infeasible or at least hard if possible at all 1 to directly apply Monte Carlo (MC) methods [10], which have been widely used in the posterior inference of likelihood based models, such as the collapsed Gibbs sampling methods for LDA [5].


To have fewer parameters, we set µ = µ i , i = 1, 2, 3 and µ i is replaced by µ in the following sections including experiments and supplementary materials.

a typical iterative minimization process based on the alternating direction method of multipliers (ADMM) [15,16] can be written explicitly as minimizing the augmented Lagrangian function with respect to M i , L and E using ADMM is expensive in practice, and moreover, the global convergence can not be guaranteed.


Ideally, the policy would simply be updated in the direction that increases the true value function.

the true value function is unknown and therefore, for both prediction and control, a sampled return is instead used as a proxy.


The latter work introduced training of segmentation models for specific losses.

if the segments are allowed to be long enough, these models have polynomial but impractical inference complexity.


Then each block update only needs to call the inference oracle once for the instances related to the current x feature.

it cannot alleviate the large number of inference oracle calls unless the data is very sparse such that every instance appears only in very few blocks.


TREEWEIGHT is particularly attractive because it can be calculated without any additional computational expense above the standard training procedure.

as the training procedure in random forests combines several complex ingredients-bagging, random selection of predictor subsets at nodes, line search for optimal impurity reduction, recursive partitioning-theoretical investigation into TREEWEIGHT is extremely challenging.


Thus they need all data to be accessible so that the partial gradient of the block gradient can be exactly obtained.

such a "batch" setting may be computationally expensive in practice.


For simplicity, we instantiate our algorithm for standard LSTM based architecture.

our solution is independent of the base architecture and can be applied to other RNN based models like GRU [9], svdRNN [?