For instance, when the data are high dimensional and the sample size is large, constructing the estimator using standard methods may be computationally prohibitive.

for each combination of the values of c and B, we vary n, the dimension of the mean vector, which is also the number of observations.


Unfortunately, traditional VP detectors tend to fail in the presence of clutter, which our images exhibit to a large extent, for example generated by shadows.

hence, we have with s the index for the parking spot location within a parking area and Here, c p , π m and Σ m are defined as above, while µ m = µ m (s, l, R) ∈ R 2 is the coordinate of the parking spot location in bird's eye perspective (see Fig.


Second, we notice that in learning theory the consistency property (2) involves the control of the quantity If P is the projection on the closure of the range of A, the definition of P gives (the above equality stronlgy depends on the fact that the loss function is the square loss).


The key modification is to use (10) to show that the effect of the noise is asymptotically negligible so that for large n, This is done by separately considering the components of w in the span of the vectors a j for j ∈ I true and its orthogonal complement.

this "genie" algorithm is identical to the regular OMP method in Algorithm 1, except that it runs for precisely k iterations as opposed to using a threshold µ for the stopping condition.


Here we propose an efficient approximate solution via alternate optimization.

to address this problem, we attempt to characterizes the global manifold geometry structure by computing the full adjacency matrix, i.e., [K]  , where d is geodesic distance for general cases or Euclidean distance for flat manifolds.


In the setting of 'zeroth order' attacks [2,3,35], the model parameters are hidden and acquiring its gradient is inadmissible.

samples from [n] with replacement, and δ n = I(b < n) if samples are randomly selected without replacement.


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

sample-based EM iteratively updates its estimate of θ according to the following equation: where y 1 , .


Note that since in our application all training facts are ground atoms, we only make use of the proof success score ⇢ and not the substitution list of the resulting proof state.

subsequently, we predict a ranking of every test fact and its corruptions to calculate MRR and HITS@m. Results for the different model variants on the benchmark KBs are shown in Table 1.


data are sampled from the training dataset to update the models.

titsias [26] proposes to use is the conditional probability in the full GP.


To test the N HM O model, we took two routes, corresponding to the two methods for prediction described above.

the performance function to be optimized for .


This allows us to write the objective (the margin) as a minimum over all training points-a form we will later exploit.

in order to implement the sampling operations in time O(log n) and O(log d), we maintain a tree over the points and coordinates, with internal nodes caching the combined (unnormalized) probability mass of their descendants.


Before presenting our theoretical analysis, an important special case to discuss is ν = 1, which corresponds to a deterministic actor-critic method.

this gradient estimator is biased from two sources: off-policy state sampling ρ β , and inaccuracies in the critic Q w . as we show in Section 4, we can bound the biases for all the cases, and in some cases, the algorithm still guarantees monotonic convergence as in Kakade & Langford (2002); Schulman et al.


Remarkably, Lever, Laviolette, and Shawe-Taylor are able to upper bound the KL divergence between the two distributions by a term independent of D, yielding the following result: Here kl(q||p) is the KL divergence between Bernoulli measures with mean q and p. See Section 4 for more details.

assume 2 that, for every c > 0, there is a step size h > 0 and number of SGLD iterations n 2 O( 1 c q ), such that the n-th iterate w(S) 2 R p produced by SGLD satisfies W 2 P[w(S)|S], P[A (S)|S]  c. Markov's inequality and the definition of W 2 immediately implies the following.


We will use Xi as a shorthand for the collection of the ith coordinate of all the samples: The mean-squared loss of the protocol ⇧ with estimator ✓ is defined as and the communication cost of ⇧ is defined as The main goal of this paper is to study the tradeoff between R ⇣ (⇧, ✓), Proving Minimax Lower Bound: We follow the standard way to prove minimax lower bound.

there has been a lot of work on the paradigm of studying communication complexity via the notion of information complexity [6,7,8,9,10].


In practice, the DRIP and XCorr p-value computations are at least an order of magnitude slower than XCorr computation in Crux [21].

in practice, scoring functions are often poorly calibrated (i.e., PSM scores from different spectra are difficult to compare to one another), leading to potentially identified spectra left on the table during statistical analysis.


Note that draws from X must be consistent with the observations Y 1:n . The usual approach to the consistency issue is to make a proposal by conditioning a linear diffusion to hit some neighbourhood of the observation Y k , then to make a correction via a rejection sampling [18] or a Metropolis-Hastings [16] step.

in our experiments, the algorithms terminated in a roughly similar length of time (though no serious attempt was made to optimise the runtime of either method).


More efficient techniques could also be employed (including several proposed for CS in the presence of noise [3,5,7,10,12]).

in addition, given the (K + K 1 )c measurements for x 1 as side information, and assuming that the partitioning of x 1 into z C and z 1 is known, cK 2 measurements that describe z 2 should allow reconstruction of x 2 .


6, it can be inferred that the holistic feature vector X can be obtained by X = X − β ∂L ∂X , where β = α Z 2 , implying that updating weight parameters w with SGD can implicitly lead to the update of the output feature in the similar way.

considering the distribution symmetry of W , the angle range of the constrained region for class y i is 2θ = 2π c , which is inversely proportional to c. if the class number increases, the constrained region of each class will be more and more compact.


Note that θ corresponds to the adjacency matrix constructed by the p components of X as nodes, and θ ij = 0 indicates that there is an edge between X i and X j .

2011, Mazumder and In the Gaussian case, the screening rule can be attained by simply replacing the second empirical moment matrix in (4) with the sample Algorithm 1 Blockwise Minimization 1: Input: dataset X, regularization parameter λ.


It is crucial to note though that, since the experts are compared on a sequence-bysequence basis, the MR criterion ignores the possibility that different experts may induce different sequences of choices by the opponent.

. . , N r (i) the values of the registers N 1 , .


We have shown that in the rank=2 parameterization of the logistic regression function, the optimal filter coefficients has an interpretation as a solution to a generalized eigenvalue problem similarly to CSP.

secondly, simultaneous diagonalization of covariance matrices can suffer greatly from a few outlier trials as seen in subject A in Fig.


Instead, we use simulated annealing [19] with f (x) as the energy function.

to build context relation features, we treat context vectors as a bag of points and extract features that model relations between feature axes.


Second, when resampling s within the Gibbs algorithm, we require the full conditional distribution of s given the other variables, which is proportional to p(s|θ)p(y | s).

we need a new release mechanism A and inference algorithm P. We present a solution for the case when x is univariate.


For dense graphs satisfying d = Ω(n) (which is studied in [FSGC14]), we prove a stronger upper bound of α(n) = O( 1 √ n ) using the Szemerédi regularity lemma.

we show that this naive bound can be asymptotically improved upon, by constructing an α-multitaskers with α = Ω( log d d ).


In a first experiment we focused on the multi-objective optimization problem defined in (4).

in particular we defined an hybrid multiobjective training criterion for GSNs, dividing the cost function into a generative and discriminative part.


We call these experiments because the goal of solving these problems is to disambiguate nondeterministic action models.

a set of goals G is a cover of a set of states R if g∈G {s : s satisfies g} = R. Given the goal language G and a model M , the problem of experiment design is to find a set of goals G ⊆ G such that the sets of states that satisfy the goals in G collectively cover all informative states I(M ).


As another useful property of LARS/Homotopy algorithms, it is worthwhile to mention that changes of the active set only happen at the breakpoints [17,7,15].

c) The Alzheimer's disease neuroimaging initiative (ADNI; available at www.loni.ucla.edu/ADNI) studies the disease progression of Alzheimer's.


Thus, the mental look back into the past seems to occur exactly when credit assignment is to be performed.

can Sparse Attentive Backtracking (SAB) capture long-term dependencies?


When written in matrix form, the ADCLUS model seeks to uncover a feature matrix F and a weight vector w such that S ≈ FWF , where W = diag(w) is a diagonal matrix with nonzero elements corresponding to the saliency weights.

since the IBP describes a prior over infinite feature matrices, the resampling procedure needs to accommodate the remaining (infinite) set of features that are not currently represented among the manifest features F. When resampling feature assignments, some finite number of those currently-latent features will become manifest.


We strongly believe that the hold-out method will yield theoretically founded adaptive model selection for CG as well.

to simplify notation we define f m := f αm .


In particular, LFR only considers binary-valued D, and consequently, we restrict D to be binary in the experiments presented here.

convexity, robustness to limited samples), and (iv) benchmark the ensuing pre-processing transformations on real-word datasets.


In this paper we develop a Bayesian treatment of the super-resolution problem in which the likelihood function for the image registration parameters is based on a marginalization over the unknown high-resolution image.

the registration parameters are unknown.


This implies that, in principle, the predicted interval equals the universal interval.

the presented stimuli are generated from a factorial manipulation of the sources of information by systematically varying the ambiguity of each of the sources.


Finally, we use the notation of finite measure spaces for simplicity, but our approach extends to the continuous case.

the Rao-Blackwellized estimate ( 6) is more expensive to compute than (5) because we must compute conditional expectations.


Sakai & Fukai [5,6] proved that Q-learning does not lead to matching behavior.

for the delta rule without normalization, the asymptotic values gradually depend on η.


For decoupled PRD, we maintain running averages for the overall average value an value of each arm (policy).

extensive-form games extend these formalisms to the multistep sequential case (e.g.


Suppose we are given a matrix Y ∈ R d1×d2 that has decomposition Y = M * + S * , where M * is a rank r matrix and S * is a sparse corruption matrix containing entries with arbitrary magnitude.

this flow is the same for full and partial observations, though a few details differ.


When the training distribution is sufficiently close (top row), the modes "snap" together and the mean of the two modes is assigned high probability.

finally for multiple features, when the training set only contains certain combinations, e.g., red cubes but not yellow cubes (Figure 1,D), we find that the learning algorithms will memorize the combinations in the training set when it contains a small number of them (e.g., 20), and will generate new combinations (not in the training set) when there is more variety (e.g., 80).


The signal-to-noise ratio (SNR) is defined as 10 log 10 (E s /N 0 ) where E s /N 0 = ne σ 2 (n is the number of variables, σ 2 is the variance of the Gaussian additive noise, and e is the variance of the uniform distribution over the discrete set A).

the proposed variant of the BP algorithm is both computationally efficient and achieves near optimal results.


We start by defining the notion of approximate coverage, which is different than the corresponding notion in [8] for p ≥ 1, due to the fact that 0 -regression cannot be efficiently solved.

given a matrix A ∈ {0, 1} m×n , if OPT A / A 0 ≤ 1/240 then we can exactly solve the Boolean 0 -rank-1 problem in time 2 O(OPT/ √ A 0) • poly(mn).


Then the truncated subspace K n is defined as: where s h represents the presence/absence state of the component h To avoid converging to local optima, we used the directional annealing scheme [22] for our learning algorithm.

generative modelers make compromises to allow for trainability and applicability of their generative approaches.


Again, the MRes cascade was faster and more accurate than the others.

in result, the average computation per image is small, and the cascaded detector is very fast.


As in the proof of the older result , we analyze the empirical process associated with a run of the on-line learner using exponential inequalities for martingales.

an example is a pair (x , y), where x E X (which we call instance) is a data element and y E Y is the label associated with it.


As discussed above, the vast majority of approaches to clustering are derived from the application of specific algorithms, the optima of specific objective functions, or the consequences of particular probabilistic generative models for the data.

there is a crucial sense in which this result "just barely" holds, rendering it arguably less interesting to us here.


The KPCA procedure approximates this objective by considering the empirical covariance operator, denoted C n , and the subspace S D spanned by its first D eigenvectors.

this does not tell us much about the convergence of S D to S D -since two very different subspaces can have a very similar reconstruction error, in particular when some eigenvalues are very close to each other (the gap between the eigenvalues will actually appear as a central point of the analysis to come).


As a pre-computation, we train these models to maximize the likelihood of example outputs generated via SMC.

the algorithm requires many particles-and therefore significant computation-to produce acceptable results.


They are employed to assess different aspects of a given clustering: PUR measures the accuracy of the dominating class in each cluster; NMI is from the information-theoretic perspective and calculates the mutual dependence of the predicted clustering and the ground-truth partitions; RI evaluates true positives within clusters and true negatives between clusters; and FM considers both precision and recall.


First, given some region S, we must calculate an upper bound on the scores D(S ) for regions S ⊂ S. More precisely, we are interested in two upper bounds: a bound on the score of all subregions S ⊂ S, and a bound on the score of the outer subregions of S (those regions contained in S and containing its center S C ).

computing the scan statistic for all spatial regions is generally computationally infeasible, so we introduce a novel fast spatial scan algorithm, generalizing the 2D scan algorithm of (Neill and Moore, 2004) to arbitrary dimensions.


To overcome this problem, we invoke a simple reparametrization 6 that has far-reaching impact.

we advance Riemannian manifold optimization (on the manifold of positive definite matrices) as a potential replacement for Expectation Maximization (EM), which has been the de facto standard for decades.


If (x, z) = e ihz,xi ˆ (z) 1/2 and ⌫ / ˆ for 2 L 2 , then R SD ,2,⌫,M is the random Fourier feature (RFF) approximation [22] to KSD k with k(x, y) = (x y).

our next result, proved in Appendix B, shows that tilted base kernels with A increasing sufficiently quickly also control convergence.


. . , S k } to minimize the sum k i=1 f (S i ), then we have an exact algorithm for 2-clusterings and a factor 2 approximation guarantee.

we show that the optimal partitioning into 2 clusters, and approximate partitioning (guaranteed to be within a factor of 2 of the the optimal) for more clusters can be computed.


This is seen in Figures 5b and 5c; the data are at di erent levels of separation at the same position of layer parameterization, for example by comparing layer 18 in Figure 5b to layer 36 in Figure 5c.

note that these are global coordinates over the entire manifold.


To reduce this factor, we can consider a mixed strategy: if i t is in the batch B s then perform an SVRG iteration, but if i t is not in the current batch then use a classic SG iteration.

our experiments (Appendix F) indicate this strategy only gives marginal gains.


Similarly, the choice a = 0, b = -1 solves the problem if LiES_ Pi 2: LiES+ Pi + 2~.

we then drew 1000 points at random from the unit square and assigned them labels according to the partition.


Since the µ ℓ are strictly decreasing, we conclude that β ∈ O S . Moreover, choosing q ∈ J ℓ and summing both sides of equations (A.5) over j ∈ J ℓ,q we obtain that which implies that β ∈ Q J ℓ ,J ℓ,q .

the last claim in the theorem follows from the fact that the set {γ(ǫ) : ǫ > 0} is bounded and the function λ(β) is continuous.


. . , µ) = L * (θ, µ) for all µ ∈ M(Z ∩ ).

we expect our approximations to be accurate when each submodel has enough capacity to represent the posterior p m (z | x; θ m ) as a low-variance unimodal distribution.


Tracing its origins to [17] for offline optimization problems, OMD proceeds by taking a gradient step in the dual (gradient) space and projecting it back to the primal (decision) space via a mirror map generated by a strongly convex regularizer function (with different regularizers giving rise to different algorithms).

if C is nonempty and λ-stable, then it is closed, convex and contains all Nash equilibria of the game.


The set P = P(X ) of all probability distributions on X is a (|X | − 1)-dimensional simplex in R |X | .

this notion of distance is rather strong.


Mercer's condition [6], the essence of the nonlinear SVM theory, is equivalent to the fact that continuous electrostatic energy is positive, i.e., E = G (x, z) h (x) h (z) dx dz ≥ 0.

the potential indicates the sign and amount of charge in the local neighborhood.


< 2.373 be the exponent of fast matrix multiplication, the algorithm runs in We note that the runtime of our algorithm is O(nnz(A)) whenever n, k, 1/ k+1 , and 1/✏ are not too large.

kernel methods typically work with the kernel matrix K 2 R n⇥n with K i,j = (a i , a j ).


. . , y N ) and drop the superscript (m).

the study of complex networked systems is an emerging field impacting nearly every area of engineering and science, including the important domains of biology, cognitive science, sociology, and telecommunications.


Local Gaussian Smoothing As another approach to increase smoothness, the blockwise uniform distribution in (5) can be replaced by a Gaussian distribution g k = N (θ; µ k , Σ k ), with mean and covariance estimated "locally" by samples within the block.

as both are kernel-based, the two methods are limited by two major drawbacks.


The whole training process is described in Algorithm 1.

t represents the surface of the 3D face.


Critchley (1978) [3] (also mentioned in section 2.4.2 of Cox and Cox) carried out metric MDS by running the classical scaling algorithm on the transformed dissimilarities.

we can again show that the kernel MDS procedure operates on the matrix H K H. the distance 8ij in feature space is not a function of 8ij and so the relationship of equation 3 does not hold.


In experiments, we find that a typical choice of Beta(2, 1) performs surprisingly well even when it is far from the true prior.

the a j and b j can be exactly calculated by noting that E[ln x] = Digamma(α)−Digamma(α+β) if x ∼ Beta(α, β).


Fortunately, since many studies use hand indicated regions for group analysis [7], such data is readily available.

note that general-purpose white matter segmentation methods do not extract specific regions (which is often obtained via intensive interactive methods instead).


Using these results, [14] considered the algorithm [25] to solve (1.1) where J is partly smooth, but not necessarily convex and F is C 2 (R n ), and proved finite identitification of the active manifold.

only local curves after activity identification are shown.


The learner also assumes that the reward function is linear, but in features which are different from the truly relevant ones; e.g., the learner could only observe a subset of those features.

yet another way of characterizing the teaching risk is as ρ(A L ; w * ) = pr(w * ) , where pr : R k → ker A L denotes the orthogonal projection onto ker A L . Significance of teaching risk.


Since this distribution is heavy tailed, the β t variables will have more mass near 0 and 1 than they would have if γ t were fixed, adding sparsity to the latent allele frequencies.

for the DFCP the fragmentation and coagulation operators can describe more complicated haplotype structures without introducing more latent events.


It seems to be a more natural choice than W-Softmax for the proposed SphereConv and makes the entire framework more unified.

in L-Softmax [12] or A-Softmax (cosine GA-Softmax), it is not the case.


If we let Φ t = G(x t ) (assuming for sake of clarity that x t > 0), where Since the payoff of the algorithm at time step t is g(x t )b t , we have where Z is the desired bound on per step loss of the algorithm.

an important property of our algorithm is that it does not need a high imbalance between the number of ones and the number of zeros in the whole sequence to have a gain: it is sufficient for the imbalance to be large enough in at least one contiguous time window 2 , the size of which is a parameter of the algorithm.


We present the following two realizations of this operator that provides the output of a set of filters in a neighborhood of a node of interest that we refer to as the "center node": where N i is the set of neighbors of node i, W C is the weight matrix associated with the center node, W N is the weight matrix associated with neighboring nodes, and b is a vector of biases, one for each filter.

note that DCNNs use residue distances to inform the diffusion process.


We observed that on MNIST, the performance with Kp is very similar to what is obtained with unnormalized Gaussian kernels Ku(x , y) = exp _(X~Y)2.

with the double set of Lagrange multipliers, the description of the XCHDM algorithm is beyond the scope of this paper.


To test the distribution dependence of the estimates, we constructed a polygonal curve by connecting consecutive points of the sequence, and resampled 481 points by using the power distribution (1) with p = 2, 3.

. . , Finding M(r) for a data set S n = {x 1 , .


We associate a random variable F α i with each segment s α i .

our grouping is also based on the edge detection of [8], but we do not perform edge linking directly for purposes of grouping.


A portion of the learned covariance matrix can be explained by the input features and, thus, generalized to new objects via a content-based kernel smoother.

based on the approximate scaled eigenfunctions, the resulting kernel function is simply with r(w) = (r(x 1 , w), .


Though such assumption can be satisfied by using additional constraints, it actually solves a slightly different problem than the original nonsymmetric NMF (1).

although the convergence of these algorithms are observed without the proximal term and constraint (which are also not used in practice), these are in general necessary to formally show the convergence of the algorithms.


An MDP is weakly communicating (or weak accessible) if its states can be partitioned into two subsets: in the first subset all states are transient under every stationary policy, and every two states in the second subset can be reached from each other under some stationary policy.

the above methods to end an episode can not be applied to MDPs without the special features.


Also we will simply assume V = 1, T = 1 because they do not change the optimal solution for any Fisher information-related quantities.

for the infomax problem we want to maximize I(r, s) because of Eq.


In fact, the volume measure VM is related to the number of "distinguishable" probability distributions indexed by the model M.l Because of the way the model family is embedded in the space of distributions, two different parameter values can index very similar distributions.

u sing Bayes rule, the probability that the truth lies in the family f given the observed data y can be written as: Here wee) is the prior probability of the parameter e, and A(f, y) = Pr(f)/Pr(y) is the ratio of the prior probabilities of the family f and data y. Bayesian methods assume that the latter are the same for all models under consideration and analyze the socalled Bayesian posterior Lacking prior knowledge, w should be chosen to weight all distinguishable distributions in the family equally.


Tarone's testability criterion has only been successfully applied to unconditional association tests, such as Fisher's exact test [6] or Pearson's χ 2 test [11].

[18]), or (b) using Tarone's testability criterion, losing the ability to account for covariates and resulting in potentially many confounded patterns being deemed significant [15,13,7,8].


Then, by Lemma 3.3 and the fact that R1,...,R K (X | S1,...,S K ) = R1,...,R K (π(X | S1,...,S K )), we have ) be as in the statement of Lemma 3.3.

if the selected Tucker rank is too large, the computational cost of computing the Tucker decomposition (even if we allow for approximation methods) increases considerably along with space usage.


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

is to locate the correct object in the image.


However, while a single deep tree estimator is clearly not consistent in general, it is believed that combining many deep trees can effectively reduce the variance of individual trees.

suppose that η n satisfies the UW-property (Def.


Thus only some learning rules can profit from the positive correlation.

the cue orders resulting from all learning rules but the validity learning rule do not correlate or correlate negatively with the validity cue order, and even the correlations of the cue orders resulting from the validity learning rule after 100 decisions only reach an average r = .12.


We introduce a natural model that scales between A-and D-optimal design.

our motivation here is the dual problem of D-optimal design (i.e., dual to the convex relaxation of D-optimal design): this is nothing but the well-known Minimum Volume Covering Ellipsoid (MVCE) problem, which is a problem of great interest to the optimization community in its own right-see the recent book [42] for an excellent account.


Second, existing work on this topic has so far not provided any framework capable of addressing what is perhaps the most basic question about δ-sampling: given a tree T δ with its set of exposed nodes indicated -i.e., a single outcome of the δ-sampling process -can we infer the number of nodes in the original tree T ?

the key to the argument is Theorem 2.1, which asserts that with high probability, T δ has Ω(δn log k δ −1 ) nodes in total.


[18] were able to obtain a 213 × 213 regional weight matrix using 469 experiments with mice (Fig.

we only know y j outside the support of x j , which we denote supp x j , and we wish to only evaluate error for the observable voxels.


In this subsection, we consider the setting where all the elements are observed (with noise) and the goal is to recover the underlying low-rank tensor without noise.

the second ingredient of our analysis is the restricted strong convexity.


Decades of research has resulted in a variety of well-developed automated theorem provers such as Vampire [12] and E [13].

achieve an accuracy of 81.5%, showing that much of the performance comes from just the names of constant functions and values.


In recent years, the language model Latent Dirichlet Allocation (LDA), which clusters co-occurring words into topics, has been widely applied in the computer vision field.

for a word (image patch) i, a random variable d i is sampled from prior p(d i σ) indicating to which document word i is assigned.


The network generation requires quadratic computation of cosine similarity of S (t) .

our goal is to propose a simple and fast method that can take advantage of enormous amounts of Web data.


Solving this transport equation on [0, t] essentially transports the initial mass to the mass at time t. Algorithm 2: HYBRID MASS TRANSPORT Input: Sample size n, time t, ⌧ Output: μn(t), ˆ n(x, t) Generate n samples of point process: To efficiently solve the mass transport equation, we reformulate it as a banded linear ODE.

let (t) := (t|H t ) be the conditional intensity function of the point process N (t) and ˜ (x, t) := P[N (t) = x|H t ] be its conditional probability mass function; then ˜ (x, t) satisfies the following differential-difference equation: loss in mass, at rate (t) Proof sketch.


The concept class C induced by a learning algorithm L : ∪ ∞ m=1 Z m → H is defined to be the set of total Boolean functions c(z) = I{P(Z trn = z | H) ≥ P(Z trn = z)} for all H ∈ H. Intuitively, every hypothesis H ∈ H induces a total partition on the observation space Z given by the Boolean function in Definition 8.

also, given two probability mass functions P and Q defined on the same alphabet A, we will write P, Q to denote the overlapping coefficient, i.e.


Several issues remain with the kernel we describe over trees and convolution kernels in general.

the method still suffers from the lack of justification of the parameter estimation techniques.


Let subscript t − 1 denote corresponding values under the posterior measure P t−1 (•) = P(•| Ht−1 ).

our new line of analysis is inspired by rate-distortion theory, which is a branch of information theory that quantifies the amount of information required to learn an approximation [3].


First, we generate binary state-features ϕ(s) of dimension d, such that l components are set to 1 (the others are thus 0).

the horizon term is better (linear instead of quadratic) for the residual approach.


This section gives two consequences of our probabilistic interpretation of SVMs.

we could derive decision-oriented criteria for multi-class probabilistic classifiers.


The empirical estimation of R(f ) (also p f (0)) can be obtained by kernel density estimation, which is defined as: Hence, the approximation of f * can be found by learning algorithms associated with R σ z (f ).

this work was partially supported by U.S. NSF-IIS 1302675, NSF-IIS 1344152, NSF-DBI 1356628, NSF-IIS 1619308, NSF-IIS 1633753, NIH AG049371.


all experimental results are in accordance to the theoretical results.


We found that the basic implementation described above fails to predict accurate poses.

we address the task of predicting the three-dimensional shape of an object and the camera pose from a single view of the object.


If τ 1 and τ 2 do not represent pure translational motions, then they should be considered to be close if their centers of rotation are close.

4 and 5), the entropies are related, ) where E[log det(A)] may be estimated using Equation 6.


The mean ROC scores for these two kernels are 0.854 and 0.844.

we measure the utility of our hierarchy of kernels in a cross-validated, supervised learning framework.


In each iteration, it first compute the weights for a batch of N examples (decoding), and then uses the computed weights to update the feature matrix (updating).

a t+1 + βb t+1 is our potential function which decreases at each iteration up to the level h. The other claims can also be proved by the corresponding lemmas.


We do not have a formal explanation for this effect.

the nonlinearity is described by the network's so-called activation function.


The above theorem suggests using a uniform combination of multiple discriminator nets to find a better approximation of the solution to the divergence minimization problem in Theorem 1 solved over conv(F nn ).

in practice the discriminator is constrained to be in a smaller class F such as convolutional neural nets.


This can be formalized as maximizing the sum of reductions in entropy through a sequence of actions {a t }.

these guarantees assume discrete state and action spaces.


The algorithms proposed here use the second approach.

numerical results are surveyed in Section 3, and conclusions are contained in Section 4.


Recent works [2] suggested one could also run the MAB algorithm and keep updating the estimators until T end .

we present a simple modification to MAB algorithms that eliminates such a bias and provably achieves almost the revenue as if an oracle gives us the actual click probabilities.


The expression L ¬W (D; p) involves costly summation over all possibilities of integer composition of d(v) (v ∈ W ).

but agencies typically do not know the number of people in the network.


In dynamical systems theory, the logarithm of χ 1 is related to the well known Lyapunov exponent which is positive (or negative) for chaotic (or ordered) dynamics.

the scaling is chosen so that each neuron has input activity O(1).


The complete MIP formulation and the proof of correctness is presented in Appendix E. For general A 6 = 0, we need to solve a sequence of MIPs to find the optimal adjustable solution.


Any future work on improving Lemma 2 would therefore strengthen the approximation factors above.

for = 2 and the t = 16(k + √ k) cluster centers assumed in [1], Theorem 1 in the present work implies that after taking k → ∞.


As in [21], all GoogLeNet layers are fine-tuned with the learning rate that is ten times less than  the learning rate of the last layer.

this would correspond to evaluating a quadruplet-based loss similarly to [9,31].


Contribution: the contributions of this paper lie in the following three aspects.

among them, the Bayes-update Partial Monitoring (BPM) algorithm [13] is state-of-the-art in the sense of empirical performance.


The resulting clusters show two-sided continuation of the texture flow with a fixed tangential curvature (Fig.

a cluster, say, C, of edges in embedding space all have high probability of co-occurring, and the diameter of the cluster bounds the conditional co-occurrence probability of all edges in the cluster.


We analyze the following algorithm and prove that it attains logarithmic regret with respect to the observed variation (rather than number of iterations).

for y = x t+1 , we get that ∇F t (x t ) • (x t+1 − x t ) ≥ 0.


1: Results on the Extended Yale B dataset.

first, there are some computational considerations.


More recently, several types of perturbations have been shown to regularize intermediate representations effectively in deep learning.

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


In multi-instance learning, there are two kinds of prediction failure, i.e., false negative and false positive.

the principal component analysis (PCA) [15] is just the technique that we need.


Thus recovering the objects and their attributes can help reduce the ambiguities present in the world leading to better estimation of the reflectance and other intrinsic properties.

further, our reflectance and shading images visually look much better than the models of Retinex [17] and Gehler et.al.


The results below are for datasets with 7 features each, with number of batches q ranging between 1 and 7.

in Ting et al [14], the Feating submodel selection relies on simple attribute splits followed by fitting local predictors, though the algorithm itself is substantially different.


The theorem requires that the MDP contain no cycles.

to determine the splitting plane at a node, we choose a state Si at random from S, choose one of its inferior children S_, and construct the plane that is the perpendicular bisector of these two points.


They show that this transformation is useful when each block Gibbs step can be performed in parallel.

continuous problems are appealing because the gradient is on your side: Unlike discrete probability mass functions, in the continuous setting, densities have derivatives, contours, and curvature that can be used to inform sampling algorithms [6,16,18,20,27].


Figure 4 represents the histogram of ρ in the trained image transformation network, which forms a bimodal distribution as in Figure 2.

in short, normalizing styles in a neural network needs to be investigated with a careful consideration.


1%, we may decide that the cluster is multimodal.

various alternatives can be employed in order to compute a score for a split candidate based on the percentage of split viewers, or even the size of clusters.


[43,3,44] propose to first "interpolate" or "project" features into predefined regular domains, where typical CNNs can be applied.

we implemented PointCNN in tensorflow [1], and use ADAM optimizer [21] with an initial learning rate 0.01 for the training of our models.


For program synthesis [5,34,10], the search spaces are enumerable and deterministic.

see Supplementary Material A for more details about the functions.


We tested our method on two challenging datasets, where it improves the baseline model by significant margins.

captions generated for different images, especially those that contain objects of the same categories, are sometimes very similar [1], despite their differences in other aspects.


Our results show that, even on a single machine, FALKON can outperforms state of the art methods on most problems both in terms of time efficiency and prediction accuracy.

for example, if a simple gradient descent ( 6) is used, the number of iterations needed for an accurate solution of problem ( 5) is t = O(cond(K nn + λnI) log(1/ )).


We start by defining the following terms for the independent cascade model IC(G, P, S 0 ), where , the set P l (S 0 → v) is defined as the set of all paths with length l from any seed s ∈ S 0 to v. We call a path P is open iff every edge in P is open.

initial condition: For every s ∈ S 0 , s + ∈ N + (s), u ∈ V \S 0 , and v ∈ N + (u), Recursion: Equation ( 10) follows from that for any seed node s ∈ S 0 and for all l > 0, the probabilities p l (s) = 0, p l (s → s + ) = 0, and p l (s , but this results in an extremely loose bound due to the backtracking.


Finally, when the dataset satisfies certain regularity conditions, the size of I can be improved, which reduces both embedding and clustering runtime.

space H n if Notice that the inverse since φ i ∈ Φ n , we have that in the worst case the error is bounded as we know that in the best case the error can be reduced up to Note that the directions associated with the larger eigenvalues are the ones that occur most frequently in the data.


To facilitate the checking of whether a node is in Ω (step 7), Ω also stores its nodes in a self-balancing BST.

a brute-force search takes O(2 |L| ) time when k is unknown.


throughout this work we avoid repeating this fact for the sake of simplicity of the notation.


The known entries are the ratings given by users to some items.

we first compare convergence behavior of the different methods on synthetic data.


Form the second order approximation fXt (∆) := ḡXt (∆) + h(X t + ∆) to f (X t + ∆).

at most linear rates in turn become infeasible when the problem size is very large, with the number of nodes in the thousands and the number of matrix entries to be estimated in the millions.


From these plots, we notice that the risk-sensitive algorithms that we propose result in a long-term (discounted or average) reward that is higher than their riskneutral variants.

from the Bellman equation of Λ µ (x), proposed by Sobel [19], it is straightforward to derive Bellman equations for U µ (x) and the square reward action-value function [17]).


We restrict interest here to the case of simple linear decoding functions Since p(r|s) is Gaussian, (2s i − 1)f i (r) ≡ x i is also Gaussian, In general, the average over the factorised distribution p(s) can be evaluated by using the Fourier Transform [1].

we have described a general theoretically justified approach to information maximization in noisy channels.


While the boosting tree algorithm is well-known to be robust and also accurate, an individual tree has limited predictive power and usually can be built quite crudely.

for the artificial data, all other 3 rankers exhibit very large improvements over LambaRank.


In distributed environments without a high rate of connectivity, the decreased network usage of the mixture weight method should lead to substantial gains in wall clock as well.

the application of the Cauchy-Schwarz inequality to the inequality just established yields The gradient of w → L zm (w) = log y∈Y e w•Φ(xm,y) −w • Φ(x m , y m ) is given by ∇L zm (w) = y∈Y e w•Φ(xm,y) Φ(x m , y) we obtain ∇L zm (w ) ≤ E y∼p w [•|xm] Φ(x m , y) − Φ(x m , y m ) ≤ 2R and similarly ∇L z m (w) ≤ 2R, which leads to the statement of the theorem.


The number of clusters is time-varying and unknown a priori.

given U, the number of clusters can be reduced to a finite number during the inference, and it enables us an efficient sampling of variables.


To be Hölder about 1/2 it is sufficient that η is Hölder continuous, but it is not necessary.

in non-trivial situations no rate of convergence which uniformly holds for all distributions P is possible.


We note that these observations make delay-free reconstruction of the signal possible, thus allowing fast operation of neural circuits [27].

the mean relative error of the signal decoded by averaging over the Nyquist half-period: indicating that oversampling reduces transmission error.


This result implies that our recipe is complete.

under this parameterization, we then compute ∇ log p(θ|x) and, in our implementation, use boundary reflection to ensure the positivity of parameters θ kw .


For each of these 147 e-mails, we counted the number of e-mail addresses to which the message was sent, including both direct and CCed recipients.

theorem 2.1 provided the main step; from here, we simply argue, in Theorem 2.2, that T δ will have at most O(δn) branching nodes with high probability.


While we initially expected Multi-Metric LMNN to outperform Global LMNN, we suspect it struggles with clusters that are too close together.

orthogonality does not necessarily imply disjoint features.


. . , q M , where M = n 2 , denote the values of matrix Q arranged in ascending order.

hence, our approach has potential applications to yielding a better recovery.


The problem with sampling from the collapsed distribution is that for a proper sampler we need to consider all cluster probabilities including those related to clusters which are highly implausible and unlikely to be chosen for a given instance.

a multi-machine setting is also achievable by keeping the sets of sufficient statistics synchronized between computers.


To conclude, the left and right eigenvectors of the finite matrix M can be viewed as discrete approximations to those of the operators T f and T b , which in turn can be viewed as approximations to those of H f and H b .

the term ∇ψ • ∇U in ( 17) is interpreted as a drift term towards low energy (high-density) regions, and as discussed in the next section, may play a crucial part in the definition of clusters.


The food and shelter domain [Guo et al., 2013] involves an agent simultaneously trying to find randomly placed food (in one of the top five locations) while maintaining a shelter.


Let Y be the N × N binary matrix that contains these links.

the Indian Buffet Process is such a prior.


The remaining parameters are the intrinsic parameters of a neuron, such as the standard deviation of the channel noise, the functional form of voltage-dependent ionic inputs, and that of the rate constants.

the problem may be formulated as a statistical problem of estimating the hidden state using a state-space model and then it is solvable.


We support our method with both theoretical and empirical analyses.

the Curse of Horizon The importance weight w 0:T is a product of T density ratios, whose variance can grow exponentially with T . IS-based estimators have not been widely successful in longhorizon problems, let alone infinite-horizon ones where w 0:1 may not even be well-defined.


The domain D is often the product of many attributes.

we evaluate our approximate dataset following Fienberg et al.


Low-dimensional embeddings of nodes in large graphs have proved extremely useful in a variety of prediction tasks, from content recommendation to identifying protein functions.

a number of extensions and potential improvements are possible, such as extending GraphSAGE to incorporate directed or multi-modal graphs.


We now consider a 2D path planning domain with continuous states and continuous actions, which cannot be solved using VI, and therefore a VIN cannot be naively applied.

y. W. was partially funded by a DARPA PPAML program, contract FA8750-14-C-0011.


More recently, [12] proposes an approximate objective for structural SVMs that leads to an algorithm considerably faster than DLPW on problems requiring expensive inference.

in practice, since the set of active labels is not changing frequently during training, once an active label y f is sampled, it will be kept in the active set A f till the end of the algorithm and thus results in a convergence rate similar to that of an exact FMO.


We sketch the proof in section B in [21].

note that M q ≤ e M , thus we have V j q ≤ eK (for all j).


While these techniques have been remarkably successful, many of the above papers require delicate and tailored analyses to quantify the benefits of asynchrony for each particular learning task.

we run classification for the URL dataset [15]  Table 2: Ratio of the time that CYCLADES consumes for partition and allocation over the time that HOGWILD!


Assume that The computational complexity of n FSSD 2 and σ2 H1 is O(d 2 Jn).

such tests can require space partitioning [18,3], which works poorly in high dimensions; or closed-form integrals under the model, which may be difficult to obtain, besides in certain special cases [2,5,30,26].


In fact, our method guarantees a nearly optimal error rate of It is noteworthy that CRR can tolerate a constant fraction of corruptions i.e.

also let the number of corruptions k * be s. The above result establishes consistency of the CRR method with an error rate of Õ(σ d/n) that is known to be statistically optimal.


Because a sphere is rotationally symmetric, our forward model is insensitive to orientation, and similarly the external magnetic field caused by a dipole in a homogeneous sphere is invariant to the sphere's radius.

(2002), except that an additional input was associated with each exemplar, namely the (x, y, z) coordinates of the center of a sphere fitted to the head, and the forward model was modified to account for this offset.


In the case of imperfectinformation extensive-form games, one limitation is that some NEs do not prescribe optimal play after the player or the opponent has made a mistake.

there exists a ¯ > 0 such that t i ( ) has the same sign as the first non-zero derivative of t i evaluated in 0 for all 0 < < ¯ .


By considering a cost function c : Ω S × Ω T → [0, ∞[, Monge's formulation of the OT problem is to find a transport map T : Ω S → Ω T (also known as a push-forward operator) between two probability measures µ S on Ω S and µ T on Ω T realizing the infimum of the following function: When reaching this infimum, the corresponding map T is an optimal transport map.

as such, our technique can readily learn the transfer function T s→t over a limited set of gradients and generalizes appropriately to unseen gradients.


In this case the offset is minimal, thus recovering virtually all revenue.

for example a function h, that is just as likely to over-predict by η as to under predict by η will have very small error, but lead to 0 revenue in half the cases.


. . , x n } ∩ A in the graph G n,r is denoted by vol n,r (A), and correspondingly vol n,k (A) in the graph G n,k .

the question how these choices should be made has received only little attention in the literature.


Under the prior specified above, the posterior probability is the random measure given by .

this method is of limited utility in higher dimensional spaces because the number of cells in a regular partition of a p-dimensional space will grow exponentially with p, which makes the relative frequency highly variable unless the sample size is extremely large.


(2010), assume the features of different examples might be corrupted, missed, or partially observed due to various problems, such as failure in sensors gathering these features.

following-up the patient may or may not incur additional cost.


7(e)) during training, in which case full input/target sequences are accessible.

in summary, we make the following contributions: (a) We tensorize RNN hidden state vectors into higher-dimensional tensors which allow more flexible parameter sharing and can be widened more efficiently without additional parameters.


Prior work has considered strongly convex decision sets [14], yet with the additional assumption that the objective is smooth and strongly convex, leading to O(1/T 2 ) convergence.

if the constraint set is strongly convex, then this exhibits a novel projection free algorithm that grants a O(log T /T ) convergence even for non-smooth objective functions.


We prove upper bounds on the convergence rate of the classification error towards the Bayes risk for a variety of functions φ and of distributions P , in particular for SVM (Theorem 6).

these results are particularly relevant to the one-class SVM, for which the regularization can not vanish by construction, and which is shown for the first time to be a consistent density level set estimator.


Such an algorithm may then require on the order of 100, 000 days of experience (trials) to learn.

this quantity can be bounded in turn by considering the sequence of partially correct backup operators B0 , .


16 for power-law decay in the ridge leverage scores when, where C is an absolute constant.

one advantage of using deterministic rather than randomized rank-k subspace leverage score algorithms is that under the condition of power-law decay in the sorted rank-k subspace leverage scores, the deterministic algorithm chooses fewer columns than random sampling with the same error for the column subset selection bound when max((2k/ ) , where a is the decay power and C is an absolute constant (Papailiopoulos et al., 2014) (this is the counterpart to our Theorem 5).


Since the array contains empty entries, the ratings were shifted by -3.5 to have the possible ratings {-2.5, -1.5, -0.5, 0.5,1.5, 2.5} which allows to assign the value of zero to the empty entries of the array (movies which were not rated).

all the thresholds aj, bj can be recovered from the support vectors -unlike the fixed-margin scheme which required another LP pass.


This research is supported in part by Grants (CUHK 14206715 & 14222816) from the Hong Kong RGC, the Major Research Plan of the National Natural Science Foundation of China (Nos.

for the specific problem in (9) with the inner product in (10), we can derive a simpler form to solve Y k below.


In light of (3), pairwise MI quantities between adjacent nodes i and j may be expressed as i.e., purely in terms of node and edge marginal precision matrices.

then I(x R ; x y | x A ), ∀y ∈ S feas , are computed via a variant of (3).


Consider a curve γ(s) on bd(W) connecting w (1) and w (2) that is defined by the intersection of bd(W) and P and is parametrized by its curve length s so that γ(0) = w (1) and γ(l) = w (2) , where l is the length of the curve γ between w (1) and w (2) .

for −Θ t , −Θ t−1 ∈ V , w t+1 = w t . Hence, by Theorem 3.9, On the other hand, note that f i ∞ ≤ M . Then where the last inequality is due to Hoeffding's inequality.


Alternatively, a kernel matrix could be computed ignoring the missing values, that is, each 2 ), where γ 2 = 1 trace(W i W j ) .

4 is not concave, hence non-convex optimization techniques are required.


Rather than counting the number of times each of the n words are separately manifested, we may more efficiently count the number of times words in particular subsets of D are manifested.

in this context, for each draw X there is a latent class random variable C ∈ {1, . . . , L}, where the probability of class c is π c . Our goal is to design Φ such that the observed Y is most informative about the underlying X or C. When the interest is in recovering X, we design Φ with the goal of maximizing mutual information I(X; Y ), while when interested in inferring C we design Φ with the goal of maximizing I(C; Y ).


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

first, we consider "sentiment analysis" of newspaper movie reviews.


This algorithm shown uses simple heuristics such as: searching the model node with the most points and splitting a support node if it is too wide.

the detections, along with confidence levels, were automatically extracted from the images.


The data (x i , y i ) n i=1 are sampled identically and independently with respect to a probability ρ on X × R, with X a separable space (e.g.

a particular instance is kernel ridge regression given by Here λ > 0, y = (y 1 , .


5 is therefore exactly one logistic classifier, showing that the model is equivalent to a mixture of 2 K logistic regressors with shared weights.

furthermore, the model parameters, unlike in our case, are not factorized, and as a result the model cannot extract features which are shared among classes.


Note that if we examine the posterior distributions of the weights we see that if each x n contains only one nonzero value then each factor in the likelihood is dependent on only one of the K weights and can be multiplied into the corresponding k th spike-and-slab.

in our experimental setup, at each trial, n = 1, . . . , N , the experimenter stimulates R of K possible presynaptic neurons.


Lastly, to satisfy the single word constraint, a singleton factor (purple, highorder) is added such that there must be a single activated edge from "start".

briefly, for some letter we render images for all fonts and then use the resulting images to train shape models.


The mutation-type operator will easier to generalize, because it only requires a bias towards a random distribution.

-Update the parameters 'Yi(t + 1) = 'Yi(t) + a[xi -'Yi (t)] for all i.


If the dimensionality gets so large that maintaining a full covariance matrix becomes computationally infeasible, one has to resort to low-dimensional approximations [e.g., Loshchilov, 2015], which, however, bear the risk of a significant drop in optimization performance.

in contrast to previous attempts in this direction, we present an approach that comes with a theoretical justification for why it does not deteriorate the algorithm's performance.


set of observations with ground truth labels), and there is no information about other categories (i.e.

since the order of the categories introduced may have an affect on the performance of the system, five experiments were carried out in which categories were introduced in random sequences.


Its spectral radius is given by ρ = λ(β), where λ is defined in 10.

in Figure 4, we demonstrate the suitability of the eigenvectors of the Bethe Hessian as starting point for the minimization of the cost function (2).


Additionally, these methods are able to exploit algebraic structure in the data for further efficiencies [9,43,50].

thus KISS-GP provides O(tn+tm log m) matrix-matrix multiplies [50].


are initially slower than serial, due to the overheads required for atomic operations in the parallel setting.


It was also necessary to adjust the sampling of the nonlinearities (location of µ jk 's) because, as the fixed-norm filters rotated through input space, the variance of the projections can change drastically.

measured neural nonlinearities are typically softer, but when rectified noise is taken into account, a hard-rectified model has been shown to be a good description of neural variability [32].


By concatenation of the vectors n r (r = 1, . . . , 20) containing the bins of each neuron we obtain one data point x = [n 1 n 2 ... n 20 ] per trial.

hence, the feature map is defined as: each trial is represented by a vector of its alignment score with respect to all other trials where alignments are computed separately for all 20 neurons.


We pursue instead an approach to NAG (and accelerated methods in general) via a continuous-time perspective.

we approach this complexity by using the notation for elementary differentials (see Appendix E) adopted from [12]; we then induct on the order of the derivatives to bound the higher order derivatives.


Our metric includes the existing fundamental metrics for dynamical systems, which are basically defined with principal angles between some appropriately-chosen subspaces, as its special cases.

a variant of estimation algorithms, called dynamic mode decomposition (DMD), has been successfully applied in many real-world problems, such as image processing [11], neuroscience [3], and system control [16].


While it is easy to convert a stack of standard RBMs into a feed-forward neural network, turning a stack of CaRBMs into a feed-forward neural network is less obvious, because it is not clear what nonlinearity should be used.

the vector x can be recovered via x j = z j − z j−1 .


Note that while ( 5) is a matrix decomposition of the contraction, it is not a singular value decomposition (the components need not be orthogonal, for instance).

indeed the above idea can be extended more generally to the concept of deconvolving a sum of sparse and low-rank tensors from separable measurements [24].


Independence given the label would say that given that x 1 is in some positive cluster C i in X 1 , x 2 is equally likely to be in any of the positive clusters C j in X 2 .

since the stationary distribution of this walk can be viewed as having equal probability on every edge, this is equivalent to saying that for any partition of the graph into two pieces (S, V − S), the number of edges crossing the partition should be at least an fraction of the number of edges in the smaller half.


While we compare our model with InferSent that has not been trained on explanations, we want to ensure that eventual improvements are not purely due to the addition of a language model in the decoder network.

[1] (b) Predicted label: contradiction Explanation: One can not be looking and eating simultaneously.


The correlation clustering setup [2] gives equal weights to the two types of errors.

suppose Y is the optimum of Formulation (2) for a given A.


We stated that our objective, given a fixed budget N , is to find as fast as possible the image with highest classification rate, and to train the classifier with as many samples as possible.

in our experiment, only a limited number of tasks were used (four), because we limited the length of the sessions in order not to tire the subjects.


The points from the inner circle are labeled by -1 with probability 0.9, while the points from the outer annulus are labeled by 1 with probability 0.9.

removing the exponential dependence on d under reasonable assumptions is an interesting direction for future work.


1 with an invertible matrix P , called a left preconditioner.

it is well known (e.g., [B + 05, RBV10]) that the top eigenvalues of kernel matrices approximate the eigenvalues of the underlying integral operators.


Consider the least squares estimator dè` ¡ 3f gha of , where iè` ¡ 'f is the pseudo-inverse of h` .

after tokenization we lemmatized the tokens using a general-purpose finite-state morphological English analyzer and then removed stopwords (we also replaced all digits with a single special character).


Subset occurence acts as a 'score' that counts the 'successful' blocks that contain all of S, whereas projection entropy acts as a 'penalty' that quantifies how much S is being divided and segmented by the given blocks B ∈ Z.

it is more subtle and difficult to compare S 2 to S 3 .


(c) The memory curves of these two models, showing the decay of the signal-to-noise ratio (to be defined in §2) as subsequent memories are stored.

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


Afterwards, SVDGP starts to descend faster and surpass the other two methods.

as a result, we can choose M α M β , which allows us to keep the time and space complexity similar to previous methods (by choosing M β = M ) while greatly increasing accuracy.


Note that synthetic dataset II is more challenging than synthetic dataset I, because the smallest magnitude of Π * in synthetic dataset I is 0.2, while that in synthetic dataset II is much smaller (about 10 −3 ).

under a weak assumption on the magnitude of the population projection matrix, one estimator within this family exactly recovers the true support with high probability, has exact rank-k, and attains a s/n statistical rate of convergence with s being the subspace sparsity level and n the sample size.


For any (potentially non-evaluated) design x ∈ X , the posterior mean µ k (x) and posterior variance σ 2 k (x) of the GP, conditioned on S k , are known in closed-form and are considered cheap to evaluate: where is the k × 1 vector whose i th entry is κ(x i , x) (respectively y i ), and λ is the noise variance.

it requires the solution of nested maximizations and expectations for which there is no closed-form expression known.


Numerical evaluations of bias and variance of estimators discussed in the present section only rely on the computation of coefficients θ α,β defined by where α, β are non-negative integers and (Z, Z ) are bivariate normal (1) with r = ρ.

the papers [25,32] discuss quantized RPs with a focus on image retrieval based on nearest neighbor search.


The inner product of ( 9) is the margin of g(x) after this class reweighting.

in the multiclass setting, this is only part of the weighting mechanism, since the terms ρ k (x i ) of ( 9)-( 10) are coefficients of a soft-min operator over margin components F (x i ), y zi − y k . Assuming the soft-min closely approximates the min, (9) becomes where and y is the codeword of ( 11).


For each task, the best performing tLSTM is run on a random example.

5. sLSTM and 2D tLSTM-M no longer benefit from the increased depth when L = 5.


First, we notice a stark difference between predictive and executed performances from Dallaire et al.

we modify (using PILCO's source code http://mlg.eng.


In the adaptive Spike Response Model (aSRM), the dynamics of the (normalized) membrane-potential V (t) are described as a sum of integrated input current I(t) and spike-triggered currents η(t): where {t i } denotes the set of past emitted spikes, and the kernel φ(t) is a fast exponential low-pass filter on membrane currents: with τ m determined by the membrane capacitance and conductance, and is typically on the order of several milliseconds [23,17] .

this is shown in the light grey (scaled additive aSRM) and dark grey (scaled non-adaptive SRM) bars in figure 6b.


The average trajectories are able to capture the underlying structure common to all instances.

it is based on a completely different algorithmic approach using Gibbs sampling and a general technique for averaging tours.


This compares to -86.22 from [24] and -84.62 for a Deep Boltzmann Machine from [23]; however, we caution that these numbers no longer reflect true performance on the test set due to bias from AIS and repeated overfitting [23].

combining the adaptive nature of RMSprop with non-Euclidean optimization provides dramatically improved performance, seemingly converging faster and to a better optimum.


We say that X is S-incoherent in case Although not explicitly required, we only apply this definition to X such that columns of X satisfy X j 2 2 = (n), ∀ j ∈ {1, . . . , p}.

we seek bounds on the capacity of this channel.


First, we investigate the sequence loss function L seq from Sec.

this problem can be reduced to |C| binary classification problems by learning a binary classifier for each possible class.


PR can be seen as a penalty on the standard marginal likelihood objective, which we define first: over the parameters θ, where E is the empirical expectation over the unlabeled sample x, and z are the hidden states.

sparse's sparsity seems to help build a model that contains more information about the correct tag assignments.


Note that we need fewer samples to estimate Sobolev quantities of Gaussians than, say, of uniform distributions, consistent with our theory, since (infinitely differentiable) Gaussians are smoothier than (discontinuous) uniform distributions.

[29] gives applications of L 2 quantities to adaptive information filtering, classification, and clustering.


The question-generator calculates information gain I[C, A t ; q t , a 1:t−1 , q 1:t−1 ] for each question in candidate questions.

the concept of utilizing information gain in a dialog task is not new for a classical rule-based approach.


To simplify the description of the new scheme only modifications to the semi-tied covariance matrix scheme, where the nuisance dimension is zero, are considered.

a simple iterative scheme is available [3].


Since the Figure 1: Although all image patches on the left are just noise, when we show thousands of them to online workers and ask them to find ones that look like cars, a car emerges in the average, shown on the right.


b * ( w) = J( w)) and (2) higher values of σ are desirable, as they reduce φ by increasing the size of its denominator.

model-free methods are particularly exciting in this domain because direct numerical simulation can take days (Shelley et al., 2005) -in contrast optimizationg on the experimental physical flapping wing can be done in real-time, at the cost of dealing with noise in the evaluation of the cost function; success here would be enabling for experimental fluid dynamics.


We show these can be accomplished efficiently, by exploiting special properties of squared Euclidean distances and by using techniques from scheduling algorithms.

for the second move, we show that any given subtree can be relocated optimally in O(n) time, using just a single pass through the tree.


Interestingly, the identities of the nations commanding the highest prices (in order, U.S., France, Switzerland, Germany, Italy, Spain, Netherlands) overlaps significantly with the k = 3 case, suggesting a certain robustness in the relative economic status predicted by the model.

we thus will also consider a variant of this model in which at each time step, a new seller is still attached to exactly one extant buyer, while each new buyer is connected to ν > 1 extant sellers.


Let be a total order on clades (e.g., lexicographical order).

sbn-em keeps learning efficiently from the data when more samples are available.


The USPS data set consists of 11,000, 16 × 16 grayscale images of handwritten digits (1, 100 images of each digit 0 through 9) with no fixed division.

we can apply the PCT to herding by identifying It is now easy to see that, in general, herding does not converge because under very mild conditions we can always find an x * t such that w T t v t < 0.


p k is a continuous quantity whereas F is defined on at discrete 2D locations.

based on the desired output, we propose to either let the final grid be a volumetric occupancy map or a grid of features which is projected back into 2D feature maps {O i } n i=1 using the given camera poses.


We investigated how model performance varied as a function of training data, and found that LN models were more susceptible to overfitting than CNNs, despite having fewer parameters (Figure 4A).

historically, much of our understanding of the retina comes from fitting models to responses to artificial stimuli and then generalizing this understanding to cases where the stimulus distribution is more natural.


For this reason, BCM is more succinct than LDA with regard to what information must be recorded in order to define the clusters.

this would require a similar amount of memory; however, it loses information, with respect to the fact that BCM carries a full prototype within it for each cluster.


As a measure of clustering quality, we use micro-averaged precision.

comparing this behavior with the monotonicity of our rate shows how, by turning the soft assignments into the hard ones, we lose the strong optimality guarantees we have for the original soft solution.


To obtain a fast algorithm (i.e., O(poly(d)), we instead take a mean-field type approximation: where ν(z; β) := β z (1 − β) 1−z .

the goal of this paper is to present a general convergence theory for the IRF with semigroup property.


The state space S is {−1, 0, 1} m . A state can be viewed as the partial information of a patient's symptom profile x ∈ X .

our proposed REFUEL algorithm can acquire 1.31 positive symptoms.


The learner has Θ = {θ A , θ B }, and we want to teach it the fact that the world is using θ * = θ A .

this is sensible: in fact, one can show that the minimum teaching set for a D-dimensional Gaussian is the D + 1 points at the vertices of a D-dimensional tetrahedron.


Ideally, one would like to minimize the rank of a tensor that explains all the sampled entries.

but, such arguments do not generalize directly to higher order; see Section 2.5 for more discussion.


Given that tasks tested in this research involve mixtures of Multi-Armed Bandit (MAB) problems, we borrow MAB language to call a reward site, an arm, and sample a choice or pull.

we restrict ourselves to the following scenario.


Certain types of stochastic search methods, such as Markov Chain Monte Carlo (MCMC) or simulated annealing, can be proven to be consistent with respect to the identification of a structure maximizing posterior probability [4,5,6,7].

for each pair of clique candidates c and c such that c ⊂ c , ¬x c ∨ ¬x c is a logical consequence of the constraints (4).


In recent years, with the emergence of very big training data (which cannot be held in one single machine), there has been an increasing need of parallelizing the training process of decision tree.

from the table, we have the following observations.


We use the subscript k to indicate the kth iteration on the master.

it causes the "inconsistent read" at the "read" step, that is, the value of x read from the shared memory might not be any state of x in the shared memory at any time point.


We remark that T is a small integer in practice.

the sparse linear model is where X ∈ R N ×D are features, y ∈ R N are responses, β * ∈ R D are (unknown) regression coefficients, and ∈ R N are unobserved errors.


Our approach draws parameters for important dimensions from distributions with multiple modeswhile unimportant dimensions are drawn from a uni-modal distribution.

in this work, we present a generative approach for discovering a global set of distinguishable dimensions when clustering high-dimensional data.


E t = 2 log t) in a simple 2-armed bandit problem.

given total number of plays n, and parameters µ * and β of (1) otherwise, i.e.


This optimization problem can be solved using any convex optimization solver to obtain x (t+1) .

we can use CCCP to solve the nonconvex optimization problem iteratively with each iteration minimizing a convex upper bound of the original objective function.


That is, after observing infinite many samples, streaming EM converges to the true means and matches the corresponding offline results in [3,6]; to the best of our knowledge this is also first such consistency result for the streaming mixture problem.

the second shows that if the candidate centers are sufficiently close to the true centers, then the failure probability of mis-classifying a point to a wrong center is (upto constant factors) the probability of mis-classification even in the optimal solution (with true centers).


They are central tools for data analysis and of the simplest problems in a hierarchy of complex machine learning computational problems.

formally, the sampling problem we have for each row is as follows.


At each stochastic gradient descent step in network training, DropMax classifier applies dropout to the exponentiations in the softmax function, such that we consider the true class and a random subset of other classes to learn the classifier.

the graphical representation of (5) indicates the dependencies among z 1 , .


We remark that Markov Random fields have become a defining methodology in stereo reconstruction [15], along with layered EM-style methods [2,16]; see the comparison in [14].

those techniques differ in characteristics from laser-based system to an extent that renders them practically inapplicable for many applications (most notably: long-range acquisition, where time-of-flight techniques are an order of magnitude more accurate then triangulation techniques, and bright-light outdoor environments).


We used the CBCL database consisting of 2429 frontal view face images handaligned in a 19 × 19 grid.

figure 6 shows three sets of basis distributions learned for class "3" with different sparsity values on the mixture weights.


for the examples shown on Figure 2 (e), (f) we get I(x, y) ≈ 1.03 and I(x, y) ≈ 1.10 respectively).

in contrast to most applications of the infomax principle (Linsker (1988)) in stochastic channels (e.g.


The normal distribution of tensors (3) will facilitate matrix and vector computations rather than compel us to work directly with tensors.

removing the constraints on R and forcing mat(Z n ) = Id q for all n results in a probabilistic CP decomposition in which the tensor elements have general covariances.


Swimmer-5 Swimmer-3 Swimmer-3 Figure 3: Left: For a 3-link swimmer, with relatively simple dynamics, the compared methods yield similar results and possibly a slight advantage to the purely model-based SVG (1).

we were able to learn gripping and walking behavior, although walking policies that achieved similar reward levels did not always exhibit equally good walking phenotypes.


Second, coupling the norm of kernels into MHE may contradict with weight decay which aims to decrease the norm of kernels.

conventional orthonormal regularization tends to group neurons closer, especially when the number of neurons is greater than the dimension.


Note that this notion of neighbors for DME in the context of distributed gradient descent translates to two data sets F = f 1 , f 2 , .

there are many subsequent works e.g., see [21] and in particular [5] showed that stochastic quantization and Elias coding [15] can be used to obtain communication-optimal SGD for convex functions.


An incongruous item (e.g., a new individual) could then be identified by a smaller posterior probability estimated by the more specific classifiers relative to the probability from the more general classifier.

one of them is strongly constrained by specific knowledge (both prior and dataderived), the other classifier is more general and less constrained.


for the HMM s0 = 0, for the FHMM s  in a factored form.

our factorial model is exchangeable in the columns as we don't care about the ordering of the features.


The risk, or probability of error, of the classifier produced by the AdaBoost algorithm is investigated.

it is unclear whether this number can be increased.


operator, makes it impossible to express R 0 " U ! "

the intuition conveyed by the example above can be easily transformed into a generic principle for feature selection.


Retrieval metrics B-1 B-2 B-3 B-4 CIDEr METEOR R@1 R@5 R@10 MedRank New York City (CNN+LSTM) [30]  similarity metrics (BLEU) and retrieval metrics (R@K, median Rank).

when we perform the LSA-based text summarization, we select top-κ highest ranked summary sentences, among which the top-ranked one becomes the summary sentence for the associated image, and all the top-κ ones are used for training in our model.


Wikipedia: Term-document matrix of a fragment of Wikipedia in English.


Considering the case of k = n, i.e., maximal possible induced matchings that are contained in a perfect matching (that is a matching of cardinality n), we show that if a d-regular graph is an Our upper bound on α(n) establishes an inherent limitation on the multitasking capacity of any network.

first, our model is graph-theoretic in nature, focusing exclusively on the adjacency structure of tasks and does not consider many parameters that emerge in biological and artificial parallel architectures.


This expectation over S, Z, Z of this Gibbs average is simplified using integration by parts over the Gaussian noise z iµjν , z iµjν and Nishimori identities (see e.g.

on one hand the shifted profile is a small perturbation of E s which matches a fixed point, except where it is constant, so if we Taylor expand, the first order vanishes and the second order and higher orders can be estimated as |i w,L (S(E s ); ∆)−i w,L (E s ; ∆)| = O(1/w) uniformly in L. by explicit cancellation of telescopic sums i w,L (S(E s ); ∆)−i w,L (E s ; ∆) = i RS (E good ; ∆)−i RS (E ∞ µmax ; ∆).


However, along each prediction path, H-loss only penalizes the first classification mistake closest to the root.

definition 2 (Nested Approximation Property (NAP)).


Similarly, as the shapes of observed objects change over time (because the only measurement in laser is depth), morphology based object tracking algorithms and optical flow [11,12] which are commonly used in computer vision are unsuitable.

in spite of its profound formulation, it is less pragmatic for online learning due to O(N 3 ) computational cost in both learning and inference, where N is the number of data points.


Here we assume 2 frame-long filters, i.e., m = 0, 1 in Eq.

in many situations, the filters describing medium propagation are non-invertible, or have an unstable inverse, or have a stable inverse that is extremely long.


The procedures for establishing a second-order excitor and a conditioned inhibitor are similar, yet the results are drastically different.


In our application such structural information is the microeconomic information that dictates what agent behaviors are successful in a given policy and how these behaviors evolve over time.

what needs to be estimated is the causal effect of a policy change, which is defined as the difference between the objective value when the economy is treated, i.e., when all agents interact under the new rules, relative to when the same economy is in control, i.e., when all agents interact under the baseline rules.


. . , x n ), where each variable x i ∈ F p (F p is the set of all natural numbers between zero and p − 1, for a given prime p) and g : F n p → F p . The prover P seeks to prove the following claim: that is, the sum of g evaluated at 2 n points is y. P and V now engage in a sum-check protocol to verify this claim.

the inputs, weights and all intermediate values computed in the network must lie in this range.


Coming back to the problem of MIPS, if Q and P are different, the event {h(Q(x)) = h(P (x))} will not have probability equal to 1 in general.

definition: (Asymmetric Locality Sensitive Hashing (ALSH)) A family H, along with the two vector functions Q ∶ R D ↦ R D ′ (Query Transformation) and P ∶ R D ↦ R D ′ (Preprocessing Transformation), is called (S 0 , cS 0 , p 1 , p 2 )-sensitive if, for a given c-NN instance with query q and any x in the collection S, the hash function h chosen uniformly from H satisfies the following: When Q(x) = P (x) = x, we recover the vanilla LSH definition with h(.)


its margin over a seq2tree model can also reach around 20 points.


Having identified this equivalence, we are able to both solve and interpret the transient non-linear dynamics (see supplementary materials for further details).

the leakage term, -n, which is the only term in the second line of Eq.


These back-andforth transformations are very computationally intensive, and as such it would be desirable to strictly remain in the frequency domain.

we observe on a variety of popular CNN configurations that this leads to significantly faster convergence during training.


We used one object for training and provided six trajectories leading to a successful grasp from its handle.

we start by specifying a graph that loosely indicates which pairs of states are supposed to have similar actions under an optimal policy.


In this paper we improve both of these problems with oblique trees.

convergence and computational complexity Optimizing the misclassification loss L is NP-hard in general [17,21,26] and we have no approximation guarantees for TAO at present.


[ER60] Let C be a tight community with |C| = !

similarly as for the stochastic block model, edge probabilities for the independent cascade model may vary between different communities and are identical within a single community C, where all edges have weights q ic C . an edge e between two nodes in a community C is in E with probability p C := q ic C • q sb C , independently for every edge, where q ic C and q sb C are the edge probabilities in the independent cascade model and the stochastic block model respectively.


The first metric is value unfairness, which measures inconsistency in signed estimation error across the user types, computed as where E g [y] j is the average predicted score for the jth item from disadvantaged users, E ¬g [y] j is the average predicted score for advantaged users, and E g [r] j and E ¬g [r] j are the average ratings for the disadvantaged and advantaged users, respectively.

we consider the task of collaborative filtering using matrix factorization [19].


While the complete knowledge assumption seems extreme, it enables a robust assessment of the vulnerability of collaborative filtering schemes to highly motivated attacks.

we demonstrate how a powerful attacker with full knowledge of the learner can generate malicious data so as to maximize his/her malicious objectives, while at the same time mimicking normal user behavior to avoid being detected.


In addition to this, we provide an analysis that is based on Lyapunov's stability theorem (described in Appendix A).

if the curvature of the first function is flat along a direction u (which also means that K DD u = 0) we can perturb ✓ ?


Given the same learning rate, we can see that the normal SGD in Figure 2c and 2d will have higher uncertainty when there are many outliers, and emphasizing difficult examples in Figure 2e and 2f makes it worse.

then, the proposed active bias methods perform better than other baselines in this smaller model.


Note that we also require that M d (µ) 0.

we use the expressions < gl and ≤ gl to denote the graded lexicographic order, a well ordering over p-variate monomials.


The adaptation process is the same as the on-line K-means clustering method except for adding random fluctuation in the distortion error evaluation process.

it is a key to add uncorrelated random fluctuation in the similarity evaluation process for each reference vector.


When it reaches a node j, node j reads x form the token and computes ∇f j (•) to update x according to (5).

in MCGD, it is possible to have p k,j = 0 for some k, j.


Although a full optimisation of the variational parameters gives the tightest bound, it turns out that the computational complexity of this optimisation is quite large for sigmoid belief networks.

in case the given bound is a polynomial of degree k, the new bound is a polynomial of degree k + 2 with one additional variational parameter.


when the alignment of predicted and ground truth is lost and the model does not have the power to restore it, more advanced optimization methods like dynamic time warping (Müller, 2007) during the matching phase may help at the cost of the simplicity and seamless integration of the scheduled sampling, as described in Section 3.

there may be a more interesting interplay between ideal skip intervals and switching points for options, which suggest that they should ideally be learned jointly.


In particular, for t large enough, Newton's method yields k ✓t+1 ✓ ⇤ k 2  ⇠ 2,NM k ✓t ✓ ⇤ k 2 2 , and it is insensitive to the condition number of the Hessian.

if a uniform sub-sample is used, the sub-sampled Hessian will be a random matrix with expected value at the true Hessian, which can be considered as a sample estimator to the mean.


To this end, we consider to maximize the number of positive instances that are ranked above any negative instances, and develop an efficient algorithm, named as TopPush to solve related optimization problem.

this is in contrast to the InfinitPush algorithm in [1] that introduces mn dual variables and a higher computational cost.


Each contribution has a cost (C = 1M U ).

the beta distribution contains two parameters, α and β.


The plots in Figure 2 show the theoretic limits.

similarly, given a sequence (r n ) n∈N of radii, we consider the convergence of Ncut n,rn induced by S on the graph G n,rn .


Gal and Ghahramani proposed an approach based on dropout [4] to approximately sample from a posterior over neural networks.

let c t,a = |{τ ≤ t : A τ = a}| be the number of times that action a has been selected by time t. We apply a coupling argument that introduces dependencies between the noise terms W t and action counts, without changing the distributions of any observable variables.


As a simple investigation into the expectancy and variance of these distributions, we computed the empirical distribution for ρ ij conditionned on σ ij , for both distributions (Panel A).

one can easily measure so-called signal correlations which measure how different neurons' trial-averaged firing rates covary with changes in the stimulus.


Instead, effective features come from the appropriate combination of the two.

the learned DeepID2 features can be well generalized to new identities unseen in the training data.


It means that we can not use self-excitation to get an effective α > 1.

this work is partially supported by ETH Research Grant TH-20/04-2, and EU grant "DAISY" FP6-2005-015803.


This paper presented two contributions, one practical and one theoretical.

the amount of memory required by iKBSF is independent of the number of sample transitions n. This fact together with the fact that KBSF's computational complexity is only linear in n allow our algorithm to process a large amount of data within a reasonable time.


The ROI detection and unsupervised localization share a similar goal of detecting the regions of objects in cluttered images.

the unsupervised ROI detection can be though of as a chicken-and-egg problem between (1) finding exemplars of objects in the dataset and (2) localizing object instances in each image.


Early work on MAB problems (Robbins, 1952;Lai and Robbins, 1985;Gittins et al., 2011) tended to be more focused on asymptotic guarantees, whereas more recent work (Auer et al., 2002;Auer, 2003) has been directed towards a more "finite time" approach in which we can bound regret for fixed time horizons T . One of the best-known and well-studied techniques is known as the Upper Confidence Bound (UCB) algorithm (Auer et al., 2002;Auer and Ortner, 2010).

for a given threshold index j, KMUCB tracks the arm elimination process as follows: for any threshold values below j, KMUCB believes that we have determined the best arm, and plays that arm constantly.


Note that the authors of [13] use ICM to obtain a binary solution.

it then finds the discrete solution x by maximizing the dot-product with the leading eigenvector of M. The assumption is that M is a slightly perturbed version of an ideal matrix, with rank-1, for which maximizing this dot product gives the global optimum.


In a simulation of experiment 1, a separate module with its own four-weight "receptive field" was trained for each of the composite stimuli shown to the human subjects.

right bottom: the structure of a training trial (the training phase, placed between baseline and test, consisted of 80 such trials).


In this context, a significant number of works were dedicated to studying the relationship between VC dimension and the minimal size of a compression scheme (e.g.

an agnostic sample compression scheme in this setup should compress S to a subsequence and a binary string of side information, from which the average of S can be reconstructed.


Such a mixed binary-continuous problem arises in Bayesian model selection with a spike-and-slab prior and we illustrate our technique by focusing on this case.

the detailed balance condition follows directly from the conservation of energy and (y, q)-volume along the trajectory dictated by (8), see [1,2] for details.


The LINGAM approach has been extended in [11] to cyclic models, exploiting a possible non-Gaussianity of the data.

we demonstrate the performance on some simulated data and applications in flow cytometry and financial time series.


We have the following properties of Local-Global Gap: The result in Theorem 1 can be easily extended to smooth regularization which can be found in the long version [35].

p (•), we construct new functions P k (•; •) as follows: where given a data partition which is also called the local loss function.


The AP algorithm addresses this issue by that each sample is initially viewed as an examplar and then examplar-to-member and member-to-examplar messages competitively transmit among all samples until a group of good examplars and their corresponding clusters emerge.

the global descriptor ε C and the popularity character χ C are not sensitive to the local data scale at each point, leading to the robustness of Zeta merging against the variation of data scales.


The amount of data available in the world is growing faster than our ability to deal with it.

our ClusterACDM method outperforms (1.1) both in terms of theory and practice.


Clearly, for the overlapping part, T02 = T 01 .

n (•) and R(•) denote the null space and range space of a matrix, respectively.


We note that the proposed evolutional dropout achieves similar effect to the batch normalization technique (Z-normalization based on a mini-batch of examples) [5] but with different flavors.

in practice some features could be more informative than the others for learning purpose.


S pecifically, we assume exponentially decaying noise correlation with As this model is invariant under spatial shifts, the first PRF can be calculated by finding the spatial frequency at which the S NR is maximal.

if a hypothetical neuron receives input from the population, and wants to decode the presence of the stimulus a 1 , the weights of the optimal linear readout [ 1 6] could be derived from b 1 .


This results in a drop of test accuracy with respect to other settings.

then any transmission method with codelength L satisfies (Mackay, 2003) the gain (per data point) between the codelength L and the trivial codelength H(y) is the mutual information between inputs and outputs (Mackay, 2003).


Let {v i 1:t−1 } N i=1 be particles representing chains of states up to t − 1 with corresponding normalized weights The corresponding posterior for v 1:t can be approximated by propagating these particles forward.

this bias towards particles with high expected likelihood is eliminated when the final importance weights are computed in (9).


In this section, we provide empirical evaluations of our main algorithm SCREENANDCLEAN on synthetic datasets.

the number of rounds of communication is a small integer.


The multi-armed bandit problem can be viewed as a Markov decision process, where the state variable is the posterior belief after making each observation.

smaller fitted b does not imply subjects are necessarily more noisy or care about rewards less; it may simply mean that the model is less good at capturing subjects' internal processes.


If the length of X a..b is linear in n, so that b − a = αn for some α ∈ (0, 1), then its intra-subsequence distance ∆ x (a, b) (defined by ( 7)) converges to 0 with n going to infinity.

experiment 2: (Dependence on λ) Algorithm 1 requires λ ∈ (0, 1) as a lower-bound on λ min .


Moreover, we also find that recalls of the single optimal search path RL become stable with a few steps and hardly increase with the increasing of steps.

for the single optimal search path RL, it only selects the best action with the highest estimated value by the deep Q-network to obtain one next window during testing, instead of taking two best actions from the two action groups.


As a common practice [28], assume that (t, y) is Lipschitz continuous in t for all |t| ≤ C g with a Lipschitz constant L . Theorem 4 (Estimation error bound).

for 20News, we borrowed the pre-trained word embeddings from GloVe [42], and the model can be written as d-avg_pool(word_emb(d,300))-300-300-1,  ; it is one of the best architectures for CIFAR-10.


Therefore, finding the shortest path on the graph is equivalent to minimizing the total loss, which is the aim in loss-based decoding.

finally, we note that although PD-Sparse [15] and DiSMEC [2] perform better on some model size regions of the datasets, their worse case space requirement during training is linear in the number of classes K, whereas our approach guarantees (adjustable) logarithmic space for training.


Please note here that we omit the nonlinear model for shared representation [13,18,17] since they are essentially also inner product based models (when used for matching) and not designed to deal with short texts with large vocabulary.

the outputs of p-layerII are then sent to c-layer for further decision composition.


For small problem sizes, interior point methods offer superior accuracy and convergence rates.

background estimation is complicated by the presence of foreground objects such as people, as well as variability in the background itself, for example due to varying illumination.


In this tree, we have one metric for each non-leaf node of the object hierarchy, and each metric is responsible for discriminating among its immediate subcategory children.

the first two dimensions of all points are specific to the superclass decision (A vs. B), while the last two are specific to the subclasses.


The obvious choice is the so-called defining representation, whose elements are the familiar permutation matrices ρ def (σ) = P (σ) [P (σ)] p,q = 1 σ(q) = p 0 otherwise, since the corresponding loss function is The squared Frobenius norm in this expression simply counts the number of mismatches between the observed but noisy permutations τ ji and the inferred permutations σ j σ −1 i .

starting with the seminal work of Singer et al.


Here r = 2 for OU, r = 4 for MB2, and (due to the faster-than-power law decay of its eigenvalues) effectively r = 00 for RBF.

this framework has not yet to my knowledge been exploited to important to understand how GPs learn if there is some model mismatch.


We tried a few different settings for HRA: with/without normalisation and with/without each type of exploration.

if the optimal value function is very complex, then learning an accurate low-dimensional representation can be challenging or even impossible.


The ridge and normal intervals perform reasonably well across settings, with both performing much better than OLS.

the form of regularized regression we will focus on is ridge regression: where ρ > 0 is a user-specificed regularization parameter.


Most statistical regression models in use today are of the form: g(y) = f (x 1 )+f (x 2 )+• • •+f (x D ).

the Dth order additive covariance function has D D = 1 term, a product of each dimension's covariance function: In the case where each base kernel is a one-dimensional squared-exponential kernel, the Dth-order term corresponds to the multivariate squared-exponential kernel: (5) also commonly known as the Gaussian kernel.


In an extensive set of experiments we show that the proposed metric is able to disentangle the quality of generated samples from the coverage of the target distribution.

the model on the right produces more artifacts, but more varied images.


We can try to more quantitatively describe the correctness of the inpainting procedure using as metrics the discriminator score and the leastsquares rigid-body alignment error with respect to the true native structure.

the task of determining 3D cartesian coordinates given pairwise distance measurements is already well understood and has a natural formulation as a convex problem [31].


In decoding the cos(phase), a hidden variable, was the scene variable inferred.

linear methods have been shown to be quite adequate for decoding LGN, motor cortical, or hippocampal place cells' signals using population vectors or the optimal linear decoder [10,5,8].


This multi-modality in the action space makes the learning hard.

one possibility is to build a model that predicts the next visual state from the current visual state and the applied force (i.e forward dynamics model).


So far, steganographic schemes have used human-based rules to 'learn' this distribution and perturb it in a way that disrupts it least.

we first motivate our work by showing our model can produce steganographic images that are almost indistinguishable from the cover images.


When equipped with very ad-hoc variance-reduction techniques, Shamir showed that the algorithm has a better (local) performance than power method (see Table 1).

it is a (multiplicative-)approximate algorithm for computing the leading eigenvector of a symmetric matrix.


The factorization yields accurate approximate solutions which can be further refined by local search.

it seems generally difficult to representation such boundaries in terms of the bottom eigenvectors of the graph Laplacian.


Let the event E t denote the good event where U 0 , .

we hope our paper and results help generate interest in online matrix completion, and our techniques and framework prompt tighter analysis for other nonconvex problems.


This immediately gives us a linear time algorithm to pick the best q.

picking nodes greedily can be O(n) worse than the optimal.


This provides a means for generating data from any DAE (if the corruption is not degenerate, more precisely, if the above chain converges).

a formal justification for this algorithm remains an open problem.