Note in addition that efficiency is important within the speech recognition application: in our experiments we make use of around 11 million training samples, while the dimensionality of the data is D = 50.

we will develop nearest-neighbor methods that give an efficient estimate of P (y|a).


Since X and b come with the data and λ is chosen by the user, we only need to specify θ * λ0 and λ 0 .

we need to provide Slores with a dual optimal solution of problem (LRD λ ) for an arbitrary parameter.


We now present a scalable approach to both latent space modeling and inference algorithm design that encompasses all three aforementioned principles for large networks.

we build our approach on the bag-of-triangles representation of networks [8] and apply principles (2) and (3), yielding a fast inference procedure that has time complexity O(N K).


We here present the results obtained for a restricted version of the model in which eye rotation is assumed to be limited to pursuit that keeps the eye fixated on a stationary point in the scene during the observer translation.

we investigated whether a circular or bi-circular RF structure as predicted by the velocity gain model emerges in the population model.


we show that there exist non-trivial determinantal measures whose ESR versions remain SR for p in a neighborhood of 1.


We are especially interested in cases where each y n is a high dimensional vector and, therefore, we assume that there exists a low dimensional manifold that governs the generation of the data.

a temporal latent function x(t) ∈ R Q (with Q D), governs an intermediate hidden layer when generating the data, and the dth feature from the data vector y n is then produced from x n = x(t n ) according to where f d (x) is a latent mapping from the low dimensional space to dth dimension of the observation space and β is the inverse variance of the white Gaussian noise.


Using the notation bS := {b r | r ∈ S}, the following relationships between the continuous and fixed price versions of Υ, S W , and the expected utility are a consequence of the convexity of C. Their main purpose is to highlight the relationship between wealth and liquidity in MEU demands.

they show that scaling up of liquidity is equivalent to a scaling down of wealth and that the continuously priced constraints and wealth functions monotonically approach the fixed priced versions.


For the multiplicative noise model, we use the multiplicative θ-domination relation as presented in Definition 5.

the approximation ratio of PONSS with the assumption Eq.


As we had hoped, we also found that the accuracy scales in a super-linear manner with respect to bitwidth when using middle-out bit selection.

the model accuracy increases extremely quickly from 1 bit to 1.3 bits before slowly approaching the full precision accuracy.


This definition insists on the fact that the values estimated for each action should not depend on the interruptions.

it ensures the three following properties that are very natural when thinking about safe interruptibility: • Interruptions do not prevent exploration.


The Hidden Parameter Markov Decision Process (HiP-MDP) [14] was developed to address this type of transfer learning, where optimal policies are adapted to subtle variations within tasks in an efficient and robust manner.

the HiP-MDP paradigm introduced a low-dimensional latent task parameterization w b that, combined with a state and action, completely describes the system's dynamics T (s |s, a, w b ).


The relationship between Gaussian processes and Bayesian linear regression suggests that we can define a single model that exploits both similarity and rules in forming predictions.

we can do this by taking a prior that covers a broad class of functions -including those consistent with a radial basis kernel -or, equivalently, modeling y as being produced by a Gaussian process with a kernel corresponding to one of a small number of types.


Panel 1 (top left), for example, is quite crisp, while panel 3 is fairly thick, and panel 6 (top right) has thin and fainter strokes.

the Bayesian GAN is learning different complementary generative hypotheses to explain the data.


Figure 3 provides strong empirical evidence that SMaLL compares favorably to the baselines on several high dimensional OpenML datasets belonging to the Fri series.

the first number in each dataset name indicates the number of examples, and the second the dimensionality of the dataset.


Label propagation [17] is an example of these methods in which the goal is to minimize the difference between model predictions of two samples with large weighted edge.

similar samples tend to get similar predictions.


In the theorem statement below, "for almost all C" means potentially troublesome cost matrices form at most a (Lebesgue) zero-measure subset of S n×n , in the same way that almost all square matrices are invertible.

given any matrix C ∈ S n×n , perturbing C to C + σW where W is a Wigner random matrix results in an acceptable cost matrix with probability 1, for arbitrarily small σ > 0.


Although Algorithm 1 is Algorithm 1 Approximate gradient descent algorithm for tuning λ Initialize the tuning parameter λ 0 , choose a step-size selection rule, and set t = 0 for t = 0, 1, 2, . . . do calculate the approximate gradient g λ t (z n ) set λ t+1 = λ t − α t g λ t (z n ) end for more computationally efficient compared to LOOCV (saving a factor of n), it might still be computationally expensive for large values of n as it still scales linearly with n. Hence, we also present an online version of the algorithm using the stochastic gradient descent idea; see Algorithm 2.

initialize the tuning parameter λ 0 and set t = 0 for t = 0, 1, 2, . . . do choose a random index i t ∈ {1, . . . , n} calculate the stochastic gradient g Ridge regression with diagonal regressors: We consider the following regularized loss function:  we consider one regularization parameter per each model parameter.


Gabor filters [7] provide a suitable mathematical model for biological simple cells [8].

we employ a set of modified Gabor filters [9].


It is clear that for the clean data (without extra noisy covariates), the more data the better the estimation.

the model perfectly detects the cross in the survival functions.


As RDD is usually hard to verify, we consider a stronger sufficient condition inspired by Corollary 1. , then for any δ > 0, if the sample size satisfies where K is defined in Lemma 1, then with probability at least 1 − δ, Φ = A SIS X − 2τ −1 A SIS ∞ I p is restricted diagonally dominant with sparsity s and C 0 ≥ ρ.

sIS is screening consistent for any β ∈ B τ (s, ρ).


The use of such a shrinking strategy reduces the overall complexity from O(d) to O(|A|).

we (a) update the gradients just on the working set, (b) update Q ( Q) just on the rows(columns) corresponding to the working set, and (c) compute the latest entries in D t , γ t , L t and S T t S t by just using the corresponding working set rather than the whole set.


Combined however, we will see that sample-efficient learning is possible, and the combination of these two assumptions is precisely how we characterize our model.


The model described above cannot be trained by minimizing the log-likelihood alone.

there is nothing that prevents all of the information about the observation from flowing through the unspecified component.


Note that E[r k (S k , x k+1 , f k+1 )] is simply the expected improvement given, for all x ∈ X , by: where Φ is the standard Gaussian CDF and φ is the standard Gaussian PDF.

the GP is used to simulate possible scenarios, and the next design to evaluate is chosen to maximize the decrease of the objective function, over the remaining iterations, averaged over all possible simulated scenarios.


When some groups are included in others, the canonical graph can be simplified to yield a graph with a smaller number of edges.

if h and g are groups with h ⊂ g, the edges (g, j) for j ∈ h carrying a flow ξ g j can be removed and replaced by a single edge (g, h) of infinite capacity and zero cost, carrying the flow j∈h ξ g j .


4 Simple DP-UMP tests when δ = 0 In this section, we derive the DP-UMP test when δ = 0 for simple hypotheses.

given n, > 0, α > 0, θ 0 < θ 1 , and X ∼ Binom(n, θ), we find the UMP test at level α among D n ,0 for testing Before developing these tests, we introduce the Truncated-Uniform-Laplace (Tulap) distribution, defined in Definition 4.1, which is central to all of our main results.


To incorporate non-maxima suppression in the framework of RRSVM, we replaced the region ranking procedure Γ(B; w) of RRSVM by Ψ(B i ; w, α), a procedure that ranks and subsequently returns the list of regions that do not significantly overlap with one another.

we use intersection over union to measure overlap, where α is a threshold for tolerable overlap (we set α = 0.5 in our experiments).


To sample test queries, we sample from the original graph (i.e., the complete graph without any removed edges), but we ensure that the test query examples are not directly answerable in the training graph.

we ensure that every test query relies on at least one deleted edge (i.e., that for every test query example (q, v * ), v * / ∈ q train ).


Compared to Knockoff, DeepPINK obtains equivalent or better power in 9 out of 13 cases with comparable false discovery proportion.

deepPINK and BHq are the only methods that can identify mutations in DDI, TDF, and X3TC for NRTI.


In this paper, we show that the per-pixel color statistics of natural scenes-without any spatial or semantic context-can by themselves be a powerful cue for color constancy.

we describe an illuminant estimation method that is built around a "classifier" for identifying the true chromaticity of a pixel given its luminance (absolute brightness across color channels).


Let V denote all the available views of an captured action.

the encoder, parameterized by θ e , takes as input a sequence of frames for view i ∈ V , denoted as and encodes them into a sequence of low-dimensionality feature embeddings E(X i ; θe) = for each frame, we first use a downsampling CNN (denoted as "Conv") to extract a low-dimensionality feature of size h × w × k. Then, a bi-directional convolutional LSTM (denoted as "BiLSTM") runs through the sequence of extracted Conv features.


We now derive an efficient online update to jointly learn the weights while clustering the representations of the neural network.

we illustrate the sample clustering case while noting that the other types can be derived easily by applying the corresponding unfolding operator.


Notice that λ a (t) behaves like a step function.

the rate of arrivals is fixed until the next arrival.


The model has two main restrictions, one on the total number of machines and another on the memory available on each machine.

given an input of size N , and a sufficiently small γ > 0, in the model there are N 1−γ machines, each with N 1−γ memory available for the computation.


Closest to our approach are penalty methods built around the idea of mixed ℓ 1 − ℓ 2 norms.

the group Lasso method [16] assumes that the components of the underlying regression vector β * can be partitioned into prescribed groups, such that the restriction of β * to a group is equal to zero for most of the groups.


Recently, several works have focused on directly minimizing the task loss.


Equation 1 has a similar form to that of Generalized Elastic Net (GEN) [11], which has shown good performance in nonrigid image registration [12]; note that there we directly penalized Y, while here we penalize the transformation v. The φ function represents our prior knowledge about the motion, which should be smooth.

we want the velocity field v generated by template point set displacement to be smooth.


For these cases, the general strategy is to first get upper bounds and lower bounds, and then check whether any gap between the lower and upper bound can be reduced.

in general, one always has the simple upperbound: the total capacity of a newtowrk is always upperbounded by the sum of the capacities of all the individual neurons (this remains true even when the circuit contains threshold gates of different degrees and different fan-ins).


We consider approximating functions f : R d → R from point queries.

for some unknown active S ⊂ {1, . . . , d} with |S| = k d, we assume f to be of the additive form: f (x 1 , .


Obviously, R will not be z-transported individually from these domains, but it turns out that taking both sets of experiments into account, R = z2 P (a) (y|do(z 2 ))P (b) (z 2 |x, do(Z 1 )), which fully uses all pieces of experimental data available.

we were able to decompose R into subrelations such that each one is separately z-transportable from the source domains, and so is the desired target quantity.


Second, we use these bigram probabilities as a Markov model, and compute the expected number of times each bigram will occur in the answer, conditioned on the query.

as a generic model of words we assume that each letter in the word depends on the adjacent letters, but is conditionally independent of all others.


Classically, multi-view subspace learning has been achieved by an application of canonical correlation analysis (CCA) [2,3].

many successes have been achieved in using CCA to recover meaningful latent representations in a multi-view setting [4][5][6].


We say that Π is privacy-preserving if for every 1 ≤ i ≤ k, anything that party i can compute in time polynomial in n following the execution of Π, they could also compute in polynomial time given only their private input x i and the value y.

whatever information party i is able to obtain from their view of the execution of protocol Π, it does not let them efficiently compute anything they couldn't efficiently compute just from being told the final output y of Π (and their private input x i ).


While segregated graphs preserve conditional independence structure on the observed marginal of a CG for any H [20], we chose to further restrict the set H in order to ensure that the directed edges in the segregated projection retain an intuitive causal interpretation of edges in a latent projection [28].

whenever A → B in a segregated projection, A is a causal ancestor of B in the underlying causal CG.


To mitigate the cumbersome and costly process of collecting and annotating human-machine dialogs as the system learns, we utilize a model-based RL approach by training a user simulator based on a corpus of human-written relative descriptions.

to emulate a single dialog turn, where the user provides feedback regarding a candidate image relative to what the user has in mind, the user simulator generates a relative caption describing the differences between the candidate image and the user's desired image.


Recall the different lower bound conditions on the graph density that must hold to ensure that the query set size is not larger than the test set size.

these were whenever k|E| = Ω(|V | log |V |) we have that treeletStar(k) works in constant amortized time.


The idea is to approximate the infinite-dimensional GP function f by a linear combination over basis functions φ j parameterized by a weight vector α ∈ R N with a Gaussian prior distribution: Now, defining the matrix Φ ij (x, ) := φ j (x i , i ), the relationship y = Φ(x, )α gives a correspondence between and α (for fixed x and y), which we assume to be one-to-one.


By relaxing these conditions we can produce a more general definition.

an m-Markov boundary is defined as follows.


Instance (iii) is another "hard" instance, where estimating the sign of the components of θ is difficult.

one must distinguish θ from θ ′ = (−a, a, −a, a, b n−4 , ..., b n−4 ), otherwise a large error occurs.


We emphasize that the simulations do not require the use of a specific algorithm, such as the algorithms associated with the proofs of the worst-case bound (Theorem 3.2) and the average-case bound (Theorem 4.1).

the simulations show that the null experiment applied in conjunction with the forcing operations (F 1 )-(F 4 ) is typically sufficient to discover most of the causal graph.


Similarly, the model evidence in (7) can be approximated by Z, the normalization constant of q: Since all the factors in (12) are Gaussian, log Z can be readily computed and maximized with respect to σ 2 , ρ 2 , γ 2 and P to find good values for these hyper-parameters.

once EP has converged, the gradient of the natural parameters of the gj 's with respect to these hyper-parameters is zero [21].


Next, we show how to compute the Jacobian matrix J d . Recall that at the optimum of the smooth unconstrained optimization problem OPT1, the partial derivative of the objective with respect to any parameter must vanish.

the partial derivative of 1 2 w T Cw + ℓ T (w) with respect to w i vanishes when w = w ⋆ , so where C T i denotes the ith row of the C matrix.


Further, the smallest element of each partition must either be the same specification or incomparable in (Φ, ).

for each k ∈ {0, 1, . . . |X|}, the set: is a maximal anti-chain.


If G is a union of disjoint cliques, Ω (min[log log n, log ω(U)]) experiments are necessary in expectation to construct G. Observe that Lemma 3.4 explains why attempting to recursively partition the runs (used in Theorem 3.1) in sub-runs will not improve worst-case performance.

a recursive procedure may produce a large number of sub-runs and, with high probability, the trick will fail on one of them.


Most of these approaches rely on semantic parsing [19,9,1,16].

[16] introduces the problem of translating IFTTT descriptions into executable code, and provides a semantic parsing-based approach.


Graph clustering is a fundamental task in many data-mining and machine-learning pipelines.

identifying a good hierarchical structure is at the same time a fundamental and challenging problem for several applications.


By forcing the buyer to reject a price for several rounds, the seller ensures that the future discounted surplus will be negligible, thereby coercing the buyer to be truthful.

we proceed to formally analyze algorithm A r . we will quantify the effect of the parameter r on the choice of the buyer's strategy.


Formally, let us consider the iterative updates for the policy parameter θ and the discriminator parameter φ, where the point estimate of θ is obtained using the distribution over φ in each iteration.

given θ prev from the previous iteration, we want to utilize p posterior (φ) := p(φ|0 A , 1 E , θ prev ) that satisfies By using Monte-Carlo estimations for the expectations over trajectories in (18), the log posterior in (18) can be approximated as where E,t )).


We represent images with bag-of-visual-words descriptors following previous work on domain adaptation [2,4].

we extract SURF [30] features from the images, use K-means to build a codebook of 800 clusters, and finally obtain an 800-bin histogram for each image.


To compare the convergence error of two costs C and C in the next section, we require that their liquidities b and b be set so that they have (approximately) the same bias, i. Theorem 5.6 also captures an intuitive relationship which can guide the market maker in adjusting the market liquidity b as the number of traders N and their risk aversion coefficients a i vary.

holding μ and the cost function fixed, we can maintain the same amount of bias by setting b ∝ N/ā.


First, the image-sentence similarities should be consistent with the ground truth correspondences.

corresponding image-sentence pairs should have a higher score than all other image-sentence pairs.


The policy is doing so through adjusting the exploration rate of each arm based on a virtual time index τ k,t associated with that arm, rather than based on the actual time period t (which is appropriate in the absence of information flows).

the adaptive exploration policy explores arm k at a rate that would have been appropriate without auxiliary information flows at a future time step τ k,t .


Our result is tight up to constants, in terms of allowable sparsity level under the deterministic sparsity model.

if we exceed the sparsity limit imposed in S1, it is possible to construct instances where there is no unique decomposition 4 .


To address this problem, we simulate face images with various pre-defined poses (i.e., yaw angles), which explicitly augments the available training data without extra human annotation efforts and balances the pose distribution.


The underlying RL algorithm is applied to the first sample (or samples), and its performance is measured in a subsequent sample.

the algorithm starts with parameters θ, and applies the update function to the first sample(s), resulting in new parameters θ .


To find a principle to choose the y jl , assume that we have access to the row and column measurements on the true distributions π * ij .

assume that we know the true values of the column measurements φ jk = i π * ijk and row measurements ϕ ikl = j y jl π * ijk , for a chosen set of y jl values.


However, when there is prior knowledge about the unknown parameters A 0 , B 0 , e.g., when A 0 , B 0 are sparse, accurate estimation can be feasible.

[3] proved that under suitable conditions the unknown parameters of a noise driven system (i.e., no control) whose dynamics are modeled by linear stochastic differential equations can be estimated accurately with as few as O(log(p)) samples.


In addition to the existing linear constraints ((2a), (2c) and (2b)), the non-linear constraints are approximated by sets of linear constraints representing the non-linearities' convex hull.

reLUs with input of unknown sign are replaced by the set of equations: where x i[j] corresponds to the value of the j-th coordinate of x i .


The concept of basis refinement is not only applicable to the feature extraction methods we will present later, but to methods that have been studied in the past.

methods based on Bellman error basis functions, state aggregation strategies, and spectral analysis using bisimulation metrics are all special cases of basis refinement.


For our experiments, we probabilistically select which ✓ m to advance from a discrete probability distribution as a function of ✓ m 's novelty.

at every iteration, for a set of agent parameter vectors ⇧ = {✓ 1 , ✓ 2 , ..., ✓ M }, we calculate each ✓ m 's probability of being selected P (✓ m ) as its novelty normalized by the sum of novelty across all policies: Having multiple, separate agents represented as independent Gaussians is a simple choice for the meta-population distribution.


A simple choice is the uniform distribution over F , but such a distribution is not continuous over the latent space.

instead, we construct a mixture of Gaussians, each of which is centered at a vector f (y i ) in F . we generate a latent vector z 2 R k in two steps: We first sample a vector µ 2 F uniformly at random, and then draw a vector z from the Gaussian distribution N (µ, 2 ), where is a smoothing parameter that controls the smoothness of the distribution of the latent space.


The feasibility of these rules can be seen from Proposition 1 as well as the D.C. programing problem [11].

(DR1) follows from Proposition 1 that in this case T k ∩ D = ∅, i.e., the prism T k is infeasible, and (DR2) from Proposition 1 and from the definition of µ that the current best feasible solution cannot be improved in T . We first provide illustrations of the proposed algorithm and its solution on toy examples from feature selection in Section 5.1, and then apply the algorithm to an application of discriminative structure learning using the UCI repository data in Section 5.2.


The objective of graph reconstruction is to predict the possible occurrence of connections between a set of objects/individuals known to form the nodes of an undirected graph.

each node is described by a random vector X which defines a form of conditional preferential attachment: one predicts whether two nodes are connected based on their features X and X .


Again, this result is formulated for the realizable case for simplicity, but can easily be extended to the Tsybakov noise model as in the previous section.

by reasoning quite similar to that above, a cost-adaptive variant of the Robust CAL algorithm of [14] achieves error rate er( ĥ) − er(h * ) ≤ ǫ with probability at least 1 − δ using a total cost We omit the technical details for brevity.


To apply the Rand index to train our classifier, we need a simple way of relating the indicator function (ŝ i , ŝj ) in the Rand index to classifier output.

we would like a way of characterizing whether two pixels are connected in the thresholded affinity graph.


Indeed, it seems spurious to marry the idea of an exquisite on-line integration of noisy cues with an underlying rate code that requires averaging on large populations of noisy neurons and long periods of time.

most natural tasks require this integration to take place on the time scale of inter-spike intervals.


In this paper, we take additional steps towards addressing the above problems and show how the generic notion of the curvature -the deviation from modularity-of a submodular function determines both upper and lower bounds on approximation factors for many learning and constrained optimization problems.

our quantification tightens the generic, function-independent bounds in [8,2,27,7,10] for many practically relevant functions.


However, we present results for PIM and RIN only, as the results on the other datasets mostly followed the results on these and in a way these two datasets are the most extreme.

they are the smallest and largest with dimensions 768 ⇥ 8 (768 examples, and 8 dimensional feature space), and 7200 ⇥ 20, respectively.


The heuristic part of our strategy is to skip f i (x s ) or f i (x t ) if our evaluation of f i has been zero more than two consecutive times (and skipping it an exponentially larger number of times each time it remains zero).

for each example i we maintain two variables, sk i (for 'skip') and ps i (for 'pass').


The design philosophy behind RNs is to constrain the functional form of a neural network so that it captures the core common properties of relational reasoning.

the capacity to compute relations is baked into the RN architecture without needing to be learned, just as the capacity to reason about spatial, translation invariant properties is built-in to CNNs, and the capacity to reason about sequential dependencies is built into recurrent neural networks.


We repeatedly select a new task for which to receive a gold standard label from the researcher.

for this experiment we constrained active learning to use l = r. Of course, in our framework we could have just as easily queried labelers in the crowd.


BO gains this efficiency by leveraging Bayesian models that take into account all previously observed evaluations in order to better inform future evaluation choices.

typical BO methods continually maintain a posterior over f (x) that is used to select the next input to evaluate.


At the same time, the number of shared latent factors can serve as one possible measure of domain relevance that may lead to more rigorous theoretical study of TL/MTL methods.

for BMDL, we propose a novel multi-domain negative binomial (NB) factorization model for over-dispersed NGS count data.


Because this is an improper density, we define an approximate Jeffreys prior with range parameter a ∈ (0, 1].

we say that x ∼ J(a) if With this definition in mind, we present the following result.


Based on a sufficient condition presented in Section 3.1, we study how "invariance" of the subdifferential of one function would lead to nontrivial proxdecompositions.

we prove in Section 3.3 that when the subdifferential of one function is scaling invariant, then the prox-decomposition always holds if and only if another function is radial-which is, quite unexpectedly, exactly the same condition proven recently for the validity of the representer theorem in the context of kernel methods [9,10].


Nonetheless, despite learning a nonlinear mapping, GB-LMNN still underperforms χ 2 -LMNN.

it is possible that no matter how flexible a nonlinear mapping could be, it is still best to use metrics that respect the semantic features of the data.


On the other hand, the order-optimal asymptotic regret can be significantly smaller.


This yields the augmented model Note that the original model ( 2) and the augmented model (3) are exactly identical, since we can marginalise u out from (3) to get exactly (2).

we introduced u in a consistent manner, so that p(g|u, f )p(u)du = p(g|f ).


We compared the proposed method to a baseline method in which the annotations are considered to be content-related if any of the words in the annotations appear in the document.

when the category name is 'comp.graphics', if 'computer' or 'graphics' appears in the document, it is considered to be content-related.


Therefore applying Talagrand's inequality in the version of [3] to the class G r we obtain Let us define ε r := 30ϕn(r) r + 2τ v nr 2−ϑ 1/2 + 7τ nr .

then the above inequality gives with probability not less than 1 − e −τ that for all (p, f ) ∈ P × F we have and consequently we have with probability not less than 1 − e −τ that Now observe that for the functions h 1 and h 2 which we defined when estimating (12) and (13) we have and hence we can combine our estimates (16), (14), and (15) of the terms (11), (12), and (13) to obtain that with probability not less than 1 − 3e −τ we have for r satisfying the assumption (10) we have 30ϕn(r) , and 7τ nr ≤ 1 4 .


The first two approaches are based on reducing the inference problem into a weighted model counting problem.

these approaches encode the network using Boolean expressions, which are compiled to logical representations (d-DNNF or SDD), from which an arithmetic circuit is induced.


The key idea is that, rather than summing all functions and then doing the maximization, we maximize over variables one at a time.

when maximizing over W rq , only summands involving W q participate in the maximization.


, for function f with truncated wavelet basis expansion of order J, can be written as a linear combination of that truncated wavelet basis.


Then the resulting distribution Pr (X), as defined by Equation 1, is a simple-route distribution for graph G. This theorem will not hold if Pr (B) were not a simple-route distribution for graph G B .

having each distribution Pr (A i | b i ) be a simple-route distribution for graph G bi is not sufficient for the hierarchical distribution to be a simple-route distribution for G. Hierarchical distributions that satisfy the conditions of Theorem 1 will be called hierarchical simpleroute distributions.


The essence of the proposed method is to improve the prediction by i) parametrizing the targets (e.g., 3D boxes) instead of directly estimating the targets, and ii) cooperative training across different modules in contrast to training these modules individually.

we parametrize the 3D object bounding boxes by the predictions from several modules, i.e., 3D camera pose and object attributes.


On the positive side, if we restrict ourselves to tree-structured graphs, the estimator ( 6) is attractive, since it relies only on an estimate Σ of the population covariance Σ * that satisfies the deviation condition (7).

when the samples {x i } n i=1 are contaminated by noise or missing data, all we require is a sufficiently good estimate Σ of Σ * .


In fact a recent paper [11] has shown that if only the distances as encoded by the graphical model depicted in figure 1 are taken into account (nodes represent points in S and states represent points in U), exact probabilistic inference in such a model can solve the isometric problem optimally.

an energy function of the following form is minimised: In [11], it is shown that loopy belief propagation using this model converges to the optimal assignment, and that the number of iterations required before convergence is small in practice.


While sparse, some literature on model selection for deep learning nonetheless exists.

a forerunner approach was presented in [Ash, 1989] to dynamically add nodes to an existing architecture.


A hypergraph is a graph in which an edge can connect more than two vertices [2].


The next theorem presents a minimax lower bound for entropy rate estimation which applies to any estimation scheme regardless of its computational cost.

it shows that Hopt is minimax rate-optimal under mild assumptions on the mixing time.


Now, R is determined up to a scaling and ordering of the eigenvectors.

there is a permutation matrix Π and diagonal matrix D such that R = DΠR .


The basic strategy we pursue is to consider the abstract computational problem involved in function learning, and then to explore optimal solutions to that problem with the goal of shedding light on human behavior.

the problem of learning a functional relationship between two continuous variables is an instance of regression, and has been extensively studied in machine learning and statistics.


PARW is a unified framework with several popular SSL methods and PageRank [17] as its special cases, corresponding to different Λ.

the case Λ = I has been justified in capturing the cluster structures [23].


In this paper we describe a novel connection between likelihood ratio based policy gradient methods and importance sampling.

we show that the likelihood ratio policy gradient estimate is equivalent to the gradient of an importance sampled estimate of the expected return function estimated using only data from the current policy.


We can use these training clusterings to establish a scale.

we will show a meta-clustering algorithm whose output A always satisfies richness and consistency, and which satisfies the following variant of scale-invariance.


In this paper, we consider a probabilistic approach to model multi-view data, which can perform both the response-level predictions (e.g., image classification) and view-level predictions (e.g., image annotation).

we propose a large-margin learning approach to discovering a predictive subspace representation for multi-view data.


The Thompson sampling algorithm simply samples actions according to the posterior probability they are optimal.

actions are chosen randomly at time t according to the sampling distribution π TS t = α t . By definition, this means that for each a ∈ A, P(A t = a|F t−1 ) = P(A * = a|F t−1 ) = α t (a).


We also looked at spike rasters from different cell-types to gain insight into their phase relationship with the stimulus.

we present recordings for the site indicated by the arrow (see Figure 3a) for gratings moving in eight directions ranging from 0 to 360 degrees in 45-degree increments (this location was chosen because it is in the vicinity of a pinwheel, is reasonably selective, and shows considerable modulation in its firing rate).


Hence, we approximate the summation in (2) by its largest term.

each assignment vector v and each model referenced in v implies a set of pose parameters X v (extracted e.g.


Third, the method can be used in an incremental way to track the frequency of a slowly modulated sinusoid.

suppose we analyze sliding windows-shifted by just one sample at a time-of a longer, nonstationary signal.


. . , b T a sequence of strategic buyers b1 , .

. . , bT such that the regret incurred to A by b1:T is at least the switching cost regret incurred to A 0 by b 1:T . The idea behind the construction is as follows: At each iteration t we choose with probability half to present to the seller b t and with probability half we present to the seller a buyer z t that has the following statistics: z t is with probability 1 2 a buyer with value v = 1 2 and patience ⌧ = 0, and with probability 1 2 , z t is a buyer with value v = 1 and patience ⌧ = 1.


In such a case, the resulting algorithm is simply the constant step-size Exponential Weights , and the adaptive step sizes , 1 11 and Furthermore, if only one player (say, Player I) follows the above algorithm, her regret against any sequence x 1 , .

. . , x T of plays is this implies the worst-case regret of O log(nT ) √ T in the general setting of online linear optimization.


As first noted in [Now08], A can play an important role in GBS.

observe that the query selection step in NGBS is equivalent to an optimization over A rather that X itself.


We further allow some samples are corrupted and not drawn from (1).

the set of sample indices {1, 2, . . . , n} is separated into two disjoint subsets: if i-th sample is in the set of "good" samples, which we name G, then it is a genuine sample from (1) with the parameter Θ * .


We now return to the setting with inputs and show how the Bayesian strategy for the Gaussian regression model is a minimax strategy for all input sequences x ≤T .

if we fix the input sequence x ≤T , we can consider the competitor class to be we make the more stringent comparison against a model class which has full knowledge of the input sequence in advance.


The problem is solved using an EM-style algorithm [13,21].


The second innovation addresses memory usage issues in inference algorithms for the SM.

current algorithms use a Chinese restaurant franchise representation for the HPYP, where the seating arrangement of customers in each restaurant is represented by a list, each entry being the number of customers sitting around one table [3].


The classification problem consist in deciding to which population a new unlabeled observation X test (t) belongs (e.g., to decide from his or her ECG whether a person is healthy or not).

we are interested in the problem of dimensionality reduction for functional data classification.


However, in most cases of interest, the network is not singlyconnected and prior results have little to say about convergence.

gaussian belief propagation on a graph with cycles is not guaranteed to converge, as demonstrated by examples in [7].


Then, we propose to replace the context hyper-parameters with trainable models, that we learn jointly with the embeddings on an objective that preserves the graph structure (the Negative Log Graph Likelihood, NLGL).

we propose Graph Attention Models, using a softmax to learn a free-form contexts distribution with a parameter for each type of context similarity (e.g.


Therefore, by Markov inequality, we have that Pr i∼p (t) (•) err Di (g (t) ) > 12 ≤ .1 .

now consider the total weight By Lemma 1 and E, we have that Combining ( 2), (3), and (4), we have = k, we have the following inequality holds for every t = 0, 1, 2, . . . : us focus on an arbitrary player i.


Furthermore, the regularizer J(y) can be interpreted as a Reproducing Kernel Hilbert Space (RKHS) squared semi-norm, giving us additional insight into this choice of regularizer: Kp induced by the kernel with a null-space of all constant functions.

f Kp is the norm of the projection of f onto the RKHS induced by then J(f ) can be written as a squared semi-norm induced by the kernel with a null-space spanned by indicator functions 1 [ai,bi] (x) on the connected components of Ω.


We now investigate a newly introduced class of tractable ACs, called the Probabilistic Sentential Decision Diagram (PSDD) [Kisa et al., 2014].

we show that this class of circuits admits a tractable product operation and then explore an application of this operation to exact inference in probabilistic graphical models.


Collapsed Gibbs sampling has been observed to converge quickly [5].

notice from ( 8) that z ij depends on z ¬ij only through the counts the dependence of z ij on any particular other variable z i j is very weak, especially for large datasets.


This is a useful theoretical tool and can be used to design new algorithms, but it is clear that optimal policy pairs are only part of the story.

when it performs a centralized computation, the reduction assumes that we can effectively program both actors to follow a set coordination policy.


In this section, we give some example predictions.

we are interested in how the model does transitive reasoning across multiple relationships in the knowledge base.


Despite the success of these methods, there are still many issues to be discussed and explored.

the task of image captioning only requires generic sentence descriptions of an image.


. . , x p ∈ R n . Further, for a vector v, sign(v) is the vector with entries sign(v An outline of this section is as follows: (1) We first consider the zero-noise problem W = 0, and prove several useful properties of the Lasso estimator in this case.

we show that there exists a threshold for the regularization parameter below which the support of the Lasso estimator remains the same and contains supp(θ 0 ).


The results of our current system are still not nearly as good as human performance.

it appears the network has only a very limited understanding of image invari- ances.


In order to alleviate this problem, we propose to update the weight for the existing support vector whose classification confidence is significantly affected by the new misclassified example.

we consider a support vector (x b , y b ) ∈ D for weight updating if it satisfies the following two conditions "conflicts" with the new misclassified example (x a , y a ).


This is because the joint estimator leverages the labels on the target items (whose true values are unknown), and relies less on the control items.

as the number n t of target items increases, the optimal value of k for the joint estimator decreases with a rate of 1 √ n t (see Figure 1(d)), but that of the two-stage estimator stays the same.


Such a grid search is usually expensive.

when n is large, this search is so time-consuming that one usually resorts to either default hyperparameter values or crude search strategies.


To build the rendered-100 dataset, we select different 3D models as foreground objects (e.g., bunny, hairball and metal sphere), and use natural images as backgrounds.

we select foreground objects with thin structures (e.g., furs and leaves), or having similar textures with the background, to simulate challenging scenarios.


The authors in [18] show that a neural network with ReLU activation functions can learn to perform holographic image reconstruction.

they show that compared to current approaches, this neural network based method requires less measurements to succeed and is computationally more efficient, needing only one hologram to reconstruct the necessary images.


Given that the numerical task that must be solved in KDR is the same as the one to be solved in kernel ICA, we can import all of the computational techniques developed in [9] for minimizing KGV.

the optimization routine that we use is gradient descent with a line search, where we exploit incomplete Cholesky decomposition to reduce the n × n matrices to low-rank approximations.


Our proposed complex gated RNN (cgRNN) builds on these works in that we also use unitary state transition matrices.

we adopt the parameterization of [40] in which weights are parameterized by full-dimensional unitary matrices, though any of the other parameterizations [1,13,17] can also be substituted.


Since the gradients are slow, RR is able to achieve a parallel speedup for this problem, however the speedup with ten processors is only by a factor of 5.

even in this case where the gradient computations are very slow, HOGWILD!


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

we introduce slack variables and consider the optimization problem: where the parameter ν controls the trade-off between desiring a large margin (low norm) and small error (low slack), and parameterizes solutions along the regularization path.


. . , φ(x T , g α )} can be related to coin tosses.

we associate a coin with each dimension i ∈ {1, 2, . . . , d}, and consider the set of coin bias vectors lying in the set Given a particular function g α ∈ G(δ) (or equivalently, vertex α ∈ V), we consider the oracle φ that presents noisy value and gradient samples from g α according to the following prescription: • Pick an index i t ∈ {1, . . . , d} uniformly at random.


More specifically, we are interested in the ǫ-mixing time τ (ǫ), which guarantees a distribution that is ǫ-close to P L in terms of total variation.

we must spend at least this many time steps in order to acquire a sample from a distribution close to P L . Our next result states that the chain in Algorithm 1 mixes rapidly:  One advantage of having a rapidly-mixing Markov chain as means of sampling from a DPP is that it is robust to addition/deletion of elements.


Following [3,4], we will approach this problem via neighborhood estimation, where we estimate the neighborhood of each node individually, and then stitch these together to form the global graph estimate.

if we have an estimate N (s) for the true neighborhood N * (s), then we can estimate the overall graph structure as: In order to estimate the neighborhood of any node, we consider the sparsity constrained conditional MLE.


Figure 1 presents the situation where n 1 and n 2 are fixed and the cube sizes are increasing.

the two cubes are both of size l × l, i.e., both with edge length (l, l).


Even without communication during the game, the planning phase gives the team members an advantage: for instance, the team members could skew their strategies to use certain actions to signal about their state (for example, that they have particular cards).

by having agreed on each member's planned reaction under any possible circumstance of the game, information can be silently propagated in the clear, by simply observing public information.


In these works, the idea is to select a small subset of features with maximum dependence with the target variable Y .

the task is to find a subset of variables S ⊆ {1, . . . , d} with |S| ≤ k based on the following optimization problem where X S (X i ) i∈S and I (X S ; Y ) denotes the mutual information between the random variable X S and Y .


We develop a power update method to resolve the above difficulties.

after obtaining the whitened (orthonormal) vectors {v i } c i • W µ i 1 we recover the entry η i of the linear regression model directly by computing a power update v i M y (W, W )v i .


In this field, a number of studies have focused on constructing better low dimensional representations that combine various features of brain activities [3,4], because the problem of classifying EEG signals is intrinsically high dimensional.

efforts have been made to reduce the number of electrodes by eliminating electrodes recursively [8] or by decomposition techniques e.g., ICA, which only uses the marginal distribution, or Common Spatial Patterns (CSP) [9] which additionally takes the labels into account.


Another direction of work, explores methods for exploiting the structure between object classes.

it has been observed that object classes can be organized in a tree-like structure both semantically and visually [9,11,6], making tree based approaches especially attractive.


Beyond computational and statistical efficiency, however, data analysts typically have a variety of additional criteria they must balance.

data providers often need to maintain the anonymity and privacy of those individuals whose information was collected.


We studied the problem of learning causal models with latent variables using experimental data.

we introduced two efficient algorithms capable of learning direct causal relations (instead of ancestral relations) and finding the existence and location of potential latent variables.


In these work, different tree-structured encoders are proposed for embedding the input data, and different tree-structured decoders are proposed for predicting the output trees.

in [28,18], they propose tree-structured autoencoders to learn vector representations of trees, and show better performance on tree reconstruction and other tasks such as sentiment analysis.


Our first result in this paper provides sufficient condition for W = −B ⊗ A to be concave.

it provides a connection between conditionally positive (or negative) definite functions (Wendland, 2004), and negative definiteness of −B ⊗ A: Φ is conditionally positive definite of order 1 if for all pairwise distinct points Conditionally negative definiteness is defined analogously.


Derivation of efficient preconditioners for the exact KRR problem (5) has been the subject of recent studies, [3,4,26,5,6].

[4,26,5,6] consider random projections to approximately compute a preconditioner.


The dual formulation also provides connections to other techniques.

we discussed a close link to moment matching techniques, and showed that the cost function linearization for non-linear discriminators recovers the original gradient direction in standard GANs.


It does not need to communicate the information of all attributes, instead, it only communicates indices of the locally top-k attributes per machine and the histograms of the globally top-2k attributes.

its communication cost is independent of the total number of attributes.


In addition, suppose that If σ evolves as a function of n such that σ → 0 and nσ 2d / ln n → ∞ as n → ∞, then the L 2 kernel classifier is consistent.

given training data D n = ((X 1 , Y 1 ) , .


There has been a large amount of work on differential privacy for a wide range of statistical and machine learning tasks over the last decade [6,30,13,21,33,24,1]; for overviews, see [18] and [29].

algorithms for the private maximization problem (and variants) have been used as subroutines in many applications; examples include PAC learning [25], principle component analysis [14], performance validation [12], and multiple hypothesis testing [32].


To circumvent these difficulty, we devised a modified algorithm called PMED-Hinge (Algorithm 1) that involves extra exploration.

we modify the optimization problem as follows: Let R H (1),...,(L) ({µ i,l }, {θ i }, {κ l }, {δ i,l }) = {q i,l } ∈ Q : inf {θ i }∈T c (1),...,(L) ,{κ l }∈K all :∀ l∈[L] dKL(µ (l),l ,θ (l) κ l )≤δ i,l (i,l)∈[K]×[L]:i =(l) q i,l (d KL (µ i,l , θ i κ l ) − δ i,l ) + ≥ 1 , where (x) + = max(x, 0).


Specifically, to enable GAIL to produce diverse solutions, we condition the discriminator on the embeddings generated by the VAE encoder and integrate out the GAIL objective with respect to the variational posterior q (z|x 1:T ).

we train the discriminator by optimizing the following objective A related work [20] introduces a conditional GAIL objective to learn controllers for multiple behaviors from state trajectories, but the discriminator conditions on an annotated class label, as in conditional GANs [21].


We address this notoriously hard challenge, under the assumptions that the function varies only along some low-dimensional subspace and is smooth (i.e., it has a low norm in a Reproducible Kernel Hilbert Space).

we present the SI-BO algorithm, which leverages recent low-rank matrix recovery techniques to learn the underlying subspace of the unknown function and applies Gaussian Process Upper Confidence sampling for optimization of the function.


the distribution µ is full-dimensional: there exists C µ > 0 such that for all x ∈ X and the next lemma states that, under Assumption 1, G n is a consistent estimate of G. Lemma 4 ([14, Theorem 1]).


In this section, we introduce linear universal option models which use linear function approximation to compactly represent reward independent option-models over a potentially large state space.

we build upon previous work where the approximate solution has been obtained by solving the so-called projected Bellman equations.


The streaming version of the k-means algorithm assigns the new point from the stream to the closest centroid and updates this centroid immediately.

unlike offline k-means which first assigns all the points to the respective centroids and then updates the centroids, the streaming algorithm updates the centroids after each point, making it much more space efficient.


For basal trees of CA3 pyramidal cells, this analysis yielded an estimated "corrected" value of b between 0.14 and 0.25, with a remaining much smaller than b. Interestingly, our analysis based on extrapolation shows that, regardless of the assumed amount of distortion present in the experimental data, given the numbers measured for CA3 basal trees, positive initial <α> implies positive initial b.

not only measurement errors, but also possible biological distortions of the dendritic tree may not be capable of accounting for the observed positivity of the parameter b.


The kernel is usually computed from the adjacency matrices A 1 and A 2 of the two graphs, but it must be invariant to the ordering of the vertices.

writing the kernel explicitly in terms of A 1 and A 2 , we must have k(A 1 , A 2 ) = k(A 1 ,P A 2 P ) for any permutation matrix P . Permutation invariance has proved to be the central constraint around which much of the graph kernels literature is organized, effectively stipulating that graph kernels must be built out of graph invariants.


Natural gradient descent is a first order method that relies on the curvature of the parameter manifold.

natural gradient descent takes a step that induces a constant change in the behaviour of the model as measured by the KL-divergence between the model before and after taking the step.


Note that the agreement between the empirical behavior and theoretical predictions is excellent in all cases.

panel (a) exhibits the quadratic scaling predicted for the cycle, panel (b) exhibits the the linear scaling expected for the grid, and panel (c) shows that expander graphs have the desirable property of having constant network scaling.


With this arrangement, each weight is first multiplied with the corresponding layer input as usual followed by the accumulation procedure directed by the branch index.

the multiplication result is added to a branch sum addressed by the index.


In order to solve this problem, we need to modify the model slightly to allow us to predict actions other than choices.

we need to define how preferences are related to affective responses, since the actors simply indicated their affective response to the novel object.


It is easy to see that both fully connected and convolutional networks of any depth L can realize any linear predictor β ∈ R D . The model class expressed by both networks is therefore simply the unconstrained class of linear predictors, and the two architectures are merely different (over) parameterizations of this class Thus, the empirical risk minimization problem in (4) is equivalent to the following optimization over the linear predictors β = P(w): (5) Although the optimization problems ( 4) and ( 5) are exactly equivalent in terms of the set of global minima, in this paper, we show that optimizing (4) with different parameterizations leads to very different classifiers compared to optimizing (5) directly.

consider problems (4)/(5) on a linearly separable dataset {x n , y n } N n=1 and using the logistic loss (the two class version of the cross entropy loss typically used in deep learning).


Sparse penalized regression models are analyzed with the purpose of finding, to the extent possible, regimes of dictionary invariant performance.

a Type II Bayesian estimator with a dictionarydependent sparsity penalty is shown to have a number of desirable invariance properties leading to provable advantages over more conventional penalties such as the ℓ 1 norm, especially in areas where existing theoretical recovery guarantees no longer hold.


Acknowledgement: The authors would like to thank Vitaly Feldman, and Adam Smith for helpful discussions during the course of this project.

the authors are grateful for Vitaly's ideas about the possible extensions of the results in Section 4, which we outlined in Remarks 2 and 3.


Meanwhile, a distance matrix is defined to be a dissimilarity matrix whose entries satisfy the triangle inequalities.

m is a distance matrix if and only if it is a dissimilarity matrix and m ik ≤ m ij + m jk for every triple of distinct indices (i, j, k).


For a given instantiation m i , let Σ(m i ) denote the covariance matrix implied by the model and λ k (m i ) be the value of coefficient λ k . Definition 1.

a coefficient, λ k , is identified if for any two instantiations of the model, m i and m j , we have λ k is identified if it can be uniquely determined from the covariance matrix, Σ.


In this section, we leverage unbiased gradient estimators based on (8) in conjunction with our optimal degree distribution (11) to design computationally efficient methods for solving (4).

we propose to randomly sample a degree n from (11) and estimate the gradient via Monte-Carlo method: where ∂w (k) j /∂θ i can be computed using a Rademacher vector v (k) and the recursive relation (6).


The first term is due to the difference in the mean-variance of the best arm and the arms pulled by the algorithm, while the second term denotes the additional variance introduced by the exploration risk of pulling arms with different means.

this additional term depends on the squared difference of the arm means Γ 2 i,j .


In doing so, we first sample a variable u 1 that indicates which source to sample from.

when u 1 = −1, u 1 = 0, or u 1 = l > 0, we respectively sample θ 1 from p ν , p qµ , or T (φ l , •).


Another question we can ask is what happens if we allow a larger rank than the rank of the optimal solution.

if we have f (X ⇤ ) = 0 with low rank(X ⇤ ), even rank(X ⇤ ) = 1, but consider (1) or (2) with a high r. Could we still have non-global local minima?


Even when the STA estimate is biased by the gain control signal, we can still obtain an (asymptotically) unbiased estimate of the excitatory kernel.

the true excitatory kernel lies within the subspace spanned by the estimated (biased) excitatory and suppressive kernels.


Assume that V Y X , V Y Z , and V ZX are Hilbert-Schmidt, and that the regularization constant ε n satisfies ε n → 0 and ε 3 n n → ∞.

then, we have the convergence in probability ÎNOCCO n → I N OCCO and ÎCOND n → I CON D (n → ∞) in probability.


In this section, we show that more aggressive unstructured exploration is not sufficient to achieve optimal regret.

we consider a policy that chooses arms independently and uniformly at random for some period of time, and then commits to the empirical best arm for the rest of the time.


The variance of the plug-in estimators Ĝk , Gk is given by In the above expressions, c 1,i , c 1 , c 2 , c 4 and c 5 are constants that depend only on g, f and their partial derivatives, and I = {1, . . . , d}.

the constants c 1,i , c 1 , c 2 , c 4 and c 5 are independent of k, N and M . From Theorem 1, k → ∞ and k/M → 0 for the estimators Ĝk and Gk to be unbiased.


S by π S such that π S (i) = d i /d(S) if i ∈ S and π S (i) = 0 otherwise.

in terms of the conductance of S, the following theorem gives an upper bound on the expected probability mass escaped from S if the distribution of the starting vertex is π S . Theorem 3.1 shows that most of the probability mass will be absorbed in S, provided that S is of small conductance and the random walk starts from S according to π S . a PARW will be trapped inside the cluster 1 from where it starts, as desired.


When averaged over possible outcomes of N trials, the gradient is zero for the optimal direction.

there is no specific direction towards which the deviations δv are biased.


Deep models are often employed in topic modeling.

hierarchical tree-structured models have been widely studied over the last decade, often composed of DP modules.


The high level idea is that by generating O(d) samples from a Gaussian, one can get a rough sketch of the geometry of the Gaussian.

the points drawn from a Gaussian concentrate around an ellipsoid centered at the mean and whose principal axes are the eigenvectors of the covariance matrix.


The proposed method is robust to extreme events in asset returns, and accommodates large portfolios under limited historical data.

we show that the risk of the estimated portfolio converges to the oracle optimal risk with parametric rate under weakly dependent asset returns.


2, and indicate that the early layers of VGG16 (in particular, Front and Layer3) are better predictors of human sensitivity than the deeper layers (Layer4, Layer5, Layer6).

the most noticeable eigen-distortions from representations within VGG16 become more discriminable with depth, but so generally do the least-noticeable eigen-distortions.


As shown in [19], the new formulation does not only reliably produce configurations with lower total energy, but also leads to better results in several application scenarios.

for the image segmentation scenario the results of [19] significantly outperform those of [3].


Variational approximation with Contrastive Divergence: Since the data likelihood L(Θ) is generally intractable to compute, our method is based on the efficient contrastive divergence technique [16,25,26,28].

we derive a variational approximation L v (q 0 , q 1 ) of the negative log-likelihood L(Θ) , that is: L v (q 0 , q 1 ) := R(q 0 (x, z, h), p(x, z, h)) − R(q 1 (x, z, h), p(x, z, h)), where R(q, p) is the relative entropy, and q 0 is a variational distribution with x and z clamped to their observed values while q 1 is a distribution with all variables free.


To leverage the benefits of both approaches, there has been significant interest in combining the model-based and model-free paradigms.

much attention has been dedicated to utilizing model-based priors to accelerate the model-free learning process.


However, both single metric learned by global DML and multiple metrics learned with local methods focus on exploiting locality information, i.e., constraints or metrics are closely related to the localities.

local DML approaches mainly aim at learning a set of multiple metrics one for each local area.


First, we use synthetic data to visualize the approximation of our algorithm of a bimodal posterior.

we consider a mixture of two Gaussians with parameters µ = ( 1, +1), = (0.5, 0.5), and mixing weights ⇡ = (0.4, 0.6).


This reduces the problem to showing that each term in the sum of ( 6) corresponds to the contribution of all prefixes of x li : vJ Assume we descend down the path xli : Vi] in S(y) (e.g., for the string bab with respect to the tree of Figure 2 this would correspond to (root, b, bab», then each of the prefixes t along the path (e.g., (' , , b, ba, bab) for the example tree) occurs exactly as many times as Ivs( ceil( t)) does.

prefixes ending on the same edge occur the same number of times.


The set W i→i can be partitioned according to the number of times that walks return to node i: i→i is the set of all self-return walks which return to i exactly r times.

w A walk which starts at node i and returns r times is a concatenation of r single-revisit self-return walks, so ρ(W i→i ) r . This means: This geometric series converges since the model is walk-summable.


However, overfitting in BLBF is more nuanced than in conventional supervised learning.

the unbiased risk estimator of Equation ( 2) has two anomalies.


One possible construction algorithm is an extension of Kruskal's algorithm for the MST where we pick edges without replacement and restart for every new tree.

we sort the list of N (N −1) 2 edges e ij by increasing distance d ij and visit each available edge in turn, removing it if it merges two clusters (or equivalently does not create a cycle); whenever we have removed N − 1 edges, we go back to the start of the list.


We explore a similar direction but extend this work to transparent objects.

we base our method on a novel combination of SIFT [18] and latent Dirichlet allocation (LDA) [4], two techniques used in many previous object recognition methods.


Given a joint distribution P(A, B), this method constructs a new variable T that represents partitions of A which are (locally) maximizing the mutual information about B.

the variable T induces a sufficient partition, or informative features of the variable A with respect to B.


Suppose we have learned such a model h. At test time, our goal is to make the most accurate predictions possible for an example under a fixed budget B.

given h and a loss function : Y × Y → R + , we wish to find the following: In practice, there are three primary difficulties in optimizing equation (2).


We choose K-means as the underlying clustering algorithm and vary the parameter K = 5 : 1 : 25, which is the desired number of clusters.

since different runs of K-means starting from random initialization of centroids typically produce different clustering results, we run K-means 5 times for each value of K. there are a total of 21 × 5 = 105 different input clusterings.


In this model, the stochastic reward described above is equivalent to service.

if the arm (server) that is chosen results in positive reward, the job is successfully completed and departs the system.


. . are themselves random, uniformly distributed over [0, 1].

1 it is assumed that for any policy, the mean rewards of the explored arms have a uniform distribution over [0, 1], independently of the number of explored arms.


We first start by analyzing how the Hessian spectrum and gradient change during training for small batch and compare it to large batch size and then draw connection with robust training.

we aim to answer the following questions: Q1 How is the training for large batch size different than small batch size?


In many cases, it is important that the runtime of the learned classifier will be small.

this requires that the learned classifier will only rely on the value of few features.


Hence, exploiting symmetry, there is a one to one correspondence between the assignments across the sub-theories.

there is one to one correspondence between MAP assignments across the sub-theories {M j } r j=1 .


PCA, PPCA, and FA are all static dimensionality reduction techniques.

none of them take into account time labels when applied to time series data; the time series data are simply treated as a collection of data points.


Nevertheless, only a few works establish theoretical guarantees for the EM algorithm.

for Gaussian mixture model, [10,11] establish parameter estimation guarantees for the EM algorithm and its extensions.


However, due to the high-dimensional continuous image input data and the model-free environment, we resort to the Q-learning algorithm combined with the function approximator technique to learn the optimal value for each state-action pair which generalizes well to unseen inputs.

we use the deep Q-network proposed by [22,23] to estimate the value for each state-action pair using a deep neural network.


In this paper we demonstrate how modern stochastic optimization techniques (such as SGD, ADA-GRAD [8] and ADAM [21]), can be used to solve an important class of discrete optimization problems which can be modeled using weighted coverage functions.

we show how to efficiently maximize them under matroid constraints by (i) lifting the problem into the continuous domain using the multilinear extension [37], (ii) efficiently computing a concave relaxation of the multilinear extension [32], (iii) efficiently computing an unbiased estimate of the gradient for the concave relaxation thus enabling (projected) stochastic gradient ascent-style algorithms to maximize the concave relaxation, and (iv) rounding the resulting fractional solution without loss of approximation quality [7].


Recall that G is a uniformly random subset of the fixed set P C and that B consists of the remaining elements in P C . Thus, w.h.p., the value f G (S) of all samples S is independent of which random subset G is.

no algorithm can distinguish good elements from bad elements with polynomially many samples.


Motivated by these two principles, we introduce the following sparsification operator: For any matrix A ∈ R d1×d2 : for all (i, j) where ) denote the elements of A (i,•) and A (•,j) that have the k-th largest magnitude respectively.

we choose to keep those elements that are simultaneously among the largest α-fraction entries in the corresponding row and column.


In this section, we show that our algorithmic results cannot be improved significantly.

we focus on the post-processing setting of Section 3.1.


To compute a schedule for each value of k, we first allocate the number of experiments m i across k labs as uniformly as possible.

(n mod k) labs will have n/k + 1 experiments and k − (n mod k) labs will have n/k experiments.


Our system improves upon a state-of-the art recognition method based on strict feature matching.

the rate of false alarms in the presence of textured backgrounds generating strong erroneous matches, is lower.


Given the same amount of supervision, DecoupledNet presents substantially better performance even without any post-processing than WSSL [8], which is a directly comparable method.

our algorithm has great advantage over WSSL when the number of strong annotations is extremely small.


Our method leverages on the predictive power of machine learning models to estimate counterfactuals, and achieves balanced distributions in an intermediate feature space.

an ordinal scatter discrepancy criterion is designed to extract discriminative features from observational data with ordinal pseudo labels, while a maximum mean discrepancy criterion is incorporated to achieve balanced distributions.


3) Let P (X | E, R, w, u) be defined as in (11) 2 w * ← arg max w log P (X | E, R, w, u * ) // Find e.g.

with L-BFGS using the gradient (12) 3 data using any standard density estimation technique 3 with the same features f ijk that are used in the CRF model, one can train a logistic regression model for P (• | E) : Essentially, a logistic regression model is a small CRF over only two variables.


We want to stress the importance of the last point.

for all state-of-the-art algorithms known to us, when the number of actions K is moderately large, the additive term is dominating for any realistic time horizon T . Ailon et al.


(a) Graphon W. (b) W φ weakly isomorphic to W. (c) An instance of a graph adjacency sampled from W. A very general class of random graph models may be represented as graphons.


Figure 4 (left) demonstrates that AUPR and AUPRG often disagree in ranking the models.

they disagree on the best method in 24% of the tasks and on the top three methods in 58% of the tasks (i.e., they agree on top, second and third method in 42% of the tasks).


In addition to this, the elicitation view reveals that the machine learning emphasis on convex losses φ is misguided.

it is shown that what matters is the convexity of the minimum conditional risk.


We assume that the learning algorithms on each view are able to PAC-learn from positive data only.

for any distribution D + i over X + i , and any given , δ > 0, given access to examples from D + i the algorithm should be able to produce a hypothesis h i such that (a) h i ⊆ X + i (so h i only has one-sided error), and (b) with probability 1−δ, the error of h i under D + i is at most .


We investigate whether our approach can be used to generate the future of a static image.

given a static image x 0 , can we extrapolate a video of possible consequent frames?


We demonstrate the advantage of NADE-k compared with NADE-mask under the constraint that they have a matching number of parameters.

we compare NADE-k with 1000 hidden units with NADE-mask with 670 hiddens.


3 Then we make appropriate uniformity assumptions to construct P (ι C ).

we assume that each paper is a priori equally likely to be cited, and that each author is a priori equally likely to write a paper.


Especially, we are interested in the high dimensional case when d > n. This section is devoted to the statement of our result on quantifying the convergence rate of R to Σ 0 and S to Σ.

we establish the results on the max convergence rates of the Spearman's rho correlation and covariance matrices to Σ and Σ 0 .


We assume that our algorithms have access to a supervised learning oracle, also called an argmax oracle, denoted AMO, that can find a policy with the maximum empirical reward on any appropriate dataset.

given a dataset D = {x i , y i , v i } n i=1 of contexts x i , reward feature vectors y i 2 R K with rewards for all simple actions, and weight vectors v i 2 R L , the oracle computes where ⇡(x) `is the `th simple action that policy ⇡ chooses on context x.


Our main contributions are two-fold: first, we demonstrate that spatiotemporal functional evolution can be modeled using stationary kernels with a linear dynamical systems layer on their mixing weights.

the model proposed here posits differential constraints, embodied as a linear dynamical system, on the spatiotemporal evolution of a kernel based models, such as Gaussian Processes.


Computing the concave (or convex) closure of a function is NP-hard in general, but it can be efficiently computed for certain special classes of discrete functions.

when X = {0, 1} and log f is supermodular, then its concave closure can be computed in polynomial time as it is equal to the Lovász extension of log f . The Lovász extension has a number of interesting properties.


This is qualitatively similar to what was found in pyramidal neurons in the neocortex [19] and in the hippocampus [18,20] that are able to switch from (sub)linear to supralinear integration of synaptic inputs through the generation of dendritic spikes [21].

in neocortical pyramidal neurons Polsky et al.


In this paper, we study how pre-trained sentence representations, obtained by general purpose sentence encoders, can be leveraged to train better models for text generation.

we interpret the set of sentence embeddings obtained from training on large text corpora as samples from an expressive and unknown prior distribution over a continuous space.


we introduce three types of match kernels to measure similarities between image patches, and construct compact low-dimensional kernel descriptors from these match kernels using kernel principal component analysis (KPCA) [23].


Our model does not assume or require any specific stimulus distribution.

it is not limited to white noise stimuli or elliptically contoured distributions but it can be used without modification for other stimulus distributions such as natural image sequences.


We set up the molecule environment as an OpenAI Gym environment [3] using RDKit [23] and adapt it to the ZINC250k dataset.


Then we have: We next consider when f is ν-restricted strongly convex 8 in addition to having L-Lipschitz gradient.

for x ∈ dom(f ), ∇f (x), x − Proj argmin f (x) ≥ ν • dist 2 (x, argmin f ).


We proposed a new statistical model that uses SEM to model energy-dependencies of latent variables in a standard linear generative model.

with a simplified form of scale-mixture model, the likelihood function was derived without any approximation.


We focus on an idealised resource allocation problem where the economist plays a repeated resource allocation game with multiple resource types and multiple tasks to which these resources can be assigned.

we consider a (nearly) linear model with D resources and K tasks.


In our experiments, having a fixed zero-out ratio for DropBlock during training is not as robust as having an increasing schedule for the ratio during training.

it's better to set the DropBlock ratio to be small initially during training, and linearly increase it over time during training.


Nonetheless, we observe a side effect of dropout that has long been ignored.

it tends to increase the correlation between the features it is applied to, which reduces the efficiency of representations.


What makes the reverse KL divergence more tractable to optimize is that the expectations are done over Q instead of P . This minimization also yields bounds on the log partition function, or the probability of evidence in a BN.

because KL(Q P ) is non-negative, The most commonly applied variational method is mean field, in which Q is chosen from the set of fully factorized distributions.


Let x be the bag-of-words representation of a sentence.

each x i is a word index from a fixed vocabulary of V words.


Motivated by the above, we propose a novel model-free approach for reasoning about conditional probabilities.

we shall show how conditional probabilities can be lower bounded when the only assumption made is that certain low-order marginals of the distribution are known.


That is, when action a is taken at state s, the transition probability p s,a (•) can be an arbitrary element of the uncertainty set U(s, a).

for different visits of same (s, a), the realization of p s,a can be different, possibly depends on the history.


Focusing on the task of clustering event sequences, we investigate the sample complexity of our DMHP model and its learning algorithm.

we want to show that the clustering method based on our model requires fewer samples than existing methods to identify clusters successfully.


We observe that the decomposition includes, for each variable, each and every interaction term of each and every degree weighted in a fashion resulting only from the combinatorics of possible interaction terms.

since all I(X m ; Y |B) terms are at most equal to H(Y ), the prior entropy of Y , the p terms of the outer sum of Equation 3 are each upper bounded by As such, the second level decomposition resulting from totally randomized trees makes the p subimportance terms 1 to equally contribute (at most) to the total importance, even though they each include a combinatorially different number of terms.


However, the naive NN approach also has disadvantages.

it requires storing the entire sample, which may be memory-intensive.


Therefore, regret of Algorithm 1 is within O( √ T ) from the ideal procedure of Lemma 1.

by choosing η appropriately, for an absolute constant C , Proof.


While it appears to make sense to replace the minibatch statistics with whole-data ones during inference, this changes the activations in the network.

this means that the upper layers (whose inputs are normalized using the minibatch) are trained on representations different from those computed in inference (when the inputs are normalized using the population statistics).


There exists such an n×(n−p) orthogonal matrix U 3 that its last column is 1 √ n 1 n and [U, U 3 ] is an n×n orthonormal matrix.

u 3 is the eigenvector matrix of X(X X + σ 2 I p ) −1 X corresponding to the eigenvalue 0.


In this paper, we establish a rigorous theoretical foundation for SCMD by providing optimal convergence rates (up to a logarithmic factor) in the stochastic optimization setting without boundedness assumptions on either subgradients or iterates, which in turn also shed new insights on the generalization behavior of the multi-pass SGD in the statistical learning theory setting.

we justify the immunity of multi-pass SGD to overfitting by giving estimation error bounds with a logarithmic dependency on the number of passes for square-summable step sizes, while existing bounds scale polynomially [13,21].


Now define the sets of vectors The first vector set, θ t x , represents the components of the the "true," but unknown, input vector x, its adaptive GAMP estimate x t as well as r t . The second vector, θ t z , contains the components of the "true," but unknown, output vector z, its GAMP estimate z t , as well as p t and the observed input y. x and θ t z are implicitly functions of the dimension n. Our main result, Theorem 1 below, characterizes the asymptotic joint distribution of the components of these two sets as n → ∞.

we will show that the empirical distribution of the components of θ t x and θ t z converge to a random vectors of the form where X is the random variable in the initial condition (7).


3 with non-adaptive exploration method has a constant regret bound.

note that we cannot apply the Hoeffding bound in [14] directly since the random variables 1{u x = u x+1 } we obtain during the online learning process are not mutually independent.


To efficiently use multiple cores/machines in the scheduler pool, STRADS uses pipelined schedule computations, i.e., masters compute schedule and queue jobs in advance for future rounds.

parameters to be updated are determined by the masters without waiting for workers' parameter updates; the jobs for parameter updates are dispatched to workers in turn by the coordinator.


In this case, our analysis implies that we should use an alternative kernel with faster eigenvalue decay: for example, using K 2 instead of K. This has a dimension reduction effect.

we effectively project the data into the principal components of data.


As a consequence of the above proposition, we can exploit standard results about LS.

for instance, it is easy to show that, for a generic vector h 2 R d , the excess transfer risk the gap between the performance of standard Ridge Regression (h = 0), corresponding to solving each task independently, and the best algorithm in our class (i.e.


This refines results in [2] and shows that when mixing is not too slow, the sample complexity of the empirical entropy does not depend on the mixing time.

the bias of the empirical entropy rate vanishes uniformly over all Markov chains regardless of mixing time and reversibility as long as the number of samples grows faster than the number of parameters.


For j ∈ {1, . . . , p}, define Γ σi,j to be an extensive game derived from the original game Γ where for all h ∈ H i \ G j , P (h) = c and f c (a|h) = σ i (h, a).

player i only controls her actions for histories in G j and is forced to play according to σ i elsewhere.


Consider, for example, a decision making problem that is a quadratic optimization problem.

namely, the DMP has the following form: QP Suppose that b changes over time t. b is the external signal for QP and equals to b t at time t. If we seek to learn c, the optimal solution set for QP can be characterized by KKT conditions as Here, u is the dual variable for the constraints.


This algorithm requires that the smoothed objective has a Lipschitz continuous gradient.

for some constant L, it must hold that kr f @x 1 A r f @x 2 Ak Lkx 1 x 2 k; for all x 1 ; x 2 P R n . Fortunately, by construction, the smoothed threshold extensions © wj;yj @xA all have I= Lipschitz gradient, a direct consequence of the characterization in Equation 4.


The proof of Theorem 3.2 relies on the lower-bound property of our estimator (the left-hand side of Inequality stated in Lemma 3.1).

if H contains a very good policy that has little support under π, we will not be able to detect that by our estimator.


These two implementations are slightly different from the algorithm from Panda et al.

the original PLANET algorithm has separate subroutines for distributed vs. "local" training.


While there is no native weight for data instance in GBDT, we notice that data instances with different gradients play different roles in the computation of information gain.

according to the definition of information gain, those instances with larger gradients 1 (i.e., under-trained instances) will contribute more to the information gain.


For solving the OLS problem for tensor regression (2), we use a cyclic block-coordinate minimization algorithm based on a tensor toolbox [35].

in a cyclic manner for all d 2 [D], we fix all but one and minimize the resulting quadratic loss function (2) with respect to ⇥ i , until the decrease of the objective is smaller than a predefined threshold ⌧ .


1(a), provided the phase measurement is perfect.

the detection precision is limited by the accuracy of phase measurement, rather than the highest spatial sampling density.


A model consists of a set of variables V as the nodes of a graph G = (V, E), along with a set of factors specifying a joint probability distribution p Ψ (V ) described by parameters Ψ.

this paper focuses primarily on directed models, in which the factors Ψ specify the conditional probability distributions of each variable given its parents.


This paper attempts to remedy the existing limitations of GPs in the time series setting using the same rationale by which GPs were originally developed.

kernels themselves are treated nonparametrically to enable flexible forms whose complexity can grow as more structure is revealed in the data.


As for optimization-based methods like the C&W attack and its variants, we apply the same way as in [3] to report robustness.

we do a binary search for the parameter c, in order to find the minimal distortions that can successfully attack the classifier.


More precisely, let Υ θ be the projection to P M θ and let Π θ be the projection to T M θ .

because the two hyperplanes are parallel, for any projecting onto the tangent space gives exactly the same distance as projecting onto the tangent plane, while being mathematically more convenient.


In this paper, we suggest novel modified dynamics that behave similarly to [24], but in our noninterdependent game.

they guarantee that the optimal solution to the assignment problem is played a considerable amount of time.


One interesting observation is that traditional perturbation-based adversarial examples can also be obtained as a special case of our noise-augmented attack, by choosing a suitable g ✓ (z, y) instead of the AC-GAN generator.

let T be the test dataset, and T y = {x 2 T | o(x) = y}.


The goal of learning representation that satisfies certain independence statements can be achieved by adding suitable nodes and edges to the generative distribution graphical model.

marginal independence can be the consequence of an "explaining away" pattern as in Figure 1a for the triplet {u, x, v}.


The updates have a simple intuition [9] based on balancing opposing terms in the gradient of the conditional log likelihood.

note that the fixed points of this update rule occur at stationary points of the conditional log likelihood-that is, where .


To relax Consistency even further, we could say simply that if d is an f (d)transformation of d, then one of f (d) or f (d ) should be a refinement of the other.

f (d ) may be either a refinement or a "coarsening" of f (d).


These problems can be naturally formulated in terms of multivariate regression.


Then for any strategy profile σ = (σ 1 , σ 2 ) ∈ Σ 1 × Σ 2 we define the expected utility of the strategy profile (for player 1) as An -Nash equilibrium profile (σ 1 , σ 2 ) in this case is defined analogously to (1).

none of the players can improve their utility by more than by deviating unilaterally.


Figure 1 shows an example application of image tag recommendation, where more input features (called privileged information [47]) are available at the training stage than those available at the inference stage.

the training stage has access to images as well as image titles and comments (textual information) as shown in Figure 1a, whereas the inference stage only has access to images themselves as shown in Figure 1b.


Using the NB classifier as the baseline, however, shows not only improved baseline results in general but also that the sigmoid(10) improves more often.

the KLD results are better than the baseline 16 times, sign is better than the baseline 18 times, and sigmoid (10) beats the baseline 19 times, suggesting that sigmoid (10) typically wins over the KLD case.


In this work, we consider a very common class of such problems, where a classifier trained on a class of instances is to be transferred to a second class of instances, which are loose combinations of the original ones.

we consider the problem where the original instances are objects and the target instances are scene-level concepts that somehow depend on those objects.


Inspired by the space carving theory [10], we propose a silhouette-based volumetric loss function.

we build on the premise that a 2D silhouette Ŝ(j) projected from the generated volume V under certain camera viewpoint α (j) should match the ground truth 2D silhouette S (j) from image observations.


In this paper we are interested in proving results on the sample complexity of differentially private algorithms that approximate PCA.

for a given ↵ and ⇢, how large must the number of individuals n in the data set be such that it is ↵-differentially private and also a (⇢, ⌘)-close approximation to PCA?


Now proceed by induction to determine E M +1 and ω M +1 , assuming that we have determined E M and ω 0 , ..., ω M such that P (E M = 1| C i ; ω 0 , ..., ω M ) = P (E = 1| C i ), for i = 0, ..., M . There are three cases to consider which are analogous to the cases considered in the section with two causes.

then we obtain: we see that To determine the value of ω M +1 , we must solve Then we obtain: As for the first case, To determine the value of ω M +1 we must solve ; ω 0 , ..., ω M ), then we do nothing.


For any δ > 0, 0 < ǫ < 1/2, run the algorithm in Figure 1 on a sample X drawn from f , where the parameters are set according to the equations Then with probability at least 1−δ, C is (σ, ǫ) consistent.

the clusters containing A[X] and A ′ [X], where A and A ′ are (σ, ǫ) separated, are internally connected and mutually disconnected in C(r) for r defined by Before we prove this theorem a few remarks are in order: 1.


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

given a different set of regression targets, we would compute a different H. We should therefore more properly write this non-linear operator as Hy .


Upon inspection, we find that these two dimensions correlate with two key characteristics of the eye-angles over the course of a bout.

we compute the change in eye angle between the first and last frames of a bout, as well as the mean eye angle over the 10 frames.


The constraint u q ≥ z d can simply be rewritten coordinate-wise y qt ≥ x dt .

finally, the capacity constraints assume the form d x dt ≥ |D| − C t . the number of pages allocated to higher tiers are at least |D| − C t . Define remaining capacities Ct := |D| − C t and use the variable transformation (1) we have the following integer linear program: minimize x,y v yp (4a) subject to x dt ≥ x d,t+1 and y qt ≥ y q,t+1 and y qt ≥ x dt for all (q, d) ∈ G (4b) where p = (p 1 , .


In this paper, we propose an extended level method to efficiently solve the multiple kernel learning problem.

the level method overcomes the drawbacks of both the SILP method and the SD method for MKL.


In this work, we build upon graph neural networks in order to learn useful representations for graph classification in an end-to-end fashion.

we consider GNNs that employ the following general "message-passing" architecture: where H (k) ∈ R n×d are the node embeddings (i.e., "messages") computed after k steps of the GNN and M is the message propagation function, which depends on the adjacency matrix, trainable parameters θ (k) , and the node embeddings H (k−1) generated from the previous message-passing step.


An interesting open question is to resolve the necessity of at least three mixture components in our constructions.

we believe that at least three mixture components are necessary for the log-likelihood to be poorly behaved, and that for a well-separated mixture of two Gaussians the EM algorithm with a random initialization is in fact successful with high probability.


Automatically discovering effective protocols in this space remains an elusive challenge.

the difficulty of exploring this space of protocols is exacerbated by the need for agents to coordinate the sending and interpreting of messages.


[of Theorem 4] While the sample complexity is easy to verify, we focus on the proof of the first property.

we show that when J happens (which with probability at least 1 − δ by ( 12)), we have err Di (g) ≤ for all i ∈ {1, 2, 3, . . . , k}.


In most real world applications, however, the data does not have a linear structure.

the underlying distribution may not be well-represented by any low-rank subspace of the ambient space.


eigenvalues/eigenvectors, as E . In this section we describe two general "matrix simplification" techniques and discuss their implications for Kernel PCA.

under natural assumptions on the spectral structure of E , we will prove that applying KPCA to the simplified matrix E yields subspaces which are very close to those that KPCA would find in E . As a result, when we project vectors onto these spaces (as performed by the feature extractors) the results are provably close to the original ones.


We utilize effective recent work on pedestrian detectors to detect and represent people in our images.

we make use of detectors from Bourdev et al [3] which learn poselets -parts that are tightly clustered in configuration and appearance space -from a large number of 2d annotated regions on person images in a max-margin framework.


Let ∆ T,z denote the number of times T changes labels on the its leaves over the sequence z, and R T,z denote the number of times times T has completely reconfigured itself over z.

if there is an offline adaptive k-IPtree, that makes few changes and few mistakes on the input sequence of IP addresses, then TrackIPTree will also make only a small number of mistakes.


For similar layers x, y, M (x, y) 1 and for disparate layers M (x, y) 1.

we would rather match conv3 to conv5 than not assign it, provided the structural penalty for doing so is small; conversely, we would rather not assign a conv3, than assign it to fc.


Let p(x, c) represent this distribution in which x is a vector of the features of this unit and c represents the costs associated with this unit.

let x i (1 ≤ i ≤ s) be the set of measurements (features) available to the decision maker immediately following stage i.


The first term penalizes large distances between each input and its target neighbors, while the second term penalizes small distances between each input and all other inputs that do not share the same label.

the cost function is given by: where in the second term [z] + = max(z, 0) denotes the standard hinge loss and c > 0 is some positive constant (typically set by cross validation).


Starting from these datasets, we wish to learn a learning algorithm (hence the name LTL) that performs well on a new random task sampled from the environment.

we wish to find an inner algorithm , such that, when we train it with a new dataset composed by n points 2 and sampled from the environment, the corresponding error is low.


The eigenvalue method in the previous section has one obvious shortcoming: it cannot compensate for phase changes across channels.

the real-valued linear combi- We now reconsider the problem of the previous section, looking for the linear combination of analytic signals, 8(t) = L; w;x;(t), that minimizes the cost function in eq.


When it is possible to achieve a positive margin, AdaBoost has been shown to approximately maximize the margin [2].

it is known that AdaBoost achieves a margin of at least 1 2 ρ, where ρ is the largest margin that can possibly be attained by a combined classifier (other bounds appear in [3]).


A factored, n-agent DEC-POMDP is transition independent iff the state-transition function can be separated into n + 1 distinct transition functions P 0 , .

. . , P n , where, for any next state s i ∈ S i , the next local state of each agent is independent of the local states of all others, given its previous local state and local action, and the external system features (S 0 ).


This paper presents a general framework for multiclass total variation clustering that does not rely on a recursive procedure.

we introduce a new discrete multiclass clustering model, its corresponding continuous relaxation and a new algorithm for optimizing the relaxation.


Our results do not address many features of neural network parameterization that merit further study exploiting the mathematical tools that have been developed for particle systems.

the statements we have derived are insensitive to the details of network architecture, which is among the In all cases, we see linear scaling of the empirical loss averaged with P = 10 6 .


To avoid labor-intensive manual annotation, we used an automatic process to identify positions and sizes of objects visible in each frame.

we used YOLO [26], a well-established detector that offers a good compromise between computational cost and accuracy.


Accepting that performance-communication tradeoffs are inherent to distributed algorithms, we proceed with the goal of minimizing the loss in performance relative to J(γ * ).

we now translate the stipulated restrictions on communication into explicit constraints on the function space Γ over which to minimize (2).


This allows us to model each element of the time-frequency spectrum as being generated by exactly one source at a specific location.

we model the phase difference as arising from a mixture of von Mises distributions, with each distribution corresponding to the phase differences for an individual location.


Consensus propagation can be viewed as a special case of belief propagation, and our results contribute to the belief propagation literature.

beyond singly-connected graphs, there are very few classes of relevant problems for which belief propagation is known to converge.


All data sets were generated by mixtures of spherical Gaussians with means ILk in the unit hypercube.

each data set was generated according to three parameters: the dimensionality D , the number of mixture components the means produced by both algorithms were virtually identical to those that would be obtained with infinite data.


• We extend our model to conditional text generation.

we train a conditional GAN that learns to transform a given hypothesis representation in the sentence embedding space into a premise embedding that satisfies a specified entailment relationship.


This can be a consequence of HTPC using the Laplace approximation for approximate inference [9].

there is evidence indicating that the Laplace approximation performs worse than EP in the context of Gaussian process classifiers [15].


Second, we define φ V as a sampling operator that randomly retrieve K consecutive frames.

φ V (w where i is an integer uniformly sampled from K + 1 to T + 1.


Unlabeled data One of the main advantages of having a generative model is that we can leverage unlabeled examples by marginalizing out their hidden outputs.


Hashing has emerged as a popular technique for fast nearest neighbor search in gigantic databases.

learning based hashing has received considerable attention due to its appealing storage and search efficiency.


Note that although the idea of approximating a DP problem with an LP problem has been widely studied in literature (e.g., [17,19]), the design and analysis of ALP here is quite different.

we show that ALP achieves O(1) regret, i.e., its expected total reward is within a constant independent of T from the optimum, except for certain boundaries.