We can see that for this experiment taking = 200 balances correctly the trade-offs.

when applied correctly those methods can still be used to boost the optimization process and achieve faster convergence rates.


The detail of network structures and validation accuracies are listed in the Supplementary Section E.2.

algorithm 3 finds all the v-minimal matches in polynomial time, and we can find all the simple matches in polynomial time by exploring all v ∈ X ∪ Y based on Theorem 10.


One general tool for approaching large-scale problems is that of clustering or partitioning, in essence an appeal to the principle of divide-and-conquer.

such preprocessing steps also arise in the distributed sensing and distributed computing setting, where communication and storage limitations may preclude transmitting the original data to centralized processors.


In practice, we observe that letting < 1 improves the approximation results, which opens interesting questions for future work.

8) is which can be expanded as h(z, w) is real stable in 2m variables, indexed below by S and R where R := S\T .


R d be the function that compute the top right-singular vector of some vector in (R d ) ⌦2 viewed as a matrix.

here ⌧ > 1 is treated as a fixed constant globally.


Proof of Theorems 1 and 2 Both proofs rely on a carefully selected choice of correlated stochastic losses described below.

though the algorithm by Cesa-Bianchi et al.


These limitations are addressed in [6,7], where the authors propose a method for continuous data that allows network structures associated with different nodes to change with time in different ways.

they also perform better than HetDBN-0 on the "switch off" data, but are slightly worse on the "switch on" data.


The lack of generalisation between tasks that involve the same visual feature samplers suggests that the basis functions, eg the orientation selective primary cortical cells that sample the inputs, do not change their sensitivity and shapes, eg their orientation selectivity or tuning widths.

we assume that the cortical response to the bars is additive, with mean (we often drop the dependence on E, y and write ai, or, for all the components, a) where f is, say, a Gaussian, tuning curve with height k and tuning width T, f(x) = ke-x2 /2T2, usually with T « 1.


( 7) can be obtained from the dual solution (α * , β * ) of Eq.

the gradient formula is used to efficiently solve learning and optimization problems in practice.


We say C is (✏, )-uniformly learnable with sample complexity m if, given a sample S of size m, with probability 1 , for all c 2 C, |err S (c) err(c)| < ✏: thus, any class C is (✏, )-uniformly learnable with m = ⇥ 1 ✏ 2 VC(C) + ln 1 samples.

we consider single-parameter settings with n bidders.


The overall NashProp algorithm thus consists of the (always converging) table-passing phase followed by the backtracking local assignment-passing phase.

these classes of graphs seems to generate a nice variability in the relative speed of the table-passing and assignment-passing phases of NashProp, which is why we chose them.


Initialization: From the model design, we can expect that instances in the same region have the same label.

the LSB-CMM is derived from the logistic stick-breaking process.


Row and column headers pertain to the dual objective.

in order to abstract away these details we compare the iteration cost of the vanilla versions of all algorithms.


Suppose that assumptions (A1)-(A5) hold true.

of special importance, particularly for the modeling of sequential data, is the case where the underlying undirected graphical model forms a simple linear chain.


This approach optimally utilizes the network bandwidth of all nodes.


We use the Adam solver [19] to optimize both the generator and discriminator with β 1 = 0.9, β 2 = 0.999 and the weight decay of 1e − 4.

we train a deep CNN with large datasets (FlyingChairs [8] and KITTI [10]) in an end-to-end manner.


The resulting state-space model is: The combined harmonics input vector is defined: , where the harmonics corresponding to source i in frame n are:  In order to implement the H+N source model, the parameter matrices are constrained as follows: Having described the convolutive mixing problem in the general framework of linear Gaussian models, more specifically the Kalman filter model, optimal inference of the sources is obtained by the Kalman smoother.

the linear source parameters are grouped as where Optimization of J (θ, p) wrt.


The projection step can be formulated as an SDP problem [26] as follows: Proposition 2.

the formulation of [29] is nonconvex, and therefore the optimality is not guaranteed.


In [8], it is argued that some form of weighting of states in terms of a metric of relevance should continue to be important when considering average cost problems.

they effectively transform the costs g(x, a) to g(x, a) + s 1 + λ * α + s 2 ψ(x), so that the constraint T α Φr − Φr − λ * α 1 ≥ 0 can be met.


Let M be a mergeon, S a finite subset of [0, 1], and C a clustering of S . The merge distortion is defined by d Defining the induced merge height and merge distortion in this way leads to an especially meaningful interpretation of the merge distortion.

we have taken care to define the clusters of a graphon in such a way as to be robust to changes of measure zero to the graphon itself.


Notice that we recover the original definition of S match in the case of binary probabilities, though it does not fit in the Generalized Linear Model.

if a permutation ⇧ is a solution, then the reverse permutation is also a solution.


When the scales are clearly demarcated, we have argued that it is possible to manually define a multi-resolution IHT-inspired algorithm that guarantees success in recovering the optimal support pattern; and indeed, IHT could be extended to handle a clustered dictionary model with nested structures across more than two scales.

practically speaking this adaptation can be computed by passing the prior layer's activations x (t) through linear filters followed by indicator functions, again reminiscent of how DNN gating functions are typically implemented.


The prominent recent review paper by Ratcliff and Smith, for example, relies entirely on frequentist methods for parameter estimation, and does not go beyond the application of the Bayesian Information Criterion for model selection [9].

besides the effective application of hierarchical Bayesian methods to models that assume response times follow a Weibull distribution [8], most of the inference remains frequentist.


(In practice, server power can not be adjusted too frequently due to hardware restrictions and configuration delay.)

the drift analysis is the method of deducing properties, e.g., recurrence, ergodicity, or boundedness, about Z(t) from its drift E[Z(t + 1) Z(t)|F(t)].


Principal component regression (PCR) has been widely used in statistics for years (Kendall, 1968).

let X ∼ EC d (µ, Σ, ξ) be a continuous distribution and K be the population multivariate Kendall's tau statistic.


From the above Q dev p values we can compute player p's value for deviating from an equilibrium which recommends action a in state s: it is Q dev p (s, a ) for the best possible deviation a , since p will get the one-step payoff for a but be punished by the rest of the players starting on the following time step.

we also need the values of punishment policies for for s ∈ S Compute value vector set for each joint action, then throw away unenforceable vectors  to be the value to player p of playing joint action a from state s and then following π pun p forever after.


This paper builds upon the work of Nadeau and Bengio [8], which investigated in detail the theoretical and practical merits of several estimators of the variance of cross-validation.

the eigenanalysis of the covariance matrix of errors traces the problem back to the dependencies between test-block errors, which induce the absence of redundant pieces of information regarding the average test error.


Associate a binary random variable with each edge X = [X e ] ∈ {0, 1} |E| and consider the probability distribution: for where Throughout the manuscript, we assume that cycles are non-intersecting in edges, i.e., It is easy to see that a MAP assignment x * for the GM (2) induces a MWM in G. We also assume that the MAP assignment is unique.

bP may not work even when the corresponding LP relaxation to the MAP inference problem is tight.


3 We pre-processed the game screen to 84 × 84 gray-scale images.

we will call such models an observation-prediction model to distinguish it from another form of model introduced in this paper.


Contrary, KFD produces normal distributions which have a small variance along the discriminating direction.

there are several equivalent ways to optimize (2).


SGD consists of iterations of the form for iterates x t , x t+1 ∈ R d , stepsize (or learning rate) η t > 0, and stochastic gradient g t with the property E[g t ] = ∇f (x t ), for a loss function f : R d → R. SGD addresses the computational bottleneck of full gradient descent, as the stochastic gradients can in general be computed much more efficiently than a full gradient ∇f (x t ).

the gain in communication cost of SGD with memory is very high for dense datasets-using the top 1 strategy on epsilon dataset improves the amount of communication by 10 3 compared to SGD.


( 8) via a conditional gradient algorithm [4].

[25], despite being motivated from different perspectives.


This leads to γ → 0, making it harder to meet Condition 11.

in the worst case, when D M overfits and returns 1 for all true data points, the reweighting simply leads to the uniform distribution over the training set.


Our main contribution is a novel measure of the multitasking capacity that is aimed at solving the first problem, namely networks with "high" capacity which contain a "small" task set whose edges badly interfere with one another.

we have also obtained quantitative insights.


Given a model that predicts only the angular velocities ( φ, θ, ω), we can numerically integrate to obtain the orientation (φ, θ, ω).

the Microstrain package contains triaxial accelerometers, rate gyros, and magnetometers, which are used for inertial sensing.


PAFD consistently outperforms the other methods by this measure.

the model favors more highly variable IFs at low amplitudes.


Recent work has introduced unsupervised linear classifiers [9] that achieve accuracies comparable to state of the art supervised methods.

the weights are the probabilities that the used labels are correct given the previous weight vector w old s . Let y(c s ) be the labels which are assigned to the EEG given the character prediction c s when the application constraints described above are taken into account.


Therefore, it is very suitable for real-world sparse data.

the term η u 0 is the intensity of original tweets by a user u on his own initiative, becoming the source of a cascade and the term β s v∈Fu(t) κ ω (t) ⋆ (A uv (t) dN vs (t)) models the propagation of peer influence over the network, where the triggering kernel κ ω1 (t) models the decay of peer influence over time.


The effect will depend on the mean and variance of p (f n |x n ).

a natural consideration in this setting is the effect of our likelihood function on the distribution over f n from incorporating a new data point.


Instead of a projected gradient step, we explicitly maximize L t+1 (x t+1 , λ) over λ.

it is shown how Algorithm 1 recovers the existing regret bounds, while the use of the new augmented Lagrangian (7) in the previous algorithms also provides regret bounds for the clipped constraint case.


For example, "Boston Globe" is a newspaper, and so it is not a natural combination of the meanings of "Boston" and "Globe".

these values are related logarithmically to the probabilities computed by the output layer, so the sum of two word vectors is related to the product of the two context distributions.


Our thanks to John Lafferty and Jonas August for immensely helpful discussions.

we are interested in learning a pairwise discriminative model as the interaction potential.


This makes the energy surface flat and indiscriminate.

the first step computes the optimal code by minimizing the energy for the given input.


(better viewed electronically with zooming) formation, our algorithm produces a better sharp estimate of the Sculpture image from [13], with fewer ringing artifacts and higher resolution details.

eventually the penalty can even approach the 0 norm (although images are generally not exactly sparse, and other noise factors and unmodeled artifacts are usually present such that λ will never go all the way to zero).


for readability, we have summarized some of the notations that are specified in the algorithm in Table 2.


Instead, we attempted to maximize the probability in equation 10 by computing the sum over only one term -corresponding to the y 1•••S with the highest posterior probability.

let Y be the set of all alignments of the output sequence ỹ1•••S to the input blocks.


This point was made heuristically by Bickel and Li (2006), but we show that in fact ordinary regression methods are automatically adaptive if the distribution of X concentrates on a manifold.

the first order bias term has been removed.


Note that these annotations are solely used for testing, since we follow an unsupervised approach.

we now seek batches of mutually distant cliques, so that all samples in a batch can be labeled consistently because they are either similar (same compact clique) or dissimilar (different, distant clique).


They also noted that the case of p ≥ d x = d x is of interest, but requires further analysis, even for a shallow network with H = 1.

whatever the data points of Y are, their loss values are the same.


This is traditionally conceived as a question of consummatory motivation.

the natural response associated with a stimulus (presumably as output by an action specification mechanism) is only elicited if it is motivationally appropriate, according to the current goals of the animal.


One of the most fundamental problems in causal inference is the estimation of a causal effect when variables are confounded.

. . , Z4 is chosen by adding edges uniformly at random according to the lexicographic order.


We show that it is possible to adaptively learn a state-space representation in a principled manner using the SRM technique.

in this work, we focus on the problem of forecasting, which is probably one of the most challenging and important problems in the field.


For each cell type, we want to know which chromatin marks are the most important and how they work together in controlling gene expression.

the "deconvolution' approach [36] maps hidden layer representations back to the input space for a specific example, showing those features of an image that are important for classification.


For instance, in the case of regularized risk minimization we have where L is a convex function in w•x i , such as 1 2 (y i −w•x i ) 2 for regression or log[1+exp(−y i w•x i )] for binary classification.

from this, Corollary 2 establishes T . This means that for a suitable choice of η we achieve exponentially fast convergence in T to some stationary distribution D * η .


This takes O(n) time-same as the direct computation-since all O(n) nodes need to be processed.

hence, we chose instead the following cutoff rule: which also takes into account the total number of points contained in a node.


It should be noted that this is the first method to allow users to specify weights rather arbitrarily for all possible lenghts of matching sequences and still be able to compute kernels at O(lxl + Ix' l) time, plus, to predict on new sequences at O(l xl ) time, once the set of support vectors is established.

hence, can rewrite (5) as s Eprefix (tl s Eprefix(floor(tl l i= 1 floor(t l l+l where u = floor(t), t = uv and s E prefix(v).


The drawback is that it limits directly the number of terms that we can attempt to predict given a database, and explain why we have fewer terms than [5] although we have more than twice as many studies.

learning the full distribution of x is ill-posed, as x is high-dimensional.


The camera instance parameters in (3) are modeled as Gaussian with category parameters µ s , Σ s . We represent an image as a collection of detected feature sets that are statistically generated by an instance of our object and camera.

the position of the camera is constrained to a circular arc on the y, z-plane (Figure 2).


Further work will extend our approach to processes where this reliability is not known with absolute certainty, and that can feature jumps.

a lower mean implies that, on average, the task will be harder, such that more evidence needs to be accumulated to reach the same level of performance.


In such a case, the false negative rate is R 1 = 0 but the false positive rate is R −1 = 1.

we showed that the excess risk is actually controlled by an effective class prior which depends on both the estimated class prior and the true class prior.


For model 1 the newly joined interval inherits the parameters with equal probability from the interval before or after the removed change point.

if we consider the ratio of signal to noise ratios in the two states, we obtain a quantity which is independent of the fluorescence units, namely This relationship is not enforced in our model, but, if the simple birth-death interpretation is supported by the data, it should emerge naturally in the posterior distributions.


Note however that, strictly speaking, κ also mildly influences repulsion.

we wish to fit a separate continuous DPP to each class by jointly maximizing the  variational lower bound over θ and the inducing inputs Z using gradient-based optimization.


The noise assumption is compatible with the manifold assumption within the manifold+noise model.

we propose to formulate a new assumption, the "noise assumption", which is that in the neighborhood of every point, the directions with low variance (for the unlabeled data) are uninformative with respect to the class labels, and can be regarded as noise.


We investigated the properties of the proposed PLDSID algorithm in numerical experiments, using both artificial data and multi-electrode recordings of neural activity.

for this particular data set, PLDSID and Gaussian SSID both yielded poor parameters compared to factor analysis.


Suppose Note that Wasserstein metric measures the cheapest cost (measured in • − • ) of transporting probability mass from one distribution to the other.

in multi-dimensional setting, finding LFD remains an open question in the literature.


Side-chain to backbone interaction seems to be much severe than side-chain to sidechain interactionthe backbone is more rigid than side-chains and its structure assumed to be known.

in problems where exact inference was possible max-product BP always found the global minimum of the energy function and in the full protein data set, max-product BP always found a lower energy configuration compared to the other algorithms tested.


When networks are quite deep, backward locking becomes the bottleneck of making good use of computing resources, preventing us from updating layers in parallel.

it requires large amounts of memory to store the stale gradients and suffers from the loss of accuracy.


Decoupled meta-solvers are essentially sample-based adversarial bandits [16] applied to games.

these extensions have almost exclusively treated the two-player case, with some notable exceptions [54,26].


Extensive-form imperfect-information games are a general model for strategic interaction.

when using RBP with CFR+, regret does not strictly follow the rules for CFR+.


In this paper we provided a step towards answering an open problem: Is parallel machine learning possible in polylogarithmic time using a polynomial number of processors only?

to obtain polylogarithmic runtime of R compared to T L (M ), we choose the parameter h ≈ ld M − ld ld M such that n ≈ M /2 h = ld M . the runtime of the Radon machine is in O ld κ M + r 3 ld M . This result is formally summarised in Theorem 4.


As the regressand at step 3, we use the deviation of the impression at iteration i from the baseline impression, i.e., α i − α 0 .

further, if a training pool of subjects is used to constrain model parameters (e.g., to set β or to establish priors on β and α), it's conceivable that decontamination will work without requiring much more than a single rating per item.


We essentially employ the result with p = ∞ in Theorem 1 to estimate the threshold value.

if follows that with probability larger than 1 − η(π log m) −1/2 , the following bound holds: It is easy to verify that the bound in (10) is comparable to the one in (9).


Most generalization studies on SGM consider the case where only one pass over the data is allowed and the step-size is appropriately chosen, [5,14,29,26,9,16] (possibly considering averaging [18]).

while processing each data point only once is natural in streaming/online scenarios, in practice SGM is often used as a tool for processing large data-sets and multiple passes over the data are typically considered.


Luckily, it was nothing major: nobody got hurt.

in both high and low cost-to-loss ratio cases, we see a similar behavior in which the majority of the SS players do not invest (≈ 50%).


The process ends when q(v i ) is greater than a predefined threshold 2 .

we use a different set of features to classify candidates that contain only a single segment: (e.g., wires in circuits and straight bonds in chemistry): orientation: The orientation of the segment, discretized into evenly space bins of size π/4.


More precisely, we show that for any Lebesgue-integrable 1 function f : R d → R, for any ǫ > 0, there exists a ResNet R with ReLU activation and one neuron per hidden layer such that This result implies that, compared to fully connected networks, the identity mapping of ResNet indeed adds representational power for tall networks.

some regions outside the grid cells are also raised, but were supposed to be zero.


Of course, the chain and the weights µ i can also be constructed deterministically simply by sorting the coordinates of x.

both of the theorems above hold against both oblivious as well as adaptive adversaries.


Clustering is a fundamental machine learning problem with widespread applications.

their theoretical results do not imply a nontrivial approximation for the k-center problem.


We first show that PI outperforms prior works in a comprehensive semi-synthetic study using a public dataset.

pI performs comprehensively better given enough data (see Fig.


In most cases, however, our algorithm significantly outperformed the other methods.

using the estimated Dirichlet parameters, the normality score of an image x is: Since all αi are constant w.r.t x, we can ignore the first two terms in the parenthesis and redefine a simplified normality score, which is equivalent in its normality ordering: As demonstrated in our experiments, this score tightly captures normality in the sense that for two images x 1 and x 2 , n S (x 1 ) > n S (x 2 ) tend to imply that x 1 is "more normal" than x 2 .


This new type of regularization enables provable recovery of smooth input-output maps with unknown levels of smoothness.

the authors would like to thank the anonymous referees and the area chair for useful feedback.


That is, for neurons with general non-montonic activation functions, or for neurons with monotonic activation functions whose output magnitude violates the aforementioned bounds, there are example networks that can efficiently compute any real-valued function.

if an RBN network of size m can compute a real-valued function g which represents f with margin δ, then there exists a thresholded RBM network that computes f with margin δ.


This metric of accuracy has been extensively used in the Theoretical Computer Science community in order to analyze approximation algorithms for the k-means clustering problem.

in order to drive down the failure probability of Algorithm 1, we repeated it 30 times (followed by the Lloyd' heuristic each time) and kept the partition that minimized the objective value.


Their approach augmented a traditional supervised learning algorithm with distribution information made available from the unlabeled data.

for these experiments, I selected the first 8439 tracks (3/4 of the data) for training, assigning each track to be a member of the set defined by the album it came from.


Note that this representation shows the digit more clearly than the blurred frame-based one.

a longer period τ provides a longer jump through the past timesteps for the gradient during backpropagation-through-time.


Traditional playback of real-world events is usually constrained to the viewpoints of the original cameras and microphones, which limits the immersion of the experience.

, `for some chosen reference microphone pair m ?


Large dimensional action spaces, where the rewards depend on a subset of the types of actions are considered in [14] and [15].

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


We first employ a simulated example to illustrate the effectiveness of the proposed sparse RIR model for BCI.

in matrix-vector form, the optimization can be written as where X i is the (N + L − 1) × L convolution Toeplitz matrix whose first row and first column are [x i (k − N + 1), 0, . . . , 0] and [x i (k − N + 1), x i (k − N + 2), ..., x i (k), 0, . . . , 0] T , respectively, N is the microphone signal length, L is the filter length, h i (i = 1, 2) are L × 1 vectors representing the filters, • denotes l 2 -norm, and the constraint is to avoid the trivial zero solution.


Dirichlet-multinomial conjugacy allows Φ and Θ to be marginalized out [9], while typical values for the remaining unobserved variables can be sampled from their joint posterior distribution using Markov chain Monte Carlo methods.

we defined four network statistics (i.e., four discrepancy functions) that summarize meaningful aspects of the NHC network: generalized graph transitivity, the dyad intensity distribution, the vertex degree distribution, and the geodesic distance distribution.


Our algorithm further improves upon the best existing polynomial-in-dimension bound (both computationally and in terms of regret) for loss functions with Lipschitz gradients, achieving a regret of e O T 8/13 d 5/3 .

the dependency of our bounds with respect to T is not optimal.


We describe how to use the shadow Dirichlet to model a random pmf that has bounded variation such that |θ k − θ l | ≤ k,l for any k, ∈ {1, 2, . . . , d} and k,l > 0.

we also compared with treating all six months of sales data as coming from one multinomial which we estimated as the maximum likelihood multinomial, and to taking the mean of the six empirical pmfs.


12b tells us that, because of our assumptions about linear dimension, the matrix Σ T ,H has factors R ∈ R |T |×n and Σ S,H ∈ R n× .

we also need a matrix U such that U T Φ T R is invertible; with probability 1 a random matrix satisfies this condition, but as we will see below, there are reasons to choose U via SVD of a scaled version of Σ T ,H as described in Sec.


One challenge underlying this task is that visual scenes contain multiple interrelated objects, and that global context plays an important role in interpreting the scene.

in what follows we define the permutation-invariance property for structured prediction models, and argue that permutation invariance is a natural principle for designing their architecture.


Here we only reported the results of random MDPs with 100 states, 5 actions, and 10 bases, observed consistent convergence of the dual representations on a variety of MDPs, with different numbers of states, actions, and bases.

given H we can easily recover the state-action values of π.


We estimated parameters in regression models, using the ridge regression method.

an essential problem in submodular relaxation is how to choose Γ ∈ [0, 1] n×n and to optimize x given Γ.


The experimental evaluation show that our (model independent) algorithm performs as well as the Maximum Likelihood Estimator of the BTL model and outperforms other known competitors included the recently proposed algorithm by Ammar and Shah [1].

their algorithm requires information about comparisons between all pairs, and for each pair it requires the exact pairwise comparison 'marginal' with respect to the underlying distribution over permutations.


Moreover, we can see that the generalization performance is well-behaved no matter what values of p and γ we choose.

instead of using a hard-sup operator, we may also use a soft-sup operator, which can possibly lead to consistency.


It can achieve the best approximation ratio for many subset selection problems without noise [6,18].

as shown in lines 7-15, the better one of two solutions randomly selected from Q is kept; this process is repeated for B times, and the remaining solution in Q is deleted.


Our online algorithm can be applied in environments where abstract jobs arrive one at a time, and one can complete the jobs by investing time in a number of abstract activities, according to some schedule.

benefit-maximization) problem is NP-hard.


We build a simple computational model around this theory, using sampling to approximate an ideal Bayesian observer encoding and retrieving situational co-occurrence frequencies of stimuli and retrieval cues.

they argue, phenomenologically, that recognition could also succeed successful recollection, making the process a dual composition of recollection and familiarity [20].


We resolve the problems described above by assuming that speakers and listeners deviate from normative behavior by assuming a conventional lexicon.

they then reason recursively about how this lexicon should be used to convey particular meanings in context.


(It holds when the number of rounds that a bidder can participate in is at most α 4 T , or when the discount factor is at most 1 − 1 α 4 T . See Theorem 3.1 for the formal statement.)

joint differential privacy [26] is a a relaxation of differential privacy [15,14], it can be applied to many combinatorial problems for which no differentially private algorithm gets non-trivial approximation.


The WS formalism is mainly aimed at modeling the short-diameter property often observed in real-world networks.

a FRF is a Gibbs-Boltzmann distribution over graphs, with potential functions defined for each node pair {u, v} along with some neighboring subgraph G uv .


We found this to be a necessary extension because some individuals in the ordering tasks actually were not familiar with any of the items in the ordering tasks (such as the Ten Commandments or ten amendents).

we refer to these synthesized answers as "group" answers because they capture the collective wisdom of the group, even though no communication between group members occurred.


An estimator for self-motion consisting of a linear combination of flow measurements necessarily has to neglect the dependence of the optic flow on the object distances.

the components of the estimator are simplified model neurons which have been shown to reproduce the essential receptive field properties of the fly's tangential neurons [2].


The lower level problem in ( 4)-( 5), can be, in principle, addressed by several available solvers.

finally, we suggest the initialization θ (0) = P Θ (L −1 1 P ×L +n) where n ∼ N (0 P ×L , 0.1L −1 1 P ×L ) in order to be as uninformative as possible regarding the group structure while still breaking the symmetry by adding a small perturbation.


When the maximum of held-out log-likelihood curve is achieved, glasso selects 28 edges, forest selects 7 edges, and blossom tree selects 10 edges.

. . , X d , and missing edges (i, j) ∈ E whenever X i and X j are conditionally independent given the other variables.


We now state the performance guarantee of EXP4-IX.

we studied the regret up to two interesting rounds in the game: up to T /2, where the losses are i.i.d., and up to T where the algorithms have to notice the shift in the loss distributions.


These methods retain components in input space with large variance, regardless of whether these components influence the prediction [16], and can even eliminate low variance inputs that may have high predictive power for the outputs [17].

the computational problem of data analysis involves not only data fitting, but requires that the model extracted from the data has good generalization properties.


[19,20] -and other related work [6] -assume that each agent votes for a single alternative.

for a randomized voting rule f (or simply a voting rule), the output f (π) is a distribution over the alternatives.


This point is crucial for the biological plausibility of this scheme, as it seems unlikely that these minute differences in population response width would be easily measured experimentally.

we consider a population of N neurons tasked with encoding a probability density over s. One way to do this, known as a kernel density estimate (KDE) code [1,28], is to associate with each neuron a kernel density f n (s) and then approximate the target density with a convex combination of the kernel densities: where x n denotes the firing rate of neuron n and Z = N n=1 e xn .


From our perspective, it is irrelevant how a cost is computed by reservation systems.

as a result, we obtain a policy that is consistently better than SINGLE.


The fundamental questions explored by these hypotheses are how and where temporal and spatial information are integrated.

2-D convolution), and A i is activation function at layer i.


For example, if the maximum degree scales as ∆ = O(poly(log p)) and the girth scales as g = O(log log p), then (10) is satisfied.

(A3) Local-Separation Property: We assume that the ensemble of graphs G(p; η, γ) satisfies the (η, γ)-local separation property with η, γ ∈ N satisfying: where α is given by (7) for Gaussian models and by (8) for Ising models.


Moreover, ( 6) yields In addition, if ϑ ∈ (0, 1], Lemma 3.2 implies for q := 2 2−ϑ , q := 2 ϑ , a := (n −α c σ 2 −ϑ ϑ ϑ V τ ) 1/2 , and b := (2ϑ −1 E P h f0 ) ϑ/2 , that Since E P h f0 ≥ 0, this inequality also holds for ϑ = 0, and hence (11) shows that we have with probability µ not less than 1 − Ce −τ .

moreover, several time series models such as ARMA and GARCH, which are often used to describe, e.g.


A corollary is that ACh should also control the way that bottom-up information influences the learning of top-down models.

if one takes into account the possibility that u ¨G , then the posterior distribution for ` is the two-component mixture ¥ ` !


Namely, they both require |θ 0,i | ≥ c max{σs 0 log p/ n, σ/ √ n}, which is √ s 0 larger than the ideal detection level [10].

this approach however does not provide a measure of statistical significance for the finding that the coefficient is non-zero.


But following the same approach of rewriting the quantum circuit in the language of Hilbert Space embeddings as in Section 3.2, we get exactly Kernel Bayes Rule [Song et al., 2013]: What we have shown thus far As promised, we see that the two different but valid ways of generalizing Bayes rule for QGMs affects whether we condition according to Kernel Bayes Rule or Nadaraya-Watson kernel regression.

this is one of the key insights of this paper; showing that Nadaraya-Watson kernel regression is an alternate, valid, but simpler way of generalizing Bayes rule to Hilbert space embeddings.


Besides intra-normalization, we also utilize the power normalization as suggested in [3].

as can be seen, d drops slowly with the increase in the number of Gaussians.


Many techniques have been developed to address these challenges.

2, the inference model E is designed to output two individual variables, µ and σ, and thus the posterior q φ (z|x) = N (z; µ, σ 2 ).


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

here is a brief roadmap to the rest of the paper.


Since U s (t) is varying over time, we can associate each u ∈ U with a |V|-dimensional vector τ u of change points.

based on the achieved m-by-W jumping-time matrix, we preprocess the feature vectors {g i } m i=1 and k(t ij ), i ∈ {1, . . . , m} , t ij < T , which costs O(mW ) and O(mLW ) where L is the maximum number of events caused by a particular source set before time T . Finally, we apply the projected quasi-newton algorithm [12] to find the weight w that minimizes the negative log-likelihood of observing the given event data.


an LP-based algorithm is also presented in [8], but the results are far weaker than the ones we have presented in this paper, and we suspect that the that LP-based algorithm of [8] will not scale well to high-dimensional problems.


We found both the expert pretraining and RL objective important for generating high quality molecules, thus both of them are kept throughout training.

figure 1 (a)(e) depicts the partially generated molecule state before and after an action is taken.


Linear discriminant analysis finds a projection of the data so that the inter-class separation is large while within class scatter is small.


The bounds we provide involve a multiplicative factor that depends on the target rank k. Such a dependence was deemed necessary in non-private settings.

given a matrix A 2 R n⇥d , output a rank-k orthonormal projection matrix ⇧ such that with probability at least 1 , kA A⇧k p  ↵OPT k (A) + ⌧, where OPT k (A) := min rank(X)k kA Xk p . ( The second main contribution of this paper is an algorithm that returns a differentially private rank-k orthonormal projection matrix with ↵ = O((kd log k) .


Unfortunately, despite the well-known advantages and recent advancements of multi-way classification techniques [1,19,4] in machine learning, complexity concerns have driven most research on such super large-scale data set back to simple methods such as nearest neighbor search [6], least square regression [16] or learning thousands of binary classifiers [24].

therefore we argue that the results of our work is not directly comparable with the ILSVRC10 competitions.


to fully explain the ON-OFF split in visual pathway, it seems necessary to consider a more complete model with the images as the input.


The closest to our work are AdvGAN and DeepDGA.

by reducing the distance between z and z 0 , L 1 has the effect of generating more diverse adversarial examples from class y source .


The second term grows at most as Õ( √ n), but also becomes a constant for realizable problems.

oAC performs worse than PASSIVE except at label budgets between 320 and 1280.


In TF, both encoder and decoder consists of only self-attention and feed-forward layers.

this convergence analysis  Figure 1: Effect of adaptivity level on training MNIST deep autoencoder.


A richer or more complex F helps better approximate the Bayes predictor (smaller approximation error).


When the comparator sequence follows the dynamical models closely, P T could be much smaller than P T , and thus the upper bound of Hall and Willett [2013] could be tighter than that of Zinkevich [2003].

by choosing η = O(1/ √ T ), OGD achieves an O( √ T (1 + P T )) dynamic regret, that is universal.


During training, WNLL activation plays two roles: on one hand, the alternating between linear and WNLL activations benefits each other which enables the neural nets to learn features that is appropriate for both linear classification and WNLL based manifold interpolation.

moreover, WNLL utilizes both the learned DNNs and the preserved template at test time which seems to be more stable to perturbations on the input data.


Recent work has considered the setting where each point has a few arbitrarily corrupted components.

in matrix terms, we require that every column of C 0 does not lie in the column space of L 0 .


A grayscale video sequence is a two-dimensional tensor time series because each frame is a two-dimensional array of pixels.

let p = M m=1 I m and q = M m=1 J m . If A = 0, U 0 = 0, and Q 0 = Q, then the X n of the MLDS become independent and identically distributed draws from the multilinear Gaussian distribution.


Regression diagnostics have been developed in the statistics literature to detect such points (see e.g.

the main contribution to the influence for each point will originate from the residual error, e 2 i . Consequently, we propose sampling with probability inversely proportional to the approximate residual, 1 ẽ2 i .


Input: Initial set of uniformly random samples To preclude such a scenario, we would ideally like to renormalize after each step by doing Ũt ← , where W U DW V is the SVD of matrix U t V t . This algorithm is described in Algorithm 2.

the following lemma shows the equivalence between Algorithms 2 and 3.


Moreover, the block size for downsampling only logarithmically depends on the optimization accuracy, which is nearly constant (see more details in Sections 2 and 3).

the performance becomes better as h increases from 1 to around 4.


Its solution cannot immediately be rendered as an invariant subspace.

we then derive the rate of convergence for LTSA in a special case.


Given A ∈ R n×d and Q ∈ R m×n with orthonormal columns, Achieving the per vector guarantee of (3) requires a more nuanced understanding of how Simultaneous Iteration and Block Krylov Iteration denoise the spectrum of A.

frobenius norm error seems an inherent limitation of sketch-and-solve methods.


The second task is to control multiple agents in combat against enemy bots.

it successfully solves most of the tasks, including ones that require information sharing between two or more agents through communication.


All input parameters of the GC chip are set to the learned values and the robot moves forward using a walk gait (see Fig.

figure 2: Sketch of the configuration in which the chip is used: a chain of four coupled oscillators.


These methods eliminate the strong marginal assumption in [11] and have been shown to achieve better empirical performance.

to reduce the dimensionality, [11] suggest a variable screening framework by finding a submodel  and sign( βi ) = sign(β i ), ∀i ∈ S. (2) Remark 2.1.


Usually the quality of the predictor ¤ ¦ ¡ ©¨can be measured by a loss function ¦ ¤ §¦ ¡ ¨that is problem dependent.

assume that ' )( 10 s ut D 75 2 s 2 4 ¨¡ ¤ §¦ ¡ ¨W 8 , then © 8 C W 8 £ G , with probability of at least ¥ $ !


In the framework of large-margin learning, we want to maximize the distance between dist ij and dist ik .

experiment setting for LMNN follows [7].


We show consistent improvements over an earlier system with similar technical goals, and a new state-of-the-art result on a difficult relation extraction task.

it is usually difficult to predict which SSL methods will work well on a new task, and it is also inconvenient to test alternative SSL methods, combine methods, or develop novel ones.


Note however that the definition of the atomic norms in (1) did not make use of the topology of the ambient space, and hence is applicable even when the atoms belong to some Banach space (V, 11•11).

it should be possible to derive similar faster rates for our greedy algorithm.


4 shows the connections which are strong on at least two subjects.

as we have described in Section 1, connections among ROIs play a key role in information processing.


Although the relationship between measured fMRI activity and the spiking activity of neurons is rather complex, as a first-order approximation the fMRI signal can be considered to be monotonically related to the pooled activity of the underlying neural population.

in our model the complex cell filter bank was implemented by taking the sum of squares of the outputs of four simple cells (corresponding to the wavelet pairs that are identical up to phase), followed by a fixed output nonlinearity.


Our rejection threshold will be based on a specialization of this estimator, specifically the importance weighted empirical error of a hypothesis h In the notation of Algorithm 1, this is equivalent to where S n ⊆ X × Y × R is the importance weighted sample collected by the algorithm.

note that both optimizations are over the entire hypothesis class H (with h ′ k only being required to disagree with h k on x k )-this is a key aspect where our algorithm differs from previous approaches.


Comparison of the 2D and 4D results in Table 1 reveals that the relative performance of the heuristics remains unchanged, indicating that the best heuristic for picking experiments is independent of the problem dimension.

the full GP model can be approximated well by a local GP, where only the k nearest neighbors of the query point are used to compute the prediction value; this reduces the computation time to O(k 3 log(n)) per prediction, since O(log(n)) time is required to find the k-nearest neighbors using spatial indexing structures such as balanced kd-trees.


Algorithm 3 PiSTOL: Parameter-free STOchastic Learning.

5 we will show its convergence results in the stochastic setting.


A comparison to lasso is provided in Section 4, and we suggest some future problems in Section 6.

after k iterations, the genie algorithm will have selected all the k indices in I true and terminate with correct sparsity pattern estimate I true (k) = I true with probability one.


A similarity between IOHMMs and TRBMs is that in both models, the dynamics and emission distributions are formulated as neural networks.

our results demonstrate improved performance over several baselines modeling high-dimensional 2D and 3D data.


Our method can be considered as a refinement of his approach.

for the purpose of cluster analysis, the feature set was additionally reduced by only retaining the 100 genes with highest variance across samples.


The actions used in this study are depicted in Figure 2.

in our implementation, in each episode, ε was dependent on the number of successful episodes experienced up to that point.


The rest of this paper is organized as follows.

we achieve optimal convergence rates without any prior knowledge of smoothness parameters, yielding a more robust algorithm that reduces the need for hyperparameter tuning.


In case of 3-way (and higher) c-NN problem, we have to take care of a more complicated event to create an indexing scheme.

in all we had 100 such triplets for each class, and thus 1000 overall query triplets.


With these considerations in mind, we suggest that our model variability should induce temporal dependencies across timesteps.

we preprocess and split the dataset as done in [7].


This paper presented a successful application of batch RL combined with nonlinear function approximation in a new and challenging domain of autonomic management of power and performance in web application servers.

we found only a slight improvement in Bellman error over a simple estimator of predicted power ∼ = p κ (although this is not always a good estimate).


Then, to simulate the temporary suppression experiment in [22], we take the original model that had homeostatic regulation applied with all hidden layers intact and developed hallucinations in the process, and clamp the first hidden layer to see whether that would interfere with already established hallucinations.

we would like to thank Nicolas Heess for helpful comments, Geoff Hinton for input on the mechanism underlying the ACh model (cf.


One possible role of a depressing synapse is that the input can quickly bring the neuron up to threshold when the membrane potential is close to the resting potential.

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.


Similarly, to test whether the volume occupied by two objects is exclusive, we assume that the two objects rest on the same floor plane and we compare the projection of their bottom surfaces onto the image.

figure 1 shows an example of a case where volumetric reasoning is crucial in estimating the surface layout of the room.


word2vec+SMM employs the representations of words learnt by word2vec [7] and uses them for the SMM as in SVD+SMM.

there are two main differences between these methods and the proposed method.


The standard approach is to use a local search procedure that changes one arc at a time.

this approach is weak from a variety of perspectives.


But since they still converge at linear rates they do not enjoy the foremost benefits of Newton's method.

we can double the size of the training set in each iteration when the number of samples is sufficiently large.


The Infinite Hidden Relational Model [7] further elaborated on this model and the Mixed Membership Stochastic Blockmodel (MMSB) [8] extended it to allow entities to have mixed memberships.

since entities can have more than a single feature, the model is more expressive.


[19] also provided a lazy evaluation scheme that provides significant computation benefits in practice, while still maintaining the bound.

we hope that by parsing memorability into a concise and understandable set of attributes, we have provided a description that will interface well with other domains of knowledge and may provide fodder for future theories and applications of memorability.


I-Relief [10,11] is a feature weighting method which cleverly avoids the TN change problem by considering a stochastic variant of NN classifiers (neighborhood component analysis [4] also introduced similar stochastic approximation).

such TN changes can be easily detected and handled because the TN-weight consistency conditions are represented by a set of linear constraints (see (3c)-(3e)), and we already have explicit rules (Lemmas 5 and 6) for updating the constraints.


Additionally, use of coding in distributed computing has been explored in [13,7].

recently, coding-theory-inspired approaches have been applied to mitigate the effect of straggling, through embedding redundancy in certain linear computational steps of the optimization algorithm, thus completing the computation without waiting for the stragglers.


It behaves like e y for y < 0, but grows linearly for positive y.

while sufficient for inventories of several thousand fast-selling items, Gaussian assumptions are grossly violated for the extremely large catalogues maintained by e-commerce platforms.


Other Examples: The above two examples show that our analysis recovers two well-known kernelization results for Mahalanobis metric learning.

furthermore, it is significantly better than the corresponding baseline dimensionality reduction methods.


For the top layer we use Fast Persistent Contrastive Divergence which substantially improved generative performance of GDBNs (see supplementary material for more details).

generative models have found most success in learning to model small patches of natural images and objects: Zoran and Weiss [4] learned a mixture of Gaussians model over 8×8 image patches; Salakhutdinov and Hinton [2] used 64×64 centered and uncluttered stereo images of toy objects on a clear background; Tang et al.


This is the part of standard mixture models that has to be modified in order to insert grouping constraints [15] or a grouping prior p(Y) [4,11].

we follow a different route to avoid that roadblock.


The detailed summary statistics of all datasets are shown in the SM.

our multi-layer CNN allows representation vectors to abstract information from the entire sentence, irrespective of order or length, making it an appealing choice for tasks involving long sentences or paragraphs.


[5] investigate the Lipschitz constant of DNN-based classifiers and propose Parseval training.

in this paper, we introduce "deep defense", an adversarial regularization method to train DNNs with improved robustness.


Most recently, [9] proposed an efficient low-rank point process model for time-sensitive recommendations from recurrent user activities.

it is a random process whose realization consists of a list of events localized in time, {t i } with t i 2 R + .


The domain-invariant code in combination with a target domain-specific code, sampled from a desired distribution, is fed to a generator which translates them into the corresponding target domain image.

without the domain-invariant code cycle-consistency criteria (e.g.


Extracting structure in one random variable that is relevant for another variable has been principally addressed recently via the information bottleneck method [15].

figure 3, plots document-clustering accuracy for ¡ ¢ !


At each epoch, node indices are randomly grouped into several batches.

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


To enable Equation 3 to be solved online when tasks are observed consecutively, we adapt concepts from the lifelong learning literature.

even for a single task, LfD may require numerous demonstrations.


The number of Support Vectors (SVs) has a dramatic impact on the efficiency of Support Vector Machines (Vapnik, 1995) during both the learning and prediction stages.

-Examples such that α * i = C are called bouncing SVs or margin errors and satisfy To illustrate dependence on the Bayes risk, we perform a linear classification task in two dimensions under varying amount of class overlap.


The ability to shift emphasis from one "expert" to another, in response to changes in the observations, is valuable in many applications, including energy management in wireless networks.

in the general case, the regret bound is: (T − 1) max i D(P (j|i, α * ) P (j|i, α)), where α, α * are now transition matrices, and D(• •) is the relative entropy between discrete distributions.


Firstly, tuning a full covariance matrix is time consuming and in our case this adaption process must be carried out simultaneously with searching for an appropriate set of control variables.

when for the current set of control inputs X c the chain has a low acceptance rate, it means that the variance of p(f |f c ) is still too high and we need to add more control points in order to further reduce G(X c ).


It can be easily implemented in MapReduce-style parallel computation models [8] and provides a solution that is competitive with the (impractical) centralized solution.

we can trade-off the communication cost per round with the total number of rounds.


Instead of ignoring the dependencies of the activation noise, as in section 3.1, we may retain the dependencies by interpreting dropout (9) as a form of correlated weight noise: where a m is a row of the input matrix and b m a row of the output.

from this perspective, the marginal distributions (10) then arise through the application of the local reparameterization trick, as introduced in section 2.3.


The perturbed accelerations qi = a = ā + ε is given to the system.

most interesting motor learning problems are high-dimensional reinforcement learning problems often beyond the reach of current methods.


To each function g : X → Y we associate the corresponding loss function f : Z → R defined by f (z) = L[g(x), y] where L is a loss function.

for a probability distribution ρ on F, define its j-th projection as ρ j = f ∈Sj ρ{f : p j (f ) = f }δ f , where δ f denotes the Dirac measure on f . To shorten notations, we denote the average distance between two successive "projections" by ρd 2 then for any 0 < β < 1/2, with probability at least 1 − β, for any distribution ρ, we have where χ j (x) = 4 x log 4j 2 β −1 log(e 2 /x) .


Since the ultimate goal is to use coresets for Bayesian inference, the key empirical question is how well a posterior formed using a coreset approximates the true posterior distribution.

for the moment we will consider Θ = B R for any R > 0, where We discuss the case of Θ = R D shortly.


In such a two-choice identification task, the counts k m follow a Binomial distribution: where p m indicates the probability that the mth stimulus is identified as /da/.

measures of complexity have received relatively little attention.


To summarize the testing procedure, DPP-MC, DPP-Full, DPP-MAP were used to choose the initial centroids.

sampling from a DPP requires O(n 3 ) time, as an eigen-decomposition of L is necessary [4].


due to the space restriction, we omit the proof here, but make a note that the proof relies on our SVR algorithm.


We assume ⇡ 0 (x) = N (0, 2 I) as the initial distribution, and optimize through maximum likelihood.

in order to achieve high ESS, HMC samplers typically use many leap frog steps and require gradients at every step, which is inefficient when r x U (x) is computationally expensive.


[2017], although there is no empirical study done.


Figure 1: Twelve related tasks and predictions according to independent GPs (blue, continuous line) and MTMKL (red, dashed line).

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


The cLR-GAN, which draws z vectors from the predefined distribution randomly, produces similar realism and diversity scores.

an effective option explored by concurrent work [2,3,13] is to use a mixture of models.


Running ICA on unwhitened data results in very noisy bases.

if W is overcomplete (i.e., a "tall" matrix) then this constraint can no longer be satisfied.


Results obtained on three classical benchmarks of boosting litterature show that it is worth using additional information conveyed by the patterns alone.

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


iterating between (4) and ( 5) coincides with applying k-means algorithm on all θ n and the goal of finding clusters consistent with the g.m.s for data from ANM-MM can be achieved by firstly estimating parameters associated with each observation and then conducting k-means directly on parameters.


Modern robots are designed to perform complicated planning and control tasks, such as manipulating objects, navigating in outdoor environments, and driving in urban settings.

lPAL can be reformulated as maximizing the margin min i=0,..


On each iteration, the values of W p 's are fixed, which leads to closed-form updates for conditional maximum likelihood estimates of S p 's and vice versa.

in principle, our framework supports the application of more structured priors and noise covariances but we will save the exploration of more elaborate models for future work.


Let (S i , Z(ω i+1 )) n−1 i=0 be a set of n observations.

both methods depend heavily on weights to capture dependence between the state and the outcome.


Incorporating noise models directly into such feature-based HMM systems is difficult, mainly because the explicit influence of the noise on the features is poorly understood.

this work is supported by the EU Project FP6-0027787.


( 18) can be simplified further by expanding ûτ around its leading term, resulting in an expression that recognizably converges to the sparse maximum-likelihood solution (Appendix C).

in many practical situations 1 and 2 -penalty parameters are pre-determined by cross-validation.


A typical choice of decreasing sequence (γ k ) k≥1 is of the form γ k = γ 1 k −α for α ∈ (0, 1].

regarding the sequences of estimators for ∇U , we assume that they can also be correlated but do not assume an explicit form on their relation.


The policy π takes as input the belief state b t and returns an action A t (the policy may be deterministic or stochastic).

we propose a more sophisticated FD method which overcomes this problem and establish its consistency.


Finally, we investigated the practical usefulness of the ↵ ⇤ -preserving transform.

using F(⇧ res ) to model the unlabeled and labeled data distributions makes estimation of not only ↵, the class prior, but also β, µ 0 , µ 1 a well-posed problem.


If for example we assume X ✓ R D and consider random features defined as in the previous section, computing M (x) requires M random projections of D dimensional vectors [6], for a total time complexity of O(MD) for evaluating the feature map at one point.

in this work we assume the points to be drawn uniformly at random with replacement.


Each ancestor node maintains a vector of pointers to all observations attributed to it.

each low level SLAM process was run for 75 time steps, with an average motion of 12cm for each time step.


To solve Problem 1.1 without the imperfect assumption of missing at random, as will be shown later, we need to assume that L 0 is Ω/Ω T -isomeric.

denote the (i, j)th entry of a matrix as [•] ij .


It seems that GNMDS with random input triplets performs best, but for large values of n our kernel function k 1 can compete with it.

by construction, a single triplet is useless, and what matters is the concurrent presence of two triplets: k 1 (x a , x b ) is only affected by pairs of triplets answering d(x a , x i ) is only affected by pairs of triplets answering (4).


From the above three graphs, we can see that all three methods identify the infectious states in an accurate way.

. . , 1 and m = 1, . . . , M, update ˆ (m) t t 1 ) according to t 1 )P (y ).


The difference here is that we have used a normal distribution to replace Dirac delta in Dirichlet processes.

point MAP estimation in semi-supervised MTL will not suffer as much from overfitting as in supervised STL.


Observing the fact that such additional features are usually available in real applications, how to better incorporate features into matrix completion becomes an important problem with both theoretical and practical aspects.

there is surprisingly little analysis on the effect of features for general matrix completion.


An output unit in the second layer is the maximum of d 2 branch units.

we denote the first layer input neurons as h ij , with i ∈ {1, 2, . . . , 2m} indexes the branches of second layer neurons, j ∈ {1, 2, . . . , n 0 }.


We present a method for further grouping of contours in an image using their relationship to the contours of a second, related image.

we compute the exact MAP estimate in the MN using the α − β swap graph cut algorithm ( [3]), which can maximize this type of energy.


Technical details of KMT are described in section 3.

when AutoDJ generates playlists, the user may select only one training example.


We refer the model trained without discarding the scale factor as "non fix γ", the other one as "non kernel-norm".

we point out that the winograd convolution [18] is ideal to accelerate kernel-level sparse models.


This shows that the cls scores account for the accuracy of the highest ranked proposals.

the reason is that Fast R-CNN training depends on fixed object proposals and it is not clear a priori if learning Fast R-CNN while simultaneously changing the proposal mechanism will converge.


( 7), we normalize it by division through the average of the median KL divergences taken over a fixed number of previous trajectories.

optimizing the variational lower bound in Eq.


samples from any distribution and numerically approximate the bias for any choice of the parameters.

we resolve each of these deficiencies in this paper by undertaking a comprehensive study of estimating the (differential) entropy and mutual information from i.i.d.


In this next equation, we point out the Proposal and Target Distributions used on the Metropolis Based Sampler (discussed next).

in fact, the total number of offspring at any given time is determined by the sum Next, we explore the definition of Granger causality for point processes [16,48].


It removes in each iteration the feature that minimizes the ranking value where s is a scaling factor used to simplify the computation of partial derivatives.

aging and fibrosis appear again, showing the relationship between acceptance and tenderness.


The free charge flow in S + and S − yields a distribution of charges, the α i , such that Coulomb energy is minimized.

as anticipated, the p-SVM requires far fewer support vectors.


From a qualitative standpoint, SDA-DP discovers sensible clusters in the data, as demonstrated in Figures 4a-4c.

the main contributions are a component identification optimization based on a minibatch posterior decomposition, a tractable bound on the objective for the Dirichlet process mixture, and experiments demonstrating the performance of the methodology on large-scale datasets.


The official test split released by NIST (National Institute of Standards and Technology) is used [15].

this anti-group-sparsity representation is expected to realize the desired diversity.


Though numerous variants of gradient quantization and/or sparsification have been proposed and successfully applied to different deep learning tasks [42,45,37,48,18,7,16], their impact to the convergence rate of distributed SGD (especially for non-convex optimization) is still unclear.

distributed stochastic gradient descent has been extensively studied in both deep learning and high-performance computing communities, with the goal of accelerating large-scale learning tasks [13,10,9,47,3,14,30,31,6,44,38].


A simple scheme to reduce errors in this case could be to take a majority vote after asking the same question to multiple different crowd workers.

we can also observe from Figure 4 that if q = 0.5 then the incorrect labeling is 50% because the complete information from the oracle is lost.


We shall denote by S the K max -selected variables: The computational complexity of the K max -long regularization path of LASSO solutions is Most of the time, we can see that the Lasso effectively catches the true changepoint but also irrelevant change-points at the vicinity of the true ones.

in this section, we propose to apply our method previously described to real data which have already been analyzed by Bayesian methods: the well-log data which are described in [20] and [6] and displayed in Figure 1.


The three sample-problem for dependent time series has been addressed in [9] for Markov processes and in [23] for stationary ergodic time series.

the problems of time-series clustering, homogeneity testing and the three-sample problem are addressed.


An expected small reduction in accuracy is evident in the sparse case.

an alternative re-arrangement of (10), motivated by [5], leads to a re-estimation update which typically converges significantly more quickly: Note that these Wi updates (14) are defined in terms of the computable (i.e.


Variational Autoencoders also show some promise for conditional image synthesis, in particular recurrent versions such as DRAW [Gregor et al., 2015, Mansimov et al., 2016.

simple captions involving skiing, golf and yoga tend to work, but complex descriptions and unusual poses (e.g.


This is what causes the excessive length of the embeddings of the horizontal girder-like structures which are blocking all vertical hyperplane cuts in figure 1(b).

they use an augmented Lagrangian approach to move the constraints into the objective function, which they then minimize using limited memory BFGS.


We emphasize that the algorithm only touches user data through the subroutines VOTE, and EST, each of which accesses data from a single user in at most two epochs.

in the Bernoulli case users could reason about the evolution of µ t j directly from their own samples in each epoch.


Exactly aligned n-dimensional subspaces have all n principal angles equal to 0 • .

the matrix C describes the dependence of the high-dimensional neural signals on the lowdimensional latent processes x t . equation 2 determines the firing rate of the neurons.


Intuitively, this is the amount we have to perturb function f in order to remove this branch-feature.

this general problem is hard and requires algorithms both mathematically sophisticated and computationally intensive.


Raising the fJ values increases the speed of convergence to asymptote, and the absolute values of the contingent asymptotes decrease in proportion to (fJo -fJI).

even when a task demands ratings of causal strength, the structural uncertainty should still be taken into account; we do this by considering a hierarchy of causal models.


A useful method for solving this problem is by using linear discriminant functions .

an important difference of the robustness concept and the margin concept is that outliers may not be observable with large probability from data while margin generally will.


Note that Filter-Boost uses weak learners which are simple classifiers to perform regression.

we implement MadaBoost with the same modifications as FilterBoost.


Figure 3a shows a boxplot of the L 2 loss of the predicted Y values with respect to the true values for both the baseline and our method, considering the 121 cases out of 200 in which our method does produce an answer.

as the transfer bias can become arbitrarily large (as we have seen in Example 1), the prediction accuracy of this solution strategy may be arbitrarily bad (even in the infinite-sample limit).


An immediate consequence is that given error tolerance 2 (0, 1) and with choice 2 (0, 1 4 2 ), then upper bound (10) is at most (by having each of the two terms on the right-hand side be  2 ) if n > m log 2m (i.e., = 1 + log 2 / log m), and This means that if we have access to a large enough pool of labeled time series, i.e., the pool has ⌦(m log m ) time series, then we can subsample n = ⇥(m log m ) of them to use as training data.

as a running example used throughout this paper, consider a time series that tracks how much activity there is for a particular news topic on Twitter.


Our aim was to test the efficacy of this new approach to feature extraction for text categorization, and to compare with a state-of-the-art system such as the one used in [6].


over the non-negative diagonal matrix Γ (this follows from a duality principle in Type II models [18]).

while switching between Φ = W ΦD and Φ = Φ may influence the initialization and possibly the update rules of a particular Type II algorithm, it does not fundamentally alter the underlying cost function.


We define φ(s t , a) as a concatenation of the current feature vector and a meta-feature vector that provides information about previous classification results and cost.

this method ignores the difference between distributions of states induced by executing the oracle's policy and the learner's, thus has a quadratic loss in the task horizon T . A recent approach called Dataset Aggregation [3] (DAgger) yields a loss linear in T by iteratively training the policy in states induced by all previously learned policies.


(2) If the Gram matrix is entry-wise non-negative and if the set of predictors indexed by {1, . . . , p} can be partitioned into subsets B 1 , .

since Z j 2 ≤ X j 2 and e j Σ −1 SS X S / √ n 2 ≤ {φ min (S)} −1/2 for all j, the sub-Gaussian parameters of these collections are upper bounded by σ/ √ n and σ/({φ min (S)} 1/2 √ n), respectively.


[6] defined a scoring matrix for the c-class classification problem.

given a set of n p-dimensional data points, {x 1 , .


The construction in our result is ultimately rather simple, and relies on powerful results developed in complexity theory over the last decade.

this result holds even if we ask only for policies whose expected return approximates the optimal within a polynomial factor.


The Markov matrix P defines an imposed diffusion process, shown by Coifman & Lafon (2006) to efficiently capture the diffusion geometry of a manifold M. The DM framework may be used for dimensionality reduction to embed data using the eigendecomposition of the diffusion operator.

3) 2: Define a sparsity measure ŝ(i), i = 1, ..., N (Eq.


m Φ : Sampling directions Φ (2) are designed to satisfy the RIP for rank-k matrices (cf., Section 3).

unfortunately, this leads to a collateral damage of amplifying the impact of noise if the queries are corrupted.


In contrast to previous work [3], which used a smooth prior on the concentrations, here we use a spike and slab prior.

at the behavioral level, the two algorithms make very similar predictions.


The rate T ∝ 1 σ 1/2 ε 2 does not seem to be known before.


This matrix is of rank at most r < q for every set {x i } of arbitrary size n if and only if the functions {f k } are r-linearly independent-each function can be written as a linear combination of r of the other functions.

. . , m q ) of q smooth (regression) functions, and suppose that n > q.


1 shows the segmentation for a typical image from which it can be seen that, moving horizontally from right to left, the only "legal" transitions in segmentation are B → F, F → O and O → B. Algorithm 1 is therefore modified to consider legal segmentations only.

algorithm 1 gives pseudo-code for the incremental incorporation of a measurement and greedy labelling.


If the next hypothesis p t+1 of a ROME algorithm is on H t , then by Lemma 2, it and all other members of H t satisfy D(p t+1 ||u) = D(p t+1 ||p t ) + D(p t ||u).

it improves on Pinsker's inequality (Lemma 1) when n = 2, p is small, and q is close to p. The following is a direct consequence of Lemma 8 and Theorem 6.


An implementation of EBBoost requires exhaustive enumeration of weak learners in search of the one that minimizes cost (3).

adaBoost iteratively builds S s=1 α s G s (•).


Since we do not use any feature extractors in this setting, it can be applied to mixture models that model data for which it is hard to design feature extractors, e.g.

the expected projection coordinates can thus be computed as: G = [g 1 . . . g N ] = UL.


Every other hypothesis h ∈ R H is defined as its own subregion S i , i > 1, where R H is a set of hypothesis where a region is not valid.

our framework terminates once a single feasible path is found while AEE* continues to evaluation in order to minimize expected cumulative sub-optimality bound.


In the setting of least-squares function approximation, the second-order algorithm of choice is commonly Gauss-Newton, which approximates the curvature as the Gauss-Newton matrix G := E[J T J], where J is the Jacobian of the mapping from parameters to outputs [18].

the Euclidean norm of the change depends on the parameterization θ.


While both methods have broad applications in classification, the discriminative methods have often outperformed the reconstructive methods for the classification task [15,16].

with the theoretical framework of SRSC, our objective is to achieve a sparse and robust representation of corrupted signals for effective classification.


The problem of disentangling factors of variation also plays an important role in completing image analogies, the goal of the end-to-end model proposed in [24].

for instance, the factors of variation involved in generating a speech recording include the speaker's attributes, such as gender, age, or accent, as well as the intonation and words being spoken.


The rest of the paper is organized as follows.

the second fundamental form II, which is an extrinsic quantity describing how the tangent spaces bend locally is, at every x ∈ M, a map II x : T x M → (T x M) ⊥ (in this case of class C 1 by Assumption 2) from the tangent space to its orthogonal complement (II(x) := B(x, x) in the notation of [16, p.


The computational burden of such a joint modeling seems prohibitive, and the feasibility of obtaining the global optimum is far from obvious, because each warping function is coupled to all the rest, either directly or indirectly.

here we focused on one segmented area and identified the propagation pattern within it.


( §3) 3) In order to use attention mechanisms defined under our framework in an autodiff toolkit, two problems must be addressed: evaluating the attention itself and computing its Jacobian.

we illustrate max Ω and Π Ω for various choices of Ω in Figure 2 (2-d) and in Appendix C.1 (3-d).


We partially labelled some of the images.

to deal with the above we marginalize out S n and we sample z nk from the marginalized posterior conditional P (z nk |S −n , Z −(nk) , α, X) which is computed according to P (z nk |S −n , Z −(nk) , α, X) ∝ P (z nk |Z −(nk) , α) where P (z nk |Z −n,k , α) for the infinite case is computed as described in section 3.2 while computing the sum requires an approximation.


Current binary algorithms restrict m and n to be integer values, in large part because efficient CPU implementations require parameters within a layer to be the same bitwidth.

to evaluate HBNNs we wished to answer the following three questions: (1) How does accuracy scale with an uninformed bit distribution?


In this work, we focus on optimizing the computation cost.

. . , l k . The proof is in Supplementary Section 8.6.


In addition, only when jointly optimizing the network weights (fine tuning), which requires solving a non-convex problem, the accuracy achieves state-of-the-art performance of 54.3%.

in addition, such non-linearity, akin to neural networks, has desirable properties in terms of Gaussian complexity and generalization bounds [1].


While more sophisticated methods including variational approximations, c.f., [18] are possible direct use of PPCA is often sufficient in practice.

we argue that D-PPCA can still handle missing points given the evidence below.


Section 2 and 3 give the specification of the problem and formalise the verification process.

we keep track of the global lower bound on the minimum by taking the minimum over the lower bounds of all sub-domains (line 19).


Second, the forward propagation mechanisms of these two modules seem to be similar, that is, both the two modules update the output of sub-bands/layers stage by stage.

this pre-processing step increases computation complexity because the size of feature maps is multiple.


SAIL learns a near-optimal policy using only 1000 sample episodes.

we evaluate the performance of SAIL collecting one new unsupervised sample episode in each iteration, reusing the samples collected in the past 19 episodes and compare the results against our implementation of Relative Entropy IRL [1].


In this paper, we develop a novel approach to the problem of learning sparse representations in the context of fused sparsity and unknown noise level.

the most appealing penalty, the number of nonzero elements of Mβ, leads to a nonconvex optimization problem which cannot be efficiently solved even for moderately large values of p. Instead, convex penalties of the form minimizer of the penalized log-likelihood To ensure the scale equivariance, the weights ω j should be chosen inversely proportionally to σ: ω j = σ −1 ωj .


We now proceed to explain how to model and jointly learn ⇡ ✓ and Q ✓ to achieve this objective.

one approach is to use the learned policy ⇡ ✓ to walk through the graph G to find n T . this would not exploit the known MDP transition model (1).


In this section, we outline related works with different and similar uncertainty sets, constraints and objectives.

according to the unknown density function f * of the uncertain parameter ξ.


In order to make the comparison fair, compact networks with similar compression levels are compared together.

as analyzed above, GM saves computations but suffers from the information inconsistency problem.


The transductive online model considered by Ben-David, Kushlevitz, and Mansour [2], consists of an instance space X and label set Y which we will always take to be binary Y = {−1, 1}.

one can also use the following proper learning algorithm.


While potentially effective in practice, homotopy continuation methods require both a trade-off parameter for g(x; θ) and a pre-defined schedule or heuristic for adjusting θ, both of which could potentially be image dependent.

noise and kernel dependencies notwithstanding, this reparameterization places the proposed cost function in a form exactly consistent with nearly all prototypical sparse regression problems, where 2 column normalization is ubiquitous, at least in part, to avoid favoring one column over another during the estimation process (which can potentially bias the solution).


Thus we have a fully marginalized likelihood as f (x, z, m|γ 0 , c, r) = f (z, m|γ 0 , c, r) .

it does not necessarily mean that the HDP-LDA has better predictive performance than the BNBP topic model.


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

for example if ¢k is a non-linear function, we may have to use iterative optimization to find Bit).


all of them use the vanilla binary discriminator.


( 3), hence further increasing the number of samples does not significantly change the optimization problem.

we define a family of transformations {T α | α ∈ A} parameterized by vectors α ∈ A, where A is the set of all possible parameter vectors.


• With intermittent communication, we show how different methods are better in different regimes, but even combining these methods does not match our lower bound.

• For non-smooth objectives and a stochastic prox oracle, smoothing and acceleration can improve performance in the layer graph setting.


We can also check to see that the category memberships s dc are being used effectively.

samples from f can be drawn in a variety of ways.


Experiments on both synthetic and real data show that SRHT-DRR gives significant speeds up with only small loss of accuracy.

pCA is a "keep-or-kill" estimator as it kills components with smaller eigenvalues.


Observations of X are simulated independently from N (0, 1) in M1, Unif(−1, 1) in M2 and M3, and Unif(0, 2) in M4 and M5.

its main drawback is that it neglects possible interactions between predictor variables.


Nodes C and D, children of a neutral "tax" topic, reveal how parties frame taxes as gains in terms of new social services (Democrats) and losses for job creators (Republicans).

after choosing the table (indexed by t d,s ), if the table is new, the group will select a combo of dishes (i.e., a path, indexed by c d,t ) from the tree menu.


. . , a D , we independently sample n pairs (x 1 , y 1 ), .

speech recognition on TIMIT This task requires producing accurate transcripts from raw audio recordings of conversations in English, involving 630 speakers, for a total of 5.4 hours of speech.


if several test samples are to be treated in succession, and we want to avoid a full, resource-consuming re-training using all the training samples each time, an interesting alternative is the following: learn once a function f 0 (P X , x) using the available training samples via (3); then, given a partially labeled test sample, learn a decision function on this sample only via the usual kernel norm regularized empirical loss minimization method, but replace the usual regularizer term f 2 by f − f 0 (P x , .)


4 Furthermore, note that 1(x 0 ) (I − {P (x |x, π B )} x,x ∈X ) −1 1(x) represents the total visiting probability E[ from the initial state x 0 to any state x ∈ X , which is a non-negative quantity.

we include runs using discrete observations (a one-hot encoding of the agent's position) and image observations (showing the entire RGB 2D map of the world).


-Convex minimization: A = ∂g and B i = ∂f i for a strongly-convex function g and smooth functions f i : we recover proximal-SVRG [24] and SAGA [3], to minimize min z∈E g(z) + i∈I f i (z).

there is no need to assume the existence of a function We will also consider splits which are adapted to the saddle-point nature of the problem, that is, of the form B(x, y) = k∈K B x k (x, y), j∈J B y j (x, y) , which is a subcase of the above with I = J × K, B jk (x, y) = (p j B x k (x, y), q k B y j (x, y)), for p and q sequences that sum to one.


To understand these optimality criteria intuitively, it is helpful to see their equivalence of the Gaussian distribution in the limit of large κ 1 , κ 2 and κ s . Under the condition x 1 ≈ x 2 , Eq.

κ s determines the correlation between two stimuli, i.e., how informative one cue is about the other, and it regulates the extent to which two cues should be integrated.


Similarly, circles should be closer to each other than to squares.

the most relevant related work is the work of Xing et al [11] which focused on the problem of learning a distance metric to increase the accuracy of nearest neighbor algorithms.


Many prior studies [4,10,13,2,28,27,26] have shown the advantage of using χ 2 similarity compared to other measures such as l 2 distance.

future research Many interesting future research topics can be studied.


For 2D datasets, we use the recently released Pix3D dataset to obtain 1, 515 RGB images of chairs alongside with their silhouettes [Sun et al., 2018a], with an addition of 448 clean background images crawled from Google image search.

the discriminator D shape contains 6 volumetric convolutional layers and the generator G shape contains 6 strided-convolutional layers.


(iii) Power law matrix completion: ∀i, Ai measures a random entry of X * chosen according to a power law distribution.

(7) is no longer a valid solution for (4).


In this paper we take just a few steps toward more general predictions.

in Experiment 3, on the other hand, we applied TD networks to a non-Markov version of the random-walk example, in particular, in which only the special observation bit was visible and not the state number.


We have used a similar approach to [13] to find subspace minimal perturbations.

if k denotes a class that has no boundary with class k, r k 2 can be very large and the previous curvature condition is not satisfied.


When working with a neighborhood graph, the proposed method yields high-quality codes to well preserve the neighborhood structure inherent in the data.

1-2 in the supplemental material show convergence curves of Q starting from the two initial points).


In this case, selecting an estimator is a classic regression problem: find a function that best maps the observations to the correct values, in a least squares sense.

for comparison purposes, we have included the behavior of SURE thresholding [13], in which Eq.


The reviews have an associated number of "stars," ranging from 0 to 5, rating the quality of a product.

if P is sparse, as it is in our experiments-i.e., it has only kd entries for k ≪ d-then the matrix multiply is O(d).


A sampling result then shows that a small random sample of these output trees can attain a significant fraction of the margin obtained by the complete graph.

given any unit L 2 norm predictor w on the complete graph G, our task is to investigate how the margins Γ(w, x, y), for each (x, y) ∈ X ×Y, will be modified if we approximate the (true) expectation over all spanning trees by an average over the sample T . For this task, we consider any (x, y) and any w of unit L 2 norm.


(2) The use of unlabeled data enhances our ability to avoid parameter over-fitting and over-estimation in grid based random fields even when using a learner that uses only approximate inference methods.

assume we have a set of independent labeled images, D l = " (x (1) , y (1) )), , and a set of independent unlabeled images, " .


From this last expression, we see that the risk is like a standard binary classification risk based on ( X, Y ) ∼ Q µ .

our methodology is shown to yield a consistent learning procedure, meaning that the generalization error tends to the best possible as the sample sizes N, {n i }, n T tend to infinity.


Randomized neural networks are immortalized in this AI Koan: In the days when Sussman was a novice, Minsky once came to him as he sat hacking at the PDP-6.

since others have already empirically demonstrated the benefits of random featurization [2,3,4,5], we only a present a few illustrations in this section.


This should not be too surprising given that it uses much more memory, and is known to give pointwise rather than average case guarantees.


In the supplementary material, we provide proofs of all mathematical results in the paper.

these methods can be applied only to non-attributed (unlabeled) graphs, which largely limits their applications in the real world.


In the case of probabilistic programming, recall that random variables (or ERPs) are represented as stochastic functions f i that accept parameters θ i .

making large, global proposals is very effective.


P Then r f @xA P @ f@e A A This is a consequence of our formula for r © , but see the appendix of the extended paper [21] for a detailed proof.

to prove optimality of a candidate set A, we can use a subgradient of f at e A .


Rather, we only need a ranking of the best few candidates.

by analyzing the role of the residual matrix, we see that the information pivots provide a low-rank approximation to the orthogonal complement of the space spanned by current inducing set.


In the following text we will first discuss in Sec.

thus the correct rank can be estimated using the value minimizing consecutive eigenvalues, as suggested in [14].


Lemma 1 (Linear expansion of the Gaussian Kernel).

interestingly, our network uses non-linear functions that resemble rectified linear units [1,30], even though they were not handcrafted and naturally emerge from an approximation scheme of the Gaussian kernel map.


All these works use simple Monte Carlo sampling.

in line with previous work we run experiments for the kernel approximation on a random subset of a dataset.


Handcrafting a different specialpurpose motivational system (as in the usual RL practice) should be largely unnecessary.

automatically, the skill of achieving the simpler events are learned before those for the more complex events.


This research was supported by the Natural Sciences and Engineering Research Council of Canada (RGPIN 312176-2010, RGPIN 311661-08, RGPIN-06068-2015).

{Skip exponential number of future evaluations if it remains zero.}


Thus, this concept is important because the g-values of all vertices equal their start distances iff all vertices are locally consistent.

we apply LPA* to navigation problems in known eight-connected gridworlds with cells whose traversability can change over time.


We can therefore approximate the kernel function as an empirical average of samples from the distribution.

if the data follow a Gaussian distribution, and we use a Gaussian kernel, then the eigenfunctions are given by the Hermite polynomials.


Actually, they are random samples of a centered Gaussian process indexed by the space X with covariance structure given by 1 P ϕ(x), ϕ(x ) , where we use the notation u, v = i u i v i for two square-summable sequences u and v. Indeed, E A p [ψ p (x)] = 0, and The continuity of the initial features (ϕ i ) guarantees that there exists a continuous version of the process ψ p which is thus a Gaussian process.

this is no more the case when P is not the Lebesgue measure and it seems difficult to modify the features ϕ i in order to recover the same bound, even when P is known.


At any finite rate R, the distortion term and the divergence term in (3) have strikingly opposing effects.

to train G by means of WAE-MMD and WGAN-GP we use the training parameters form [17] and [28], respectively.


Examples of this model include the dynamic mixed-membership block model [5,12] and the dynamic infinite relational model [14].

for all other entries of Θ k we use N (0, ν 2 ) as a prior distribution.


All we left is to prove iii) =⇒ ii) or equivalently i), for the case dim(H) ≥ 2.

f = h( • ) for some increasing function h : R + → R; ii).


Figure 2 illustrates the first two iterations of EBP applied to these simulated data.

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


The number of consumers was M 1 = 138, and each consumer gave scores of about M 2 = 3 different aspects (food quality, service quality, and overall quality).

another promising approach is the alternating minimization procedure which alternately updates each component of the tensor with the other fixed components.


This is surprising: because of the way the uniform train/test splits were created, all test pixels are close to multiple train pixels.

1  The proposed CoordConv layer is a simple extension to the standard convolutional layer.


For the general convex and Lipschitz continuous optimization problem, the iteration complexity of gradient (subgradient) descent is O( 1 ǫ 2 ), which is optimal up to constant factors [15].

the objective function can be rewritten as (10) And the mixed gradient can be rewritten as gk = g + ∇g t (w t ).


Here, we introduce a new approach using a near-maximum entropy model, that makes this type of analysis feasible for very high-dimensional data-the model parameters can be derived in closed form and sampling is easy.

while for small image patches the DG model provided an excellent fit to the true distribution, we were able to show that this agreement breakes down in the case of larger image patches.


Control was historically among the earliest applications of neural networks, but the recent surge in performance has been in computer vision, speech recognition and other classification problems that arise in artificial intelligence and machine learning, where large datasets are available.

in fact, the trajectory costs for both MPC and our method are very similar.


#grad / n   Given 2B IFO calls, SGD implements updates on two fresh batches while SCSG replaces the second batch by a sequence of variance reduced updates.

by leveraging the batch and mini-batch sizes, we obtain a counterpart of Corollary 3.3 as below.


2) Per-label decomposition [16] trains one classifier for each output label and makes independent decision for each of those.

the results show nicely how the assumptions made during training influence the prediction characteristics.


Note that four of these examples are sufficiently hard to be unsolved by a variable elimination-based exact solver, even with several orders of magnitude more computational resources (200GB memory, 24 hour time limit).

importantly for this work, this same relaxation can also be used to define a proposal distribution for importance sampling that yields finite-sample bounds [15].


A fundamental question is discovering new, non-native folds or structural elements that can be used for designing these novel proteins.

we found that the generator was able to learn to construct meaningful secondary structure elements such as alpha helices and beta sheets.


Our algorithm learned a good policy under significant observation noise in less than 30 seconds of system interaction.

the joint distribution over the updated (random) belief and the (non-random) action is Next, the filtering 'prediction step' computes the predictive-distribution of b t+1|t = p(x t+1 |z 1:t , u 1:t ) from the output of dynamics model f given random input bt|t .


Table 2 shows the statistics of symptom acquisition.

the symptom space of the disease diagnosis problem is sparse.


Then, we can learn these embeddings by a ranking model.

this still involves a summation over Y, however, so it requires O(|Y|) calculation.


The constant c controls the relative importance of these two competing terms and it can be chosen via cross validation.

given n input examples x 1 , ..., x n in ℜ D and corresponding class labels y 1 , ..., y n , the technique in [9] learns the D × D transformation matrix L that optimizes the following objective function: where η ij ∈ {0, 1} is a binary variable indicating whether example x j is one the k-closest points of x i that share the same label y i , c is a positive constant, y il ∈ {0, 1} is 1 iff (y i = y l ), and h(s) = max(s, 0) is the hinge function.


This approach assumes discrete features and a model of the environment.

this weighting corresponds to model confidence -since the flow regularization penalizes the network heavily when it predicts large translations, the model has more confidence that an object is there if the predicted translation is large.


For any signed graph, the complete w-reductions are obtained by first using reductions (w1,w2) and then reducing the bridges (w3) because (w3) always makes the degree bigger and does not make a loop.

if the graph is a tree, however, they are efficiently computed by the belief propagation algorithm [1].


A different label is fed into DPN to switch among response policies by linking the shared convolution layer with the corresponding control layer, achieving convenient fast policy switch.

deep BPR+ inherits all the advantages of BPR+ and empirically shows better performance in terms of detection accuracy, cumulative rewards and speed of convergence compared to existing algorithms in complex Markov games with raw visual inputs.


Two non-uniform sampling distributions based on block norm squares and block partial leverage scores are considered.

one should expect these algorithms to perform well when n d and the problem is moderately conditioned.


Our maximum leverage score assumption is very mild and much weaker than the standard incoherence assumptions used for example, in matrix completion, which allow for uniform sampling based approaches.

since the SOLS instance has a much smaller size, its per iteration computational cost is much lower than that of OLS.


Ulmnn and mt-lmnn global metric perform much better than the Euclidean metric, with U-lmnn giving slightly better classification.

in this paper we introduced a novel multi-task learning algorithm, mt-lmnn.


We extend this idea to SMC-based inference in general PGMs, and we also propose a novel way of constructing the twisting functions, as described below.

log Z-which is what we actually compute-is negatively biased and it therefore typically holds that higher estimates are better.


Our algorithm GREEDI partitions V into sets V 1 , V 2 , .

for any value of m, and k, there is a data partition and a monotone submodular function Algorithm 1 Exact Distrib.


In the experiments, we demonstrate that the markers obtained using our approach are capable of retaining bit strings that are long enough to be practical.

one can set the recognizer to have a certain architecture, fix the variability and the strength of the adversarial effects that need to be handled, and then the synthesizer will adapt so that the most "legible" codes for such circumstances can be computed.


While the optimization ( 14) is convex, the running time of lasso is significantly longer than OMP unless A has some particular structure [10].

the lasso method, which will be described in detail in Section 4, is based on a convex relaxation of the optimal detection problem.


Because all A i share a global critic, C, all that remains of each module is the actor A i .

in this section we review the aspects of the conjugate Markov decision process (CoMDP) framework that are relevant to this work.