For every classifier h ∈ H, and a confidence parameter δ ∈ [0, 1], the bad event B(h, δ) is defined as the region where the desired property on the classifier h does not hold, with probability δ.

further, it assumes that this region is nondecreasing in δ.


The aim was to find an alignment between both halves such that the dependence between them is maximized.

given x i being the left half of the image and y i being the right half, we want to find a permutation π which lines up x i and y i .


We use the given query Q, which is part of the data x, to construct indicators, ι s = δ(s ∈ Q) ∈ {0, 1}, denoting for every token s ∈ S its existence in the query Q, where δ denotes the indicator function.

based on this definition, we formulate the energy function as follows: where w s,c is a parameter connecting a word s ∈ S to an image concept c ∈ C. w t = (w s,c : ∀s ∈ S, c ∈ C).


One of the main objectives in logistic regression is to control the classification performance.

we are interested in predicting labels from features.


Let s(L) be the SVM objective function trained on the labeled set, As discussed in the previous section, the lower bound is s(L).

now our branching strategy consists in selecting the following point in U , arg max we want to find the unlabeled point x * and its label y * which would make the objective function increase as much as possible.


The following result shows that it does not: for some problems, the dependence on m must be (nearly) linear.

we consider estimation in a normal location family model, where each machine receives an i.i.d.


In Figure 3, we compare the performance of these four algorithms as we vary the minibatch size b.

the first column (b = 4) shows that ProxSVRG+ and ProxSVRG perform similar to ProxSGD and ProxGD respectively, which is quite consistent with the theoretical results (Figure 1).


The noise is generated as w ∼ N (0, σ 2 I n ).

we fix p = 200, σ = 0.1, and let β i = ±1/ √ s over its support i ∈ S, where |S| = s. only s of the p = 200 variables are predictive of the response.


We show through information-theoretic arguments that an appropriate prior P can be designed to yield rates of convergence of the same order as that of the best pruning of T 0 .

our resulting weighting scheme maintains ideal properties of pruning approaches such as adaptivity to the intrinsic dimension of data (see e.g.


The non-adaptive bandit learning model fits into the general combinatorial multi-armed bandit (CMAB) framework of [7,20] that deals with nonlinear reward functions.

we can treat the pair collision variable in each community C i as a base arm, and our expected reward in Eq.


We structured the modules in our BU networks to take advantage of residual connections.

each BU module f b i computes: with operations defined as for Eq.


We propose a non-parametric Bayesian framework for modeling collections of such data.

we use a Dirichlet process framework for learning a set of intensity functions corresponding to different categories, which form a basis set for representing individual time-periods (e.g., several days) depending on which categories the time-periods are assigned to.


We characterize conditions for the output of the algorithm to be unique, and we also obtain some general characterizations that help us to determine which method of breaking leads to a consistent GMM.

full breaking (which uses all pairwise comparisons in the ranking) is consistent, but adjacent breaking (which only uses pairwise comparisons in adjacent positions) is inconsistent.


Even though this explanation is widely accepted, we seem to have little concrete evidence supporting it.

we still do not understand the link between ICS and training performance.


We now define the utility of ALG (negative of the utility of ADV) in our zero-sum game as follows: Suppose the expected utility of ALG is non-negative at the equilibrium of this game.

suppose ALG's randomized strategy ẑi (in Algorithm 1) guarantees that for every strategy x ⇤ i of ADV the expected utility of ALG is non-negative.


Note that the review [16] discusses additive noise models [9] and information-geometric causal inference [4].

an extensive experimental evaluation of these methods across a wide range of hyperparameter settings is performed.


We show here that not only can we handle partial observations, but in fact subsampling the data in the fully observed case can significantly reduce the time complexity from the guarantees given in the previous section without sacrificing robustness.

for smaller values of r, the complexity of Algorithm 2 has near linear dependence on the dimension d, instead of quadratic.


The second term in the cost function incorporates the idea of a margin.

for each input x i , the hinge loss is incurred by differently labeled inputs whose distances do not exceed, by one absolute unit of distance, the distance from input x i to any of its target neighbors.


We convert them into the format (x m , x n , s mn ) that SCA expects.

for every training data point, we select its 15 nearest neighbors among samples in the same class and formulate 15 similar relationships.


Convergence of the ET algorithm is governed by the spectral radius of A.

if p(A) > 1, then the algorithm will not converge, whereas if p(A) < 1, then (xn -x) n~ 0 geometrically at rate 'Y ::@, p(A) 10.


Here we propose an efficient approximate solution via alternate optimization.

the objective function ( 2) is decomposed into two submodels, corresponding to the optimizations of the integer matrix F and the projection matrices P x , P z , respectively.


Then, for any A such that |A| = n 0 < n, denoting by σ(A) the expected number of nodes reached by the cascade starting from A: where γ 1 is the smallest solution in [0, 1] of the following equation: Corollary 1.

under the same assumptions: when ) and the regime is sub-critical.


They recover the structure of the scenario.

average trajectories computed at temperatures which are too low, start to overfit to noise present only in the instance for which they were computed.


The normalization constant DM appearing in (10) can also be computed for the quadratic surrogate (11) under the assumption of well-specification (see [14, Appendix F] for details).

we have DM = L 2 max ξ(κ(F ) √ rRQ max ), ξ(z) = z 2 + z, where L max denotes the maximal value of all elements in L, κ(F ) is the condition number of the matrix F and r in an upper bound on the rank of F. The constants R and Q max come from the kernel ASGD setup and, importantly, depend only on the data distribution, but not on the loss L or score matrix F . Note that for a given subspace F, the choice of matrix F is arbitrary and it can always be chosen as an orthonormal basis of F giving a κ(F ) of one.


The discriminator D or critic f w and the generator G are typically parameterized by neural networks.

in our setting, the data distribution is the distribution P (h x ) of sentence embeddings, h x = E(x), obtained by applying sentence encoder E to samples x ∼ P D from a dataset D. our critic and generator are trained with objective In presenting the Wasserstein GAN, [3] argue that while KL divergence is a good divergence for low-dimensional data, it is often too strong in the high-dimensional settings we are often interested in modeling.


All dynamic task-specific data will be represented at nonpositive addresses.

the current instruction pointer ip(r) 2 4 se !7 c ut dX "! !


Before data collection can even begin in an experiment, many choices about its design must be made.

design parameters such as the sample size, the number of treatments (i.e., conditions or levels of the independent variable) to study, and the proportion of observations to be allocated to each treatment group must be chosen.


Supermodularity is defined analogously by reversing the sign of this inequality.

if a function F is submodular, then the function −F is supermodular.


We conduct experiments to exam the usefulness of each component in our model.

we compare different question representation pooling mechanisms, i.e., mean pooling and max pooling.


The inaccuracy in the response (as measured by the standard deviation in the average response curves for non-reward trials) is also proportional to the time interval.

the ratio of the standard deviation to the mean response time (the coefficient of variation) is a constant independent of the time interval.


The base measure is the mean of the prior on the unknown token generating distribution, and α can be thought of as an "inverse variance" that determines how similar the random measures are to G. The Dirichlet process [14] is defined by the property that for all finite partitions of V, the distribution over the measures of those partitions is Dirichlet.

for all finite, measurable partitions A 1 , .


We then exploit submodularity to find a locally optimal parse from an exponentially large set, without enumerating all such parses.

we optimally combine the parses of the subconstituents of a production to create a parse as that production.


Specifically, for each child, we randomly pick one class, without replacement, from the label set of the parent.

for each row of P , randomly pick a column and set the column to 1.


More interestingly, ADD-1 2 -SMOOTHED LOW-RANK lends itself to a host of generalizations.

an important smoothing technique, absolute discounting, is very well suited for heavytailed data such as natural language [11,21,5].


In this paper, we show that different types of anatomical constraints that govern finger flexion can be exploited in this context.

we incorporate these constraints in the construction, structure, and the probabilistic functions of a switched non-parametric dynamic system (SNDS) model.


In the sequel, we parameterize C ∈ R n×n in terms of some hyperparameter vector d ∈ R k as the diagonal matrix, C(d) = diag(exp(d)).

under this representation, C(d) is necessar-ily positive definite, so OPT2 can be written as an unconstrained minimization over the variables d ∈ R k . let ℓ T (w) = − m i=1 log P y (i) | x (i) ; w denote the training logloss and ℓ H (w) = − m i=1 log P ỹ(i) | x(i) ; w the holdout logloss for a parameter vector w. Omitting the dependence of C on d for notational convenience, we have the optimization problem For any fixed setting of these hyperparameters, the objective function of OPT2' can be evaluated by (1) using the hyperparameters d to determine the regularization matrix C, (2) solving OPT1 using C to determine w ⋆ and (3) computing the holdout logloss using the parameters w ⋆ .


By now, it has been shown that CMOL circuits can combine high performance with high defect tolerance (which is necessary for any circuit using nanodevices) for several digital applications.

cMOL circuits with defect rates below a few percent would enable terabit-scale memories [7], while the performance of FPGA-like CMOL circuits may be several hundred times above that of overcome purely CMOL FPGA (implemented with the same F CMOS ), at acceptable power dissipation and defect tolerance above 20% [8].


For each coordinate i 2 [n], we consider a subproblem.

define a two-player zero-sum game played between the algorithm player (denoted by ALG) and the adversary player (denoted by ADV).


Then the θ-th power of the kernel k is a function k θ : X × X → R defined by This is again a reproducing kernel [22,Proposition 4.2], and defines an RKHS called the θ-th power of the RKHS H: This is an intermediate space between L 2 (Q) and H, and the constant 0 Indeed, H θ is nesting w.r.t.


In this paper, we take another approach to this problem by constraining the network such that the corresponding optimization landscape has good theoretical properties without significantly compromising performance.

for two-layer neural networks we introduce Porcupine Neural Networks (PNNs) whose weight vectors are constrained to lie over a finite set of lines.


This gives the following result: where and It is possible to compute the gradient of log Z with respect to θ kj , i.e., the j-th hyper-parameter of the k-th covariance function used to compute K k . Such gradient is useful to find the covariance functions c k (•, •), with k = 1, . . . , l, that maximize the model evidence.

one can show that, if EP has converged, the gradient of the free parameters of the approximate factors with respect to θ kj is zero [18].


Ratings increased more with the introduction of the first cause as compared to subsequent causes.

participants considered the presence of at least one cause explaining the presence of the common-effect to be sufficient grounds to grant an exemplar a relatively high category membership rating in a common-effect category.


Integrating out φ and π results in the following expression for sampling z ij : where n (s,i,j,v) = 1(z ij = s, x ij = v).

if x ij takes feature value v for feature j and is assigned to cluster s, then n (s,i,j,v) = 1, or 0 otherwise.


Theorem 1 shows that the cross-polytope LSH achieves essentially the same bounds on the collision probabilities as the (theoretically) optimal LSH for the sphere from [2] (see Section "Spherical LSH" there).

substituting the bounds from Theorem 1 for the cross-polytope LSH into the standard reduction from Near Neighbor Search to LSH [6], we obtain the following data structure with sub-quadratic space and sublinear query time for Near Neighbor Search on a sphere.


for (r, k) ∈ {1, . . . , d} × {1, . . . , K} do The (r, k)-element of f is updated as  To learn the nonlinear tensor factorization model ( 1), we propose to optimize the regularized empirical risk in an alternating way.

we optimize each component f (r,k) with the other fixed components {f (r ,k ) } (r ,k ) =(r,k) .


Next we study genes sets that are related to specific stage of cell cycle where we expect to see periodic behavior.

we obtain gene sets known to be related to G1, S and S/G2 stage respectively.


In this case our threshold for a given location is that L(block) < .7L(background) (where L(x) represents the negative log likelihood of x).

a location has to look at least marginally more like a given block than it looks like the background.


Finally, we assume that the centers µ * corresponding to C * are the centers of mass of the corresponding clusters.

note that this is the case for example when the oracle's clustering is the optimal solution to the Euclidean k-means clustering problem.


We characterize the complexity of the problem and introduce sample allocation strategies that pull arms to identify the best arm with a fixed confidence, while minimizing the sample budget.

we show the importance of exploiting the global linear structure to improve the estimate of the reward of near-optimal arms.


Substituting the particular values for our case, we obtain and .

for reaching a reasonable approximation of the optimal, the number iterations required are O(log [max j n j ]), which is nearly-independent of the number of kernels.


. . , p n be random variables such that {p i } i2H0 are independent and sub-uniformly distributed so that max i2H0 P(p i  x)  x.

for any k 2 {0, 1, . . . , n}, let ⌘  4 log(9/ ) any procedure that chooses a set {i :  by the standard BH result.


if we choose the step sizes as γ ≤ 1/σ α and β t as in (15), then (i) the above quantity is upper bounded as C(t) ≤ C for all t ≥ 1, where such that M is an upper bound to M (t) , and (ii) the MCGD method converges to an -optimal solution to (5) in T iterations, i.e., F 0 (α (T ) , Θ (T ) ) − F 0 ( α, Θ) ≤ , where as C(T ) ≤ C, at most C( −1 − (F 0 (α (0) , Θ (0) ) − F 0 ( α, Θ)) −1 ) + iterations are required for the MCGD method to reach an -optimal solution to (5).


Its probability mass function is given by 4 Variational Approximation of Posterior Generally, there are two approaches to learning a mixture model from observed data, namely Maximum likelihood estimation (MLE) and Bayesian learning.

maximum likelihood estimation seeks an optimal point estimate of ν, while Bayesian learning aims to derive the posterior distribution over the mixtures.


These results suggest that STDP may be difficult to detect in vivo, requiring even longer recordings or, possibly, different electrode configurations.

with the electrode array used here (Utah array, 400 µm electrode spacing), neurons are unlikely to be mono-synaptically connected.


Motivated by this property, we exploit the concave-convex procedure to perform inference on continuous Markov random fields with polynomial potentials.

we show that the concave-convex decomposition of polynomials can be expressed as a sum-of-squares optimization, which can be efficiently solved via semidefinite programing.


We now explore the surprising relationship between our stochastic price update and standard stochastic optimization techniques.

we will relate our model to a stochastic mirror descent of the form where at each step ξ ∼ Ξ are i.i.d.


We denote by weight(I, A t ) ∈ [0, 1] the weight of the interval I according to the CDF A t , where the value at missing points in the domain is achieved by linear interpolation.

a t represents a piecewise-linear CDF (corresponding to a piecewise constant histogram).


from q(z|v k ) 1 for any fixed value of v k , and a classification target k. A drawback of this method is the lack of axis-alignment detection.

we believe a truly disentangled model should only contain one latent variable that is related to each factor.


Semi-Supervised Smoothness Assumption (SSS): The regression function m(x) = EY | X = x is very smooth where the density p(x) of X is large.

if there is a path connecting X i and X j on which p(x) is large, then Y i and Y j should be similar with high probability.


Results for a MCMC-based DPFM of size 64-32, with the same setting used for the first experiment, indicate that pharmaceutical topics derived from this analysis form clinically reasonable clusters of pharmaceuticals, that may be prescribed to patients for various ailments.

we found that layer-1 topic 46 includes a cluster of insulin products: Insulin Glargine, Insulin Lispro, Insulin Aspart, NPH Insulin and Regular Insulin.


Here one wants to learn a ranking model f : X → R that assigns higher scores to positive instances than to negative ones.

the goal is to learn a ranking function f with small bipartite ranking error: , where (x, y), (x , y ) are assumed to be drawn iid from D; this is the probability that a randomly drawn pair of instances with different labels is mis-ranked by f , with ties broken uniformly at random.


Inspired by the work in [8] and [9], we propose a semi-supervised learning algorithm for DRFs that makes full use of the available data by exploiting a form of entropy regularization as a prior over the parameters on D u .

for a semi-supervised DRF, we attempt to find θ that maximizes the following objective function The first term of ( 4) is the conditional likelihood over the labeled data set D l , and the second term is a conditional entropy prior over the unlabeled data set D u , weighted by a tradeoff parameter γ.


However, once a group becomes inactive, it can never be active again.

once a group dies, it can never be alive again.


We do not use any data augmentation for this task.


On the surface, CRM appears to be very similar to one of the intermediate models considered by Blei and Jordan [3].

their GM-mixture model employs a nearly identical dependence structure among the random variables involved.


For large data, this leads to a significant performance boost over the state-of-the-art kernel methods.

we are able to match or improve the results reported in the literature at a small fraction of their computational budget.


A major drawback of Algorithm 1 is its lack of robustness.

its competitive ratio can be unbounded if the prediction y is small but x b.


Our starting point is a simple and schematic model of vision problems embodying the idea that images are generated by a set of hidden variables with local dependencies.

we assume that each observed image element x i is connected to a hidden variable z i by a directed edge, and each hidden variable is connected to its neighbors (in set c i ) by an undirected edge (thus implying that each hidden variable is conditionally independent of all others given its neighbors).


In the next experiment, we demonstrate how the size of the graphical model affects convergence of the various chains.

we plot the convergence of all chains on six different hoop-structured models containing three, four, six, eight, ten, and twelve variables (Figure 2).


Let C be a cluster tree, and suppose M is a mergeon representing C. Then C ∈ C(λ) if and only if C is a cluster in M at level λ.

the cluster tree of M is also C. Claim 3.


After performing M runs of AIS, the importance weights w AIS can be used to obtain an unbiased estimate of our model's partition function Z S : where Z 0 = 2 F . Observe that the Markov transition operators do not necessarily need to be ergodic.

if we were to choose dumb transition operators that do nothing, for all s, we simply recover the simple importance sampling procedure of Eq.


For convenience, we define which is a full-dimensional update version of Step 3.

one can observe that z (k+1) is updated as Notice that from ( 5), ( 6), ( 7) and ( 8) we have which together with (10) yields in Step 4, we only need to update the block coordinates x and set the rest to be y i .


In a key contribution of this paper, we impose a very natural assumption on general listwise ranking functions, which we term exchangeability, which formalizes the notion that the ranking function depends only on the object features, and not the order in which the documents are presented.

as detailed further in Section 3, we define exchangeable ranking functions as those listwise functions where if their set of input objects is permuted, their output permutation/score vector is permuted in the same way.


( 1) can be implemented like Generative Adversarial Networks (GANs).

q(s) and the divergence between Q(s o ) and P (s o ) are parameterized with two neural networks, i.e., one generator and one discriminator, and then play an adversarial game [12].


The relaxation error in the binary case has been thoroughly studied in [2,14].

theorem 2 in [2] shows that if a large margin surrogate loss is convex, differentiable and decreasing in a neighborhood of 0, then the loss is Fisher consistent.


When module collapse occurs, the resulting log-likelihood is lower than the log-likelihood of the non-module-collapsed trained model.

our approach is not a regularizer that biases the model towards a desired form of a sub-optimal minimum -it is a critical component of the algorithm to ensure finding a high-valued optimum.


( 1) is equal to λ max (A * k ), where A * k is the k × k principal submatrix of A with the largest maximal eigenvalue.

the non-zero elements of the optimal sparse factor x are exactly equal to the elements of u * k , the principal eigenvector of A * k . This underscores the inherent combinatorial nature of sparse PCA and the equivalent class of cardinality-constrained optimization problems.


Each node in X has either an outgoing arc into target node, Z, or receives an arc from Z.

each node is either a parent or a child of Z.


Also Theorems 1 and 2 in [5] show that the logarithmic dependence on |S m | is optimal asymptotically.

[5, Theorem 1] matches with the growing diameter result in Remark 1(ii), while [5,Theorem 2] shows that if Λ is absolutely continuous w.r.t.


( 3) is conceptually related to [7] in which the discriminator loss is introduced to provide sequence-level training signals.

the discriminator is responsible for assessing both the genuineness of a response and the relevance to its corresponding source.


Function f is M-smooth for some matrix M 0.

for all x, y, the following inequality is satisfied: Assumption 3.2 is fairly standard in the CD literature.


It has been shown that the responses from a population of phase-tuned disparity energy are more comparable than the responses from a population of position-tuned disparity energy neurons [12].

the preferred disparity of the neuron with maximum response in a population of phase tuned neurons is a more reliable indicator of the stimulus disparity than the preferred disparity of the neuron with maximum response in a population of position tuned neurons, especially for neurons with small phase shifts.


While of interest in its own right, it is also possible to express important performance criteria as particular cases of d α,p .

the so-called reconstruction error [13]: Note that d R is a natural criterion because a k-truncated PCA estimate minimizes a suitable error d R over all subspaces of dimension k. Clearly, d R (S ρ , Ŝ) vanishes whenever Ŝ contains S ρ and, because the family { Ŝk n } n k=1 of PCA estimates is nested, then d R (S ρ , Ŝk n ) is non-increasing with k. As shown in [13], a number of unsupervised learning algorithms, including (kernel) PCA, k-means, k-flats, sparse coding, and non-negative matrix factorization, can be written as a minimization of d R over an algorithm-specific class of sets (e.g.


Further, the noise in the observations varies over time.

sometimes the variance of the first observation is Σ v,11 = Var(v t,1 ) = 2 6 The parameters A ∈ R 4×4 and B ∈ R 4×2 are obtained from a standard 747 ("yaw damper") model, which may be found in, e.g., the Matlab control toolbox, and various texts such as [6]. )


Intuitively, RDPS reveals the reason why an object (denoted as object A) should be ranked higher than another object (denoted as object B).

the probability of any ratings consistent with the preference 1 is larger than that of its dual ratings (obtained by exchanging the labels of object A and object B while keeping others unchanged).


We consider this problem in a stream-based selective sampling model, and are interested in two quantities: the number of mistakes the algorithm makes on the first T examples in the stream, and the number of label requests among the first T examples in the stream.

we study scenarios in which the distribution may drift within a fixed totally bounded family of distributions.


Formally, fix s 2 (0, 1) such that 1/s is an integer.

define M i (s) to be the sub-interval (5.1) the set M s := {M s (i) : i = 1, . . . , 1/s} is a partition of [0, 1) into 1/s sub-intervals of length s each.


Well-known algorithms include MUA [6], projected gradientd descent [7], alternating nonnegative least squares (ANLS) [8], and hierarchical ALS (HALS) [9].

aNLS (which uses the block principal pivoting algorithm to very efficiently solve the nonnegative least squares) and HALS achive the state-of-the-art performance.


The tracking dynamics of a CANN has also been studied by other authors.

zhang proposed a mechanism of using asymmetrical recurrent interactions to drive the bump, so that the shape distortion is minimized [4].


Our third approach uses the intuition that the 0-1 loss and the AP loss differ only when some of the samples are difficult to classify (that is, some positive samples that can be confused as negatives and vice versa).

when the 0-1 loss over the training dataset is 0, then the AP loss is also 0.


For this, we apply another sequence of relational embedding modules.

the output of the previous object-relational embedding module O 4 ∈ R N×C obj , and the intermediate feature O 3 ∈ R N×256 are taken as inputs as: where the argmax is conducted row-wise and produces an one-hot encoded vector O 4 which is then mapped into R N ×200 by a parameter matrix K 1 .


MOCHA is also equipped to handle heterogeneity from changing systems environments, such as battery power, memory, or network connection, as we show in Figure 2.

we simulate systems heterogeneity by randomly choosing the number of local iterations for MOCHA or the mini-batch size for mini-batch methods, between 10% and 100% of the minimum number of local data points for high variability environments, to between 90% and 100% for low variability (see Appendix E for full details).


We assume that, for every label y, the set ⌃ y is non-empty.

every column of the loss matrix has a zero entry.


This is a complicated bi-level optimization problem (as Q implicitly depends on θ) with an inner variational inference procedure, which we can again train end-to-end using our results.

we can optimize the following algorithm end-to-end with respect to θ.


While this formulation is capable of providing a full cross-amplitude spectrum between two channels, it contains no information about a crossphase spectrum.

each channel is merely a weighted sum of q R q latent functions where R q = rank(B q ).


In both cases, the compatibility function becomes Comparing the optimization problems (10)/( 11) and ( 12)/(13) to the ordinary SVM dual, we see that MLSP couples |Y| binary SVM problems by the joint kernel function and the summed-over box constraints.

whenever only a feasibly small subset of variables has to be considered, we can solve the problem using a general purpose QP solver, or a slightly modified SVM solver.


The probabilities of each left/right transitions in the tree are modeled by a set of binary logistic regressors and the probability of a given word is then obtained by multiplying the probabilities of each left/right choice of the associated tree path.

let l(v i ) be the sequence of tree nodes on the path from the root to the word v i and let π(v i ) be the sequence of binary left/right choices for each of those nodes (e.g.


If one uses as initialization of RatioDCA, f 0 = 1 A , then either RatioDCA terminates after one step or it yields an f 1 which after optimal thresholding as in Theorem 3.1 gives a partition (B, B) which satisfies The above "improvement theorem" implies that we can use the result of any other graph partitioning method as initialization.

we can always improve the result of spectral clustering.


In their work, it is assumed that kz i k 2  and kGk ⇤  p dn .

sample complexity results of the form O(dn log n) are obtained.


Hansen and Zhou propose to use the mean duration to determine the amount of discounting, however this approach does not work.

abstract actions with non-zero probability of never terminating have an infinite mean duration.


In order to generalize DA to our Banach space setting, we develop an analogous duality result in Theorem 1.

we show that the correct notion of strong convexity is (uniform) essential strong convexity.


In the following, we will base our approach on the Poincaré ball model, as it is well-suited for gradient-based optimization.

let  where x ∈ B d and g E denotes the Euclidean metric tensor.


Our goal is to compute the CATE conditioned on this set of covariates, jointly denoted X. Computing ground-truth CATE: The STAR RCT allows us to obtain an unbiased estimate of the CATE.


A separate computational line of reasoning leads to the claim that some transformations of visual inputs that preserve viewed object identity are class-specific.

the 2D images evoked by a face undergoing a 3D rotation are not produced by the same image transformation (2D) that would produce the images evoked by an object of another class undergoing the same 3D rotation.


A convex body K is said to be µ-well-conditioned for µ ≥ 1, if there exists a function F : R d → R such that K = {x|F (x) ≤ 0} and for every x ∈ ∂K: This notion of well-conditioning of a convex body to the best of our knowledge has not been defined before, but it intuitively captures the notion that the convex body should "curve" in all directions to a certain extent.


In the limiting case where λ tends to 1 and ∞, this cost function reduces to the average depth and worst case depth, respectively.

as mentioned in Section 2, GBS is tailored to minimize L 1 (Π), and hence may not produce a good suboptimal solution for the exponential cost function with λ > 1.


we consider a slightly inflated set X g,ρ = {x ∈ X ; f − f (1) (x) ≤ ζ (1) + ργ (1) }, of X g where ρ > 0.


Uniform stability of a learning algorithm is a classical notion of algorithmic stability introduced to derive high-probability bounds on the generalization error (Bousquet and Elisseeff, 2002).

for a loss function with range bounded in [0, 1], the generalization error of a γ-uniformly stable learning algorithm on n samples is known to be within O((γ + 1/n) n log(1/δ)) of the empirical error with probability at least 1 − δ.


Each random forest was fit with 500 trees, using defaults known to work well in practice [6].

in each training instance, the number of randomly chosen splits to consider at each tree node was √ p, where p is the number of input variables.


In practice, we decide the number of additional losses according to the depth of the network (See Section S4 in the supplementary material).

we insert 3 losses to ResNet-50 and ResNet-56, and 2 additional losses to VGGNet and ResNet-18.


In essence, if τ is too small, there is insufficient regularization.

if the minimum expected degree δ = O(ln N ), then we need τ ≥ c( ) ln N to have enough regularization to satisfy condition (b) on δ + τ . Alternatively, if τ is too large, it washes out significant eigenvalues.


A potential concern for an adaptive method is that stimulus responses are susceptible to neural noise.

spike counts are subject to Poisson-like variability, which might not be entirely averaged away based on a finite number of stimulus repeats.


. . , T , which are all 1-Lipschitz with respect to ∆, such that the regret (without movement costs) is Ω T d+1 d+2 .

in many natural metric spaces in which the upper and lower Minkowski dimensions coincide (e.g., normed spaces), the bound of Theorem 9 is tight up to logarithmic factors in T. and quite surprisingly, we see that the movement costs do not add to the regret of the problem!


The intersection graph, denoted by G int , is a graph whose vertex set is V = {x 1 . . . x n } and x i is adjacent to x j if the sets A i and A j intersect.

there exists an output of the blackbox that depends both on x i and x j (see Figure 2 for an illustration).


At the phrase level, 1-dimensional convolution neural networks are used to capture the information contained in unigrams, bigrams and trigrams.

we convolve word representations with temporal filters of varying support, and then combine the various n-gram responses by pooling them into a single phrase level representation.


Probabilistic models provide a precise definition of evidence: Evidence is the likelihood of a decision alternative under a noisy measurement where the likelihood is defined through a generative model of the measurements under the hypothesis that the considered decision alternative is true.

this generative model implements assumptions about the expected distribution of measurements.


In this section we establish an explicit tradeoff between the performance of a multi-player algorithm and the number of communication rounds it uses, in terms of the accuracy ε.

our observation is that by allowing O(log(1/ε)) rounds of communication, it is possible to achieve the optimal speedup of factor k. we do not gain any improvement in learning performance by allowing more than O(log(1/ε)) rounds.


To estimate ARI in this experiment, we used simple least-squares linear regression.

for each k ∈ {2, . . . , 9}, we fit ARI as a linear function of Silhouette scores using all the data from the meta-training set in the partition pertaining to k: each dataset in the meta-training set provided 10 target values, corresponding to different runs where number of clusters was fixed to k. As is standard, we define the best-fit k * i for dataset i to be the one that yielded maximum ARI score across the different runs, which is often different from k i , the number of clusters in the ground truth (i.e., the number of class labels).


Therefore, the study of on-line learning should focus more on single-pass performance.

after processing all available training examples once, the learned model should generalize as well as possible so that used training example can really be removed from memory to minimize disk I/O time.


Although the Riemannian approach is appealing, our knowledge of it is fairly limited.

there is little analysis about its global complexity (a.k.a.


Our answer-generator module assumes the answer distribution is independent from the history h t−1 = (a 1:t−1 , q 1:t−1 ).

we approximate the likelihood as p(a t |c, q t , a 1:t−1 , q 1:t−1 ) ∝ p (a t |c, q t ).


To conquer these limitations, we reexamine the original L-BFGS algorithm and propose a new L-BFGS update procedure, called Vector-free L-BFGS (VL-BFGS), which is specifically devised for distributed learning with huge number of variables.

we replace the original L-BFGS update procedure depending on vector operations, as known as two-loop recursion, by a new procedure only relying on scalar operations.


This grid partitions the real number line into intervals [u + nδ, u + (n + 1)δ] for all integers n. The probability that two points x and y fall in the same bin in this grid is max 0, 1 − |x−y| δ [13].

if we number the bins of the grid so that a point x falls in bin x = x−u δ and y falls in bin ŷ = y−u δ , then Pr u [x = ŷ|δ] = k hat (x, y; δ).


After proving the theorem, we also present the regret bound for O-REPS when used in a full information setting where the learner gets to observe t after each episode t. Theorem 1.

assuming bandit feedback, the total expected regret of O-REPS satisfies setting η = L Proof.


We provide novel physics-based insights into the differential equation approaches for optimization.

we connect the optimization algorithms to natural physical systems through differential equations.


This paper studies the computational efficiency and convergence of the Perceptron and Winnow algorithms over such expanded feature spaces of conjunctions.

we study the use of kernel functions to expand the feature space and thus enhance the learning abilities of Perceptron and Winnow; we refer to these enhanced algorithms as kernel Perceptron and kernel Winnow.


. . , (x m , y m ) are drawn independently from a distribution supported on , where w ≤ W , and u : R → [0, 1] is a known nondecreasing 1-Lipschitz function.

then for any δ ∈ (0, 1), the following holds with probability at least 1 − δ: there exists some iteration t < O(W m/ log(1/δ)) of GLM-TRON such that the hypothesis the theorem implies that some h t has small enough ε(h t ).


Here we approximate the expectation using Monte Carlo sampling with a small set of samples of the labels.

given a batch of points X, we approximate (5)  We will call the batch policy described above batch-ENS.


Several recent papers [6,10,9,11] have considered the problem of recovering the connected components of {x : f (x) ≥ λ} for a user-specified λ: the flat version of our problem.

the algorithm of [6] is intuitively similar to ours, though they use a single graph in which each point is connected to its k nearest neighbors, whereas we have a hierarchy of graphs in which each point is connected to other points at distance ≤ r (for various r).


Let us define the weight of an example i under the current model as the rate at which loss decreases as the margin of i increases: (5) Now, to compute the gain (Equation 4), we note that: We recursively split leaf nodes by choosing the best atomic splitting feature that will allow us to increase the gain.

we consider splitting each leaf node n using atomic feature â, where â = arg max Splitting using â would create children nodes n 1 and n 2 , with ϕ(n 1 ) = f ∧ â and ϕ(n 2 ) = f ∧ ¬â.


Note that we did not try to optimize the running time in our experiments.

considerable time savings could be achieved by using warm-start.


I believe that these results have some important consequences for our thinking about language acquisition.

they offer a different perspective on the argument from the poverty of the stimulus, and thus on one of the most central "problems" of language acquisition research: the logical pmblern of lang'uage acquisition.


To monitor the annotation quality, we conduct an initial quality filtering stage.

we randomly sampled 1,000 images as a quality monitoring dataset from the MS COCO dataset as an initial set for the annotators (they do not know this is a test).


We can see that, DBA slightly outperforms the baselines in terms of precision, and significantly performs better in terms of the recall scores.

for recall, DBA can achieve a gain of more than 50% relative to MNB and SVM baselines.


For players with perfect recall, the realization form is the projection of the sequence form, where variables related to non-terminal sequences are dropped.

when the perfect-recall property is satisfied, it is possible to move between the sequence-form and the realization-form representations by means of a simple linear transformation.


We consider the problem of computing a restricted nonnegative matrix factorization (NMF) of an m × n matrix X.

we seek a factorization X ≈ BC, where the k columns of B are a subset of those from X and C ∈ R k×n ≥0 .


Note that the basic SyncNet performances in Table 2 differ from the results in Table 1.

the DEAP dataset performance is worse; this is due to significantly reduced information when considering a 4 second window instead of a 60 second window.


Unfortunately, neither (7), (8) nor the model evidence can be computed in closed form.

it is not possible to compute the required integrals analytically.


Since the time taken for a forward and backward pass scales O(T ) with the sequence length T , following a standard linearly increasing curriculum could potentially take O(T 2 ), if the same amount of training was required at each step of the curriculum.

h was doubled whenever the average training loss dropped below a threshold for a number of episodes.


However, these restricted latent models cannot capture the richness of dynamics that recurrent networks exhibit.

systems that converge toward point or line attractors, exhibit limit cycle oscillations, or even transition into chaotic regimes have long been of interest in neural modeling.


(Here, the expectation is with respect the randomization of the training set z 1 , .

. . , z n used to produce w.) We make the following assumptions over the loss function f . First, we assume that for any fixed parameter z ∈ Z, the function f (•, z) is α-exp-concave over the domain W for some α > 0, namely, that the function exp (−αf (•, z)) is concave over W. We will also assume that f (•, z) is β-smooth over W with respect to Euclidean norm • 2 , which means that its gradient is β-Lipschitz with respect to the same norm: this property implies that f (•, z) is differentiable.


if the corresponding graphical model has low treewidth, then the problem can be solved exactly using methods based on tree decompositions, such as the junction tree algorithm [1].


In this paper, the dynamic programming framework [3] is employed to tackle the aforementioned issues.

we first establish the fundamental theory of optimal campaigning over social networks where the user activities are modeled as a multivariate Hawkes process (MHP) [4,5] since MHP can capture both endogenous and exogenous event intensities.


[16]: a linear denoising function ẑ(L) , where a i and b i are parameters, turns the denoising cost into a stochastic estimate of the contractive cost.

our -model seems to combine clustering and label propagation with regularization by contractive cost.


One natural way to quantify the extent of similarity between arms in a given subtree is via the maximum difference in expected payoffs.

for each internal node v we define the width of the corresponding subtree Note that the subtree widths are non-increasing from root to leaves.


3) The loss function incurs a low computational cost and encourages faster convergence.

the searching cost of the hard positive pair ( î, ĵ) is very small since the positive pair set P is usually much smaller than the negative pair set N in an m-sized mini-batch.


However, a crucial observation that we exploit in our work is that for observed data such as natural sensory input or data generated by a sparse coding model, the activity of latent components (or causes) can be expected to be concentrated in low-dimensional subspaces.

for a given observed data point, all except for a very small fraction of the latent components can be assumed to be non-causal or irrelevant, hence the corresponding latent space can be neglected for the integration over � s. For a sparse initiation (i.e., π � 1) of the spike-and-slab model ( 1) to (2), we consider such low dimensional subspaces to be spanned by a few (approximately πH) of the H latent space coordinates.


The representational framework we described is both productive and effectively systematic.

it has the ability, as a matter of principle, to recognize as such objects that are related through a rearrangement of mesoscopic parts, without being taught those parts individually, and without the need for abstract symbolic binding.


First, we assume that there exists some feasible parameter set Θ ⊂ R n that is known to contain the parameter θ * = (θ Acc , θ Sim ) that models the true distribution π * of the data: Next, we must be able to accurately learn θ * if we are provided with labeled samples of the true distribution.

there must be an asymptotically unbiased estimator θ that takes some set of labeled data T independently sampled from π * such that for some c > 0, Finally, we must have enough sufficiently accurate heuristics so that we have a reasonable estimate of Y.


To accomplish this, we multiply w c i by H( wyi c − ), where H(•) is the Heaviside step function.

we note that w c i refers to the weight of example x i to be borrowed by the target class c, whereas wyi c refers to the average weight of examples that class y i borrows from the target class c. if the examples that class y i borrows from class c have low weights on average (i.e.


Let Φ ∈ R N H be such that its first d-coordinates are equal to C(n)U A S 1/2 A , and its remaining entries are 0.

if ρ(n) = ω(log n) and K (F and κ) is well-conditioned, then with high probability: (2) by letting t = ρ 2/3 (n), we have Φ − Φ F = O √ nρ −2/87 (n) .


Theorem 7 essentially implies that by exploiting the multi-stage convex relaxation framework, our proposed DC proximal Newton algorithm gradually reduces the estimation bias for "strong" signals, and eventually obtains an estimator with better statistical properties than the `1-regularized estimator.

let e K be the smallest integer such that after e K stages of convex relaxation we have C 7 0.7 , which is equivalent to requiring e K = O(log log d).


These techniques exhibit improvements on both the theoretical and practical sides.

they admit exact recovery conditions (i.e., on the underlying maps can be recovered from noisy input maps).


[40] proposed to first sparsify the benefit matrix and then run the greedy algorithm on this new sparse matrix.

[40] considers t-nearest neighbor sparsification, i.e., keeping for each row the t largest entries and zeroing out the rest.


We identify a greedy item placement strategy which outperforms all alternative approaches considered on real-world datasets, and can be proven to have a non-trivial recovery property: it recovers hidden co-clusters of items in probabilistic inputs subject to a recovery condition.

we show that, given a set of hidden co-clusters to be placed onto k components, the greedy strategy will tend to place items from the same hidden cluster onto the same component, with high probability.


Those topics, as latent factors, can be interpreted by distributions over words and used to derive low dimensional representations of the documents.

most existing topic models are built on top of the following generative process: Each topic is a distribution over the words (i.e., word distribution, WD) in the vocabulary; each document is associated with a topic proportion (TP) vector; and a word in a document is generated by first drawing a topic according to the document's TP, then sampling the word according to the topic's WD.


Most of these applications reduce to some instance of a tensor decomposition problem, and the growing interest in joint matrix decomposition is largely motivated by such reductions.

in the past decade several 'matricization' methods have been proposed for factorizing tensors by computing the joint decomposition of sets of matrices extracted from slices of the tensor (see, e.g., [10,22,17,8]).


We will assume that each feature, whether observed or missing, is a linear function of an "information vector" drawn from Q .

the N training data samples depend on information vectors φ (1) , .


If p ≥ n then the set of solutions is convex, with the value of ∇ θ f ( θ; x) constant across all solutions.

if p ≥ n and |∇ θt f ( θ; x)| < λ for some solution θ, then θ t = 0 for all solutions.


Consequently, we can write f = 1 T d + K 1 e, and so our formulation becomes: The solution to this optimization problem is for our coefficients d and e to be linear estimates on y, our vector of observed values.

there exist matrices Υ d (c, m) and Υ e (c, m), dependent on our smoothing coefficient c and our exponent m, such that: c, m) is the influence matrix [9] which provides the function estimate over the entire graph.


In this paper, we propose a framework that provides an efficient estimator of the probability mass function of point processes.

we design a key reformulation of the prediction problem, and further derive a differential-difference equation to compute a conditional probability mass function.


This paper then seeks to understand what other algorithms are good for this objective.

is there a divisive algorithm with strong theoretical guarantees?


In each round t, we design a portfolio, that represents the proportion of the current wealth invested in each of the d assets.

a portfolio can be expressed as a vector x t = [x t1 , .


Our motivation is that labeled bags should be correctly classified and the soft labels of the bags or instances defined on the graph G should be as smooth as possible.

a pair of nodes linked by an edge tend to possess the same label and therefore the nodes lying on a densely linked subgraph are likely to have the same labels [20].


While we have used loopy BP to approximate the MMs, any approximate inference can be used inside BMMF to derive a novel, approximate MPCs algorithm.

the algorithm suggested by Wainwright et al.


We have been able to prove the theorem only for the variant of H-RLS storing all instances at each node.

every eligible node at time t is updated, irrespective of whether |w i,t x t | ≤ (5 ln t)/N i,t .


On the other hand, controlling directly the error (PS) is much less sensitive to this.

this suggests a stronger dependency of the residual approach to the mismatch between the sampling distribution and the discounted state occupancy measure induced by the optimal policy.


For sub-exponential design and noise, the difference compared to the sub-Gaussian case is the dependence on the exponential width instead of the Gaussian width of the unit norm ball.

using known results on the Gaussian widths of unit 1 and group-sparse norms, corollaries below are derived using the relationship between Gaussian and exponential widths derived in Section 3: Corollary 2 If R(•) is the group-sparse norm, for sub-exponential design matrix X and noise ω, For Gaussian and sub-Gaussian X, previous work has established RIP bounds of the form RIP is satisfied w.h.p if the number of samples is of the order of square of the Gaussian width of the error set ,i.e., O(w 2 g (A)), which we will call the sub-Gaussian RE sample complexity bound.


The high-level view of the above result is that choosing support points y i to form an ✏-cover with respect to the metric g, and then optimizing over their weights w i via our stochastic algorithm, will give us a consistent picture of the behavior of the true barycenter.

also note that the proof above requires an ✏-cover only of the support of v ⇤ , not all of K. an ✏-cover of the convex hull of the supports of µ j is sufficient, as this must contain the barycenter.


The priors select some large scale features that are the most important to learn first and fill in the details as more data become available (see [11]  One can summarize this in an Occam-like fashion [11]: if two models provide equally good fits to data, a simpler one should always be used.

the predictive information, which quantifies complexity [11], and of which A is the derivative, in a QFT model is ......, N 1 / 2 TJ, and it is . . . . . . , kc log N in the parametric case.


Since exact sufficient statistics are not available for GLMs, we propose to construct approximate sufficient statistics.

we propose to approximate the mapping function φ with an order-M polynomial φ M . We therefore call our method polynomial approximate sufficient statistics for GLMs (PASS-GLM).


On the other hand, we show that these stability results can be translated to predictive models by controlling their norm in the functional space.

the RKHS norm controls both stability and generalization, so that stability may lead to improved sample complexity.


Finally, while most approximation algorithms output an approximation of the optimum value of the linear program (1), we also describe a simple, parallelizable rounding algorithm that provably outputs a feasible solution to (1).

for any ε > 0 and bounded, non-negative cost matrix C, we describe an algorithm that runs in time O(n 2 /ε 3 ) and outputs P ∈ U r,c such that P , C ≤ min P ∈Ur,c We emphasize that our analysis does not require the cost matrix C to come from an underlying metric; we only require C to be non-negative.


In this paper we present a novel approach for robust scene text recognition.

we study the problem of text recognition in a cropped image that contains a single word, which is usually the output from some text localization method (see [2] for a thorough review on this topic).


Interestingly, the same matrix-variate t distribution can be equivalently derived by putting another hierarchical generative process on the covariance R, as described in Figure 1(c), where R follows an inverse-Wishart distribution.

integrating the covariance on either side, we obtain the same model.


relatively larger functions θ i , θ i,j and f ) than pmap, and that the bottleneck of the complete inference procedure is running the trwbp updates.

the added complexity from our method is minimal and the runtime is dominated by the message passing updates of TRWBP.


In our experiment we test the performance of our method against methods that are as simple as training a vanilla version of neural network.

from the family of modified loss function we chose the two variants of the regularized cross entropy loss suggested by [33] (soft and hard bootsrapping).


We compute prediction confidences for the surface normals and depths using Monte Carlo dropout [27].

we forward propagate through the network 10 times with dropout during testing, and compute the prediction variance v i at each pixel.


Therefore the value of the expected function F at w is 3/4 whereas the minimum of F is 1/2.

there exists an ERM algorithm with generalization error of at least 1/4.


Further these algorithms also provide improved bounds in the context of monotone submodular minimization subject to combinatorial constraints.

these algorithms provide bounds which are better than 1 ν , where ν is a parameter related to the curvature of the submodular function.


As shown in Table 2, a 71.5% CB513 accuracy is achieved by our 12-block CNN* † , which is much higher than the results of the previous model, shown in the bottom of the table.

it is more accurate than the previous best accuracy of 70.3%, for a single model [2].


Several researchers have used the Warfarin data for developing personalized approaches to medical treatments.


To represent causal inference in this setting, we generalize earlier developments for hidden variable causal DAG models to hidden variable causal CG models.

we first define a latent projection analogue called the segregated projection for a large class of hidden variable CGs using segregated graphs (SGs).


Our explicit knowledge module aims to enhance region features with kinds of explicit knowledge forms.

as shown in Figure 3, this module updates edge connections between each pair of region graph nodes in Ĝ, supervised by a mapping of the ground truth from a class-to-class knowledge graph Q.


We denote the number of paths that have gone from x to a node with a strictly higher position in the stick-breaking distribution than y i as N (x,>yi) .


In order to learn from distributions, we employ a compact representation that not only preserves necessary information of individual distributions, but also permits efficient computations.

we adopt a Hilbert space embedding to represent the distribution as a mean function in an RKHS [8,9].


Since set F does not exist in input networks, one can sample α target nodes k (with probability proportional to in-degree m k ) to form negative examples (i, k) .

given source node i, we emphasize the existence of link (i, j) by distinguishing whether the corresponding target node is observed ((i, j) ∈ E) or not ((i, k) ∈ F ).


If we assume that the body may be modeled as a kinematic tree, and motion of a particular rigid segment is known, then the motions of the rigid segments that are connected through that segment are independent of each other.

we can model a probability distribution of the full body-pose as a tree-structured graphical model, where each node corresponds to pose of a rigid segment.


Most related work is based on the strong and limiting assumption that Z is a binary random variable (e.g., Z = 0 for the source domain, and Z = 1 for the target domain).

(Pan et al., 2011;Gong et al., 2013;Baktashmotlagh et al., 2013;Zemel et al., 2013;Ganin and Lempitsky, 2014;Ajakan et al., 2014;Edwards and Storkey, 2015;Louizos et al., 2015) are all based on the minimization of some form of divergence between the two distributions of f (X)|Z = 0 and f (X)|Z = 1.


Given the data available for both tasks, our objective is to build a good estimate for the conditional density p t (y|x).

to address this domain adaptation problem, we assume that p t is a modified version of p s . we assume that p t is obtained in two steps from p s . First, p s is expressed using an R-vine representation as in (10) and second, some of the factors included in that representation (marginal distributions or pairwise copulas) are modified to derive p t . All we need to address the adaptation across domains is to reconstruct the R-vine representation of p s using data from the source task, and then identify which of the factors have been modified to produce p t . These factors are corrected using data from the target task.


Specifying how `¡ can change over time requires making an assumption about the nature of the context.

novelty plays a critical role in model evolution.


Quite interestingly, because of the algebraic structure we designed for the computation strategy (i.e., equation ( 10)), the decoding process can be viewed as a polynomial interpolation problem (or equivalently, decoding a Reed-Solomon code).

in this example each worker i returns which is essentially the value of the following polynomial at point x = i: Hence, recovering C using computation results from 4 workers is equivalent to interpolating a 3rddegree polynomial given its values at 4 points.


The sequence (ϑ t ) t≥1 in Theorem 3 is not a parameter of the algorithm, but rather a parameter in the regret bound.

(11) holds true for any such sequence, and we will use this fact later on to obtain explicit bounds by instantiating (11) with a particular choice of (ϑ t ) t≥1 .


An important distinction between our model and Fisher's, including its graphical extension [16], is that our model allows buyers (i.e., villages) to invest the goods (i.e., loans) in productive projects, thereby generating revenue that can be used to pay for the goods (i.e., repay the loans).

the crucial modeling parameter of "endowment" is no longer a constant in our case.


They benefit from a theoretical foundation similar to that of standard maxent probabilistic models used for density estimation [8].

a duality theorem for conditional maxent model shows that these models belong to the exponential family.


The new formulation, however, does not yield computational advantage due to the constraints entangling the two types of variables.

[11] employs a hybrid method (DLPW) that alternatingly optimizes model parameters and messages, but the algorithm is not significantly faster than directly performing stochastic gradient on the structured hinge loss.


Our work distinguishes itself from these directions mainly in the objective, since we require the non-discrimination to happen in the long-term instead of at any time; this extends the classical batch definitions of non-discrimination in the online setting.

we only focus on situations where there are enough samples from each population of interest and we do not penalize the algorithm for a few wrong decisions, leading it to be overly pessimistic.


The domain is the entire Banach space W = p . Then, for any δ > 0 and any a > 0, with probability at least 1 − δ over a sample of size n, we have that for all w ∈ W = p (of any magnitude): Corollary 2 allows us to analyze the rate of convergence of the regularized risk for p -regularized linear learning.

training by minimizing the empirical average of: where (z, y) is some convex loss function and x q ≤ B.


Another approach to solving (1) is deterministic gradient descent methods.

nesterov [2007] proposed an accelerated gradient descent (AGD) method for solving (1).


One possible explanation for why the SVM is unable to gain performance over Euclidean distance is that the wide range of degrees for nodes in these graphs makes it difficult to find a single threshold that separates edges from nonedges.

the "search engines" category had an extremely skewed degree distribution, and is where SPML shows the greatest improvement.


The main bottleneck is sampling, storing, and applying a random rotation.

to multiply a random Gaussian matrix with a vector, we need time proportional to d 2 , which is infeasible for large d. Pseudo-random rotations.


For a network using simulation-on-the-fly, 20000 training batches were run and evaluated on the same test set.

we ran both the simulation on-the-fly and fixed training set for the same number of iterations with a batch size of 50, but the simulation-on-the-fly draws a fresh datapoint from the generative model upon each update so that no datapoint is used more than once.


While the typical existing approaches encode images using feature vectors and generate captions sequentially, the proposed method generates captions in a compositional manner.

our approach factorizes the captioning procedure into two stages.


The slope of the connecting line determines the trade-off between the classes under which any linear combination of A and B would yield equivalent performance.

test set accuracy assuming uniform misclassification costs is represented by accuracy isometrics with slope (1 − π)/π, where π is the proportion of positives [5].


In order to perform cost-sensitive exploration in the Bayesian RL (BRL) setting, we cast the problem as a constrained partially observable MDP (CPOMDP) [11,12] planning problem.

we take a model-based BRL approach and extend BEETLE [4] to solve the CPOMDP which models BRL with cost constraints.


is not known and to be learned from the expert (Section 3).

in the former case, we propose using a generalized linear model to represent ⌧ !


Weighted finite automata (WFA) are finite state machines that allow one to succinctly represent such functions.

wFAs can compute any probability distribution defined by a hidden Markov model (HMM) [13] and can model the transition and observation behavior of partially observable Markov decision processes [26].


We demonstrate our approach on the task of manipulating objects with a robotic arm.

we run experiments on three different tasks: pushing, sliding, and pick-and-place, in each case using only binary rewards indicating whether or not the task is completed.


Given the small size of candidate pool, we adopt the unbiased offline evaluation method of [10] to compare various bandit algorithms.

we collected randomized serving events for a random fraction of user visits; in other words, these random users were recommended an article chosen uniformly from the candidate pool.


(Lemma 1 from [6]) Let k : X × X → R be a universal kernel on a compact subset X or R d and Φ : X → H be a feature map of k. The Φ is continuous and defines a metric on X such that id : (X, • ) → (X, d k ) is continuous.

n ((X, d k ), ε) is finite for all ε > 0.


Consider two possible profiles of reward distributions, ν and ν , that are "close" enough in the sense that it is hard to distinguish between the two, but "separated" enough such that a considerable regret may be incurred when the "correct" profile of distributions is misidentified.

assume that the decision maker is a priori informed that the first arm generates rewards according to a normal distribution with standard variation σ and a mean that is either −∆ (according to ν) or +∆ (according to ν ), and the second arm is known to generate rewards with normal distribution of standard variation σ and mean zero for both ν, and ν .


Our next step involves generalizing the earlier proposition to multivariate symmetric functions by representing them as tensors, which then yields a corresponding spectral theorem of product decompositions for such functions.

note that when the feature vector of each document takes values only from a finite set X , of size |X |, a symmetric function h(x 1 , x 2 , .


Interestingly, if γ > 1 and 0 < T < 1, then LoSST is neither convergent nor diligent, but rather strikes a balance between the desiderata.

these versions (a) tend to converge towards stable structures, but provably do not actually converge since they remain sensitive to outliers; and (b) respond quickly to change in generating structure, but only exponentially fast in the number of previous datapoints, rather than within a fixed interval.


Update the weights (see equation 2): We first assume that the stage at which to add a new subclassifier and the subclassifier to add have already been chosen: ī and h, respectively.

h will become h ī,mī+1 but we simplify it for ease of expression.


6 where G = [g;:" In Q space, the solution to eq.

5 lies along a single axis in the set of axes represented each row of G. gIll =< 0,.


From Figure 2, the DST-NN has overall higher storage and generalization capacity than NN and RNN.

for hidden layer sizes larger than or equal to 8, the DST-NN performance are superior to those of NN and RNN, regardless of their sizes.


To include the information of observable pattern methods in the factorization, we augment the RESCAL model with an additive term that holds the predictions of observable pattern methods.

let X P t0, 1u N ˆN ˆK be a third-order adjacency tensor and M P R N ˆN ˆP be a third-order tensor that holds the predictions of an arbitrary number of relational learning methods.


In this paper, we focus on the problem of competing against the arm with the best risk-return tradeoff.

we refer to the popular mean-variance model introduced by [10].


We assume a one-shot scenario in which all questions are asked simultaneously and then an estimation is performed after all the answers are obtained.

we do not allow allocating tasks adaptively based on the answers received thus far.


Our more formal model provides interesting insights into learned Bloom filters, and how they might be effective.

here we: (1) clarify what guarantees can and cannot be associated with such a structure; (2) show how to estimate what size the learning function must obtain in order to obtain improved performance; (3) provide a simple method for optimizing learned Bloom filters; and (4) demonstrate our approach may be useful for other similar structures.


Form the matrix X * ∈ R N ×K from X by normalizing each of X's rows to have unit length.

project each row of X onto the unit sphere of ).


Videos in our dataset vary in all these parameters.

there are 15 different materials -cardboard, dough, foam, hollow rubber, hollow wood, metal coin, metal pole, plastic block, plastic doll, plastic ring, plastic toy, porcelain, rubber, wooden block, and wooden pole.


Therefore, we propose the following class of estimators: where g λ (•) is a filter function and λ is referred to as a shrinkage parameter.

the matrix-valued function g λ (K) can be described by a scalar function g λ : [0, κ 2 ] → R on the spectrum of K. if K = UDU ⊤ is the eigen-decomposition of K where D = diag(γ 1 , .


In particular, a diffeomorphic mapping has the property that it does not lose any information.

given the mapping itself and the lower dimensional representation of the data set, it is always possible to reconstruct the original data.


. . , (x m , y m ), the average training loss of a matrix W is: L(W ) = 1 m P (x,y)2S `(W, (x, y)).

we aim at approximately solving the problem find the matrix W with minimal training loss among all matrices with column sparsity of at most s, where s is a user-defined parameter.


This motivates us to add an extra log-barrier regularizer to ONS for our problem.

we define our regularizer to be the following mixture: xi , where η t,i is individual and time-varying learning rate.


The training of decoder aims at recovering the architecture x from its continuous representation e x = E(x).

we would like to maximize log P D (x|E(x)) = T r=1 log P D (x r |E(x), x <r ).


Let M be a model with hidden and visible variables z = (x, y) that satisfy a Markov network factorisation.

the joint density can be written as a product of clique-potentials 'lj;j, P(zI9) = g(9) TI j 'lj;j (Cj ,9), where each clique Cj is a subset of the variables in z.


For example, we can vary P G and determine what changes in P on .P off are required to maintain a pre-specified level of detection performance.

we can investigate how human performance depends on the geometrical distribution P G of the curves.


As the main result, we provide finite sample analysis of NNQL for a single, arbitrary sequence of data for any infinite-horizon discounted-reward MDPs with continuous state space.

we show that the algorithm outputs an "-accurate (with respect to supremum norm) estimate of the optimal Q-function with high probability using a number of observations that depends polynomially on ", the model parameters and the "cover time" of the sequence of the data or trajectory of the data utilized.


A node can potentially be called several times (with different parameters) during the run of TrailBlazer and may reuse (some of) its stored (transition and reward) samples.

after node s receives a call from its parent, node s may perform internal computation by calling its own children in order to return a real value to its parent.


Given the apparent difficulty of learning models that are robust to adversarial perturbations, we propose tackling the simpler problem of developing adversarially robust features.

given a dataset and metric of interest, the goal is to return a function (or multiple functions) that 1) is robust to adversarial perturbations, and 2) has significant variation across the datapoints.


1 and KL Compute output dist Backprop ∇ θ and ∇ φ , reparam and KL inference methods directly aim to tighten this gap.

the evidence lower bound (ELBO) is a parameterized bound over a family of distributions q(z) ∈ Q (with the constraint that the supp q(z) This allows us to search over variational distributions q to improve the bound.


This technique defends against adversarial data growth that could dramatically increase the relative entropy between the public histogram and the true database incorporating the new data, allowing us to maintain the accuracy guarantee of the static setting through unbounded data growth.

static PMW works on a fixed database of size n and answers k linear queries.


We further propose that this interscientific incorporation may provide a valid tool where objective brain imaging data are used for the clinical purpose of diagnosis of psychopathology.

in our case study we will model neuronal circuits associated with reward processing in drug addiction.


Moreover, [19] has recently established the rate which is faster than ours, if and only if β > 1+p 1+2p .

for highly smooth kernels such as the Gaussian RBF kernels, where p can be chosen arbitrarily close to 0, their rate is never faster.


It is possible to show that the isd posterior is marginally consistent at least in the Gaussian mean case (one element of the exponential family).

marginalizing over an observation and its associated marginal's parameter (which can be taken to be x N and θ N without loss of generality) still produces a similar isd posterior on the remaining observations X /N and parameters Θ /N .


Reweighting-based strategies use inverse-probability weighting (IPW) to change measure from the outcome distribution induced by a logging policy to that induced by the policy ⇡.

these methods use the fact that, under unconfoundedness, V IPW (⇡) is unbiased for V (⇡) [15], where Optimizing V IPW (⇡) can be phrased as a weighted classification problem [3].


The partitioning is guided by the ties in the single node beliefs.

for each variable X i we find states whose single node beliefs are tied at the maximum.


In this paper, we focus on the large-scale graph scenario when the dimension d is large and hence assume the true precision matrix to be sparse such that Θ 1 ≤ L. We formulate a procedure for testing Θ ∈ S using an estimated precision matrix Θ obtained from samples X 1 , .

. . , X n . Θ can be estimated via the node-wise regression [21], the CLIME [5], or the graphical lasso [11].


Despite the popularity of metric learning methods, few works have studied how problem complexity scales with key attributes of the dataset.

how do we expect generalization error to scale-both theoretically and practically-as one varies the number of informative and uninformative measurements, or changes the noise levels?


Our convex formulation in Section 2 bounds δ from above.

our LMI problem (10) with optimal value η is equivalent to the following variant of ( 13) with optimal value δ ub (x, Z) = (1 − η )/(1 + η ).


The subtlety in proving these results is that there could exist false mixtures that agree with the observed entries, even if the sampling is uniquely completable for LRMC and HRMC (see Example 1).

there exits samplings that are identifiable for LRMC (and HRMC) but are not identifiable for MMC, and so in general it is not enough to simply have K times more samples.


In this paper, we develop a convex formulation of multi-layer learning that allows multiple latent kernels to be connected through nonlinear conditional losses.

each pair of successive layers is connected by a prediction loss that is jointly convex in the adjacent kernels, while expressing a non-trivial, non-linear mapping between layers that supports multi-factor latent representations.


The most useful versions of Wasserstein distance are p = 1, 2, with p = 1 being the weaker of the two (by Hölder's inequality, p ≤ q ⇒ W p ≤ W q .)

"results in W 2 distance are usually stronger, and more difficult to establish than results in W 1 distance" [35, p. 95].


The intuition here is that directed edges differ from undirected edges due to collider bias induced by the former.

dependence between parents of a block is created by conditioning on variables in the block.


Real data (Figure 1) provides evidence that users tend to be approximately consistent and therefore simpler patterns, i.e., patterns that mostly stick to a single rounded value y(t) = y correspond to larger sets of sequences {x i (t)} t , obtained from a real population.

for each app there is always one pattern (corresponding to having one fixed y(t) = y across all 31 days) which blends the majority of users (> 2 million).


Suppose for a downstream task the model is a deep multi-layer network.

each layer is denoted as a function h that takes in features H = (h 1 , • • • , h T ) and possibly additional inputs, and outputs features (h 1 , • • • , h T ).


In time-critical applications, however, they are of limited use due to their computationally expensive decision functions.

the time complexity of an SVM classification operation is characterized by two parameters.


More specifically, we study sparse inverse covariance estimation (SICE), also known as exploratory Gaussian graphical models, for brain connectivity modeling.

we apply SICE to learn and analyze functional brain connectivity patterns from different subject groups, based on a key property of SICE, called the "monotone property" we established in this paper.


Although false negatives remain unknown, the filtering system is scored according to the overall number of wrong relevance judgements it makes.

both false positives and false negatives are counted as mistakes.


However, the discrete nature of the prior makes Bayesian inference a very challenging problem.

for M linear weights, inference under a spike and slab prior distribution on those weights requires a combinatorial search over 2 M possible models.


Firstly, we iteratively apply the model to predict one more time step into the future by treating the prediction as input in a recursive way.

for predicting multiple time steps in the flow anticipating network, we warp the most recent frame X t−1 using the output prediction Ôt to get the Xt which is then combined with X t−k−1:t−1 to feed the flow anticipating network to generate Ôt+1 , and so forth.


The purpose of this paper is to investigate how ranking methods for multivariate data with binary labels may be exploited in order to extend the rank-based test approach for testing homogeneity between two samples to a multidimensional setting.

the testing principle promoted in this paper is described through an extension of the Mann-Whitney Wilcoxon test, based on a preliminary ranking of the data through empirical AUC maximization.


Joint object/feature sparsity via 1 / 2 + 1 (sparse group) regularized LR (LRG1) The groupregularized LR does not, however, yield sparsity within a group (object) for those groups with nonzero total weights.

if a group of parameters is non-zero, they will all be non-zero.


More generally, if y is discrete and T (x, y) consists of |Y| repetitions of a fixed feature function t(x) (as in Figure 1a), then we can write Provided η ⊤ y t(x) is convex in x for each η y , the level sets of A as a function of x form the boundaries of convex sets.

exactly normalizable sets are always the boundaries of convex regions, as in the simple example Figure 1a.


2, left, bottom) reveals that smoothing actually helps to obtain a slightly better solution here.

the soft-max CD (with = 0.001) and L 2 -max AGD (with = 0.01), as well as the primal (SDCA) and dual (AGD) algorithms for the smooth and strongly convex objective, are able to recover the optimal solution within the allowed number of iterations.


Instead, as illustrated in Figure 1 (left), they rely on hidden states H l−1 t and cell states M l−1 t (l ∈ {1, ..., L}) that are updated by the previous layer at current time step.

the bottom LSTM unit receives state values from the top layer at the previous time step: The four layers in this figure have different sets of input-to-state and state-to-state convolutional parameters, while they maintain a spatiotemporal memory cell and update its states separately and repeatedly as the information flows through the current node.


The reactions used for training are atom-mapped so that each atom in the product graph has a unique corresponding atom in the reactants.

reaction Center A reaction center is a set of atom pairs {(a i , a j )}, where the bond type between a i and a j differs from G r to G p . a reaction center is a minimal set of graph edits needed to transform reactants to products.


We model free recall data by combining the underlying assumptions of TCM with the latent semantic space provided by LDA.

we reinterpret TCM as a dynamic latent variable model where the mental context vector specifies a distribution over topics.


In this section we will argue that if one is given access to a value optimization oracle (1), then one can run BISTRO+ efficiently.

we will show that the minimizer of Equation ( 7) can be computed efficiently via Algorithm 2.


Suppose there exists an invertible function ψ : ∆ n → V . Then can be written as a composition of a loss λ defined on the simplex with ψ −1 .


We solve the two-sample testing problem when the inputs are two CBNs over the same DAG G in n variables; for a given > 0 and DAG G, call the problem C2ST(G, ).

we show an algorithm to solve C2ST(G, ) that makes O(log n) interventions on the input models X and Y, uses O(n/ 2 ) samples per intervention and runs in time Õ(n 2 / 2 ), when G has bounded in-degree and c-component size.


As expected, the datasets on which the approximation made a difference were those that had a larger number of attributes.


3 In the current work, we study regression losses instead of classification ones.

the provided results express upper bounds on E f ⇠ ⇢ L D (f ) for any (bounded, sub-Gaussian, or sub-gamma) losses.


In the second experiment, we compared variable vs. constant label-request rate.

we fixed a few values for parameter b, run the selective sampling algorithm in Figure 2, and computed the fraction of labels requested over the training set.


Specifically, for each Ü we define a conditional distribution over points such that If all points in the same class were mapped to a single point and infinitely far from points in different classes, we would have the ideal "bi-level" distribution: Furthermore, under very mild conditions, any set of points which achieves the above distribution must have the desired geometry.

assume there are at least Ö • ¾ points in each class, where Ö rank ℄ (note that Ö Ö).


In this work we utilize the channel features detectors [9, 7, 1, 2], a family of conceptually straightforward and efficient detectors for which variants have been utilized for diverse tasks such as pedestrian detection [10], sign recognition [22] and edge detection [19].

for our experiments we focus on pedestrian detection and employ the aggregate channel features (ACF) variant [7] for which code is available online 2 .


Intuitively, a model with default values is used to encode the first few data; then the model is trained on these few encoded data; this partially trained model is used to encode the next data; then the model is retrained on all data encoded so far; and so on.

we call p a prediction strategy for predicting the labels in Y knowing the inputs in X if for all k, p(y k+1 |x 1:k+1 , y 1:k ) is a conditional model; namely, any strategy for predicting the k + 1label after already having seen k input-output pairs.


Moreover, assume that (RI), (3.2) and (3.3) hold.

then for all k large enough, If ρ(M ) < 1, then given any ρ ∈]ρ(M ), 1[, there exists K ∈ N such that ∀k ≥ K, if s = 1, then ρ(M ) < 1 if R is locally polyhedral around x or if a 0 = b 0 .


In fact the dendrites can be seen as active filters which change the shape of backpropagating spikes during their journey to the distal parts of the dendrite [18].

the decay time of the BP spike is increased in the distal parts of the dendrite [15].


This paper develops (conic) geometric optimisation on the cone of hpd matrices, which allows us to globally optimise a large class of nonconvex functions of hpd matrices.

we first use the Riemannian manifold structure of the hpd cone for studying functions that are nonconvex in the Euclidean sense but are geodesically convex (g-convex), hence globally optimisable.


Critically, our approach is a black-box reduction that parallelizes any serial online learning algorithm, streamlining prior analysis and allowing us to leverage the significant progress that has been made in designing adaptive algorithms.

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


That is, they receive the instance, make some prediction, incur a loss, and update an associated parameter.

the algorithms are entirely sequential in their nature.


We prove the effectiveness of common neighbors for link prediction as well as local clustering around a query node, under the stochastic blockmodel setting.

we show the existence of a semi-dense regime where common neighbors yields the right cluster w.h.p, and a semi-sparse regime where an additional "cleaning" step is required.


Here we aim at finding an interpretable perturbation δ ∈ X ∩ x 0 such that after removing it from x 0 , arg max i [Pred(x 0 )] i = arg max i [Pred(δ)] i .

x 0 and δ will have the same top-1 prediction class t 0 , indicating that the removed perturbation δ is representative of the model prediction on x 0 .


Suppose that on any bounded subset of the domain of F , it holds that F θ (w, V ), ∇F θ (w, V ) and ∇ 2 F θ (w, V ) are all Lipschitz continuous in (w, V ).

then every local minimum (w, V, θ) of F satisfies the objective F has no spurious local minima with value above the smallest attainable with a linear predictor.


the next step is to show that the empirical Markov chains converge to Markov chains M, M a and M b induced by some distribution ⇡ over F. we construct an empirical distribution ⇡ and distributions ⇡a and ⇡b corresponding to player's deviations (see Definition B.5), and show that these induce the Markov chains M, Ma and Mb respectively (Lemma B.7).


These methods use built-in randomness to solve difficult problems that cannot be solved analytically.

such methods are one of the main options for performing approximate inference in Bayesian networks [11].


(1), it is possible to show that JointBoost in fact learns a matrix W with additional constraints.

the features x are assumed to be decision stumps and each column W •,i is constrained to be That is, the stump is shared by all classes in the subset C i . JointBoost chooses such shared decision stumps in a greedy manner by applying the GentleBoost algorithm on top of this presentation.


A natural next question is whether we can say anything positive when the planted vertex cover C is not minimal.

if C is not minimal, can we still ensure that some parts of it must be contained in U (|C|), the union of all minimal vertex covers of size at most |C|?


However, these are exactly analogous to the classical ellipsoid method.

the equation for B τ +1 is known in closed form [11].


Yet, we cannot enforce this ancestral constraints using independent, local constraints on the parents that each variable can take.

the choice of parents for variable X 2 and the choice of parents for variable X 3 will jointly determine whether X 1 is an ancestor of X 3 .


Theorem 1 also implies a bound estimation result for Dantzig selector by letting F 0 = ∅ and p = 2.

we set F 0 = ∅, N = 0, and λ = σ 2 log m−s η 1 in the multi-stage method, and set p = 2, l = s, η 1 = m−s m η, and η 2 = s m η for a convenient of comparison with Theorem 1.


Since J t (f ) is convex, (1) is solved by setting the gradient (or, if necessary, a subgradient) to 0.

using the fact that (2) Since it is difficult to determine ∂ f R(x t , y t , f t+1 ) in closed form, an explicit update, as opposed to the above implicit update, uses the approximation ∂ f R(x t , y t , f t+1 ) ≈ ∂ f R(x t , y t , f t ) to arrive at the more easily computable expression [1] ∂ if we set 2 and ∂ f G(f ) = f , and we obtain the familiar stochastic gradient descent update f t+1 = f t − η t ∂ f R(x t , y t , f t ).


The key for the efficient optimization is solving the 'argmax' problem efficiently.

we note that the space of all multilabels is exponential in size, thus forbidding exhaustive enumeration over it.


It is important to note that we did not use any special training strategy to adapt the network.

we did not use any perturbations such as stochastic depth during training.


To this end, we consider a new setup for optimization that allows us to interplay between stochastic and deterministic gradient descent methods.

we assume that the optimization algorithm has an access to two oracles: • A stochastic oracle O s that returns the loss function g i (w) and its gradient based on the sampled training example (x i , y i ) 2 , and • A full gradient oracle O f that returns the gradient ∇G(w) for any given solution w ∈ W. We refer to this new setting as mixed optimization in order to distinguish it from both stochastic and full gradient optimization models.


When the generator of a trained GAN produces very realistic images, it can be argued to capture the data manifold well whose properties can be used for semi-supervised learning.

the tangent spaces of the manifold can inform us about the desirable invariances one may wish to inject in a classifier [36,33].


For this purpose, we adopt the accelerated gradient method due to its light computation per iteration, and refer the obtained algorithm as TopPush.

we choose the Nesterov's method [30,29] that achieves an optimal convergence rate O(1/T 2 ) for smooth objective function.


Functional scans were realigned to the last volume, corrected for slice timing, co-registered with structural maps, spatially normalized into the standard Montreal Neurological Institute (MNI) atlas space, and then spatially smoothed with an 8mm isotropic full-width-at-half-maximum (FWHM) Gaussian kernel using standard procedures in SPM8.

we construct a general linear model (GLM) and run a first-level analysis modeling brain responses related to outcome while informing the judgments of others.


Our distributed learning algorithm for the 1 -metric builds on the recent centralized algorithm of [2].


Specifically, the tail of the future discounted reward sum for each state depends on the empirical value at time t in the following way, Substituting this into Equation ( 5) and exchanging the order of the double sum, s and R t s depend only on quantities known at time t. The only unknown quantity is v t , which we have to replace with our current estimate of this value at time t, which is V t st .


In other words, the seemingly naive procedure of using generalized or loopy belief propagation to compute the statistics in the E-step and use it in the M-step, can be interpreted as alternate minimization of the Kikuchi approximation of the exact free energy.

algorithm (5) can be interpreted as a bound optimization algorithm for minimizing which we hope to be a good approximation (not necessarily a bound) of the original 4 There are two kinds of approaches for finding the minimum of the Kikuchi free energy.


They also define the property of decomposability of a regularization function, which captures the suitablity of a regularization function R to particular structure.

a regularization function R is said to be decomposable with respect to a subspace pair (M, M ?


In addition to having different transfer models, we introduce a simple decipherment baseline based on word frequency.

we assume that words shared between X 1 and X 2 do not require translation.


Due to the particular proposed methodology, we are able in principle to apply our method to any learning algorithm.

when the algorithm generates a linear model we can exploit the data preprocessing in Eq.


We observe the similarity between the updates of hard EM and hard gradient descent.

if we reparameterize the SPN so that each child of a sum node is weighted by w i = e w i , the form of  ∂S [1,1|x] ∂w the partial derivative of the log MPN becomes This means that the hard gradient update for weights in logspace is ∆w i = ∆c i , which resembles structured perceptron [13].


This allows for a useful degree of flexibility in applying these bounds.

optimal bounds under various degrees of smoothness of f at x easily follow.


To allow for an analytic calculation of the loss L(β, X, P), we assume that the distribution P is a d-dimensional mixture of Gaussians [1,8].

the data are generated as follows: A natural approach for choosing λ is cross-validation procedure, which can be performed efficiently for the iterative methods such as Landweber and accelerated Landweber.


The activation map of a couple of these units, however, seemed to suggest that they might be tuned to respond to complicated textures.

one unit seems more activated by seemingly blank background, while another seems to like textures of leaves (Figure 6).


The connection between the exp-concavity condition, the Bernstein condition and the v-central condition was studied in [46].

the exp-concavity implies a v-central condition under an appropriate condition of the decision set W (e.g., well-specificity or convexity).


These changes correspond to genuine external events.

both models capture the long-term drop and rebound in bias which corresponds to the time period where the item was highlighted on a top-level page, as well as the two rightmost short downward spikes which correspond to technical problems that made downloads temporarily impossible.


When transferring label information across tasks, it often makes sense to assume hierarchical task relations.

in computational biology, where evolutionary processes often impose a task hierarchy [22].


Recently, Kim and Park [8] derived a connection between the BLCP and the Karush-Kuhn-Tucker (KKT) conditions for LARS.

they noted the solution to the minimization problem in equation ( 1) has the form: where the vector −c follows the constraints in equation ( 2) with l i = −β and u i = β.


The system uses a variant of co-training [3] to exploit unlabeled data from a new, previously unseen site.

pages are labeled using a simple bag-of-words classifier, and the results are used by a restricted wrapper-learner to propose potential "main-category link wrappers".


The inclusion of a spherical ball centered at C p allows us to expand substantially the range of ω for which conical coverage continues to hold.

we can reduce the lower bound on ω in Proposition 1, since we only need to cover the regions near the vertices of B with cones using the following proposition.


For the second set of experiments we compare the performance of Lock-Free SVRG with stochastic gradient descent.

we compare with the variants of stochastic gradient descent, DSGD and CSGD, described earlier in this section.


From this, we make the following important observation: During retraining with the poison data, the network modifies its lower-level feature extraction kernels in the shallow layers so the poison instance is returned to the base class distribution in the deep layers.

the poison instance generation exploits imperfections in the feature extraction kernels in earlier layers such that the poison instance is placed alongside the target in feature space.


. . , κ N , we instantiate F and Fmax in Definition 4.3 via: F in Definition 4.4 trades off between exploitation (maximizing the plausible F h 's) and exploration (disambiguating plausibility in F h 's) by allowing each Fh to reach its maximum by either F h reaching α i or G h reaching κ i .

each Fh can be satisfied with either a sufficiently large utility F h or large distance G h . Figure 3 shows the logical relationships between these components.


In Section 3, we describe how to determine whether the dependence returned via HSIC is statistically significant, by proposing a hypothesis test with HSIC as its statistic.

we show that this test can be parameterised using a combination of covariance operator norms and norms of mean elements of the random variables in feature space.


We model such prior knowledge in the form of constraints on a valid grouping configuration.

we see that all such prior knowledge defines a partial  generative models.


Formally, we construct for each k a binarylabeled sample S k = {(x j , C k • y j )} n j=1 and for each S k we learn a binary classification function T k : X → using a logistic regression algorithm.

for each original instance x j and induced binary label C k • y j we posit a logistic model that estimates the conditional probability that Given a predefined code matrix C the learning task at hand is to find T k that maximizes the log-likelihood of the labelling given in S k , Defining 0 log 0 = 0, we can use the logistic estimate in Eq.


Going beyond the special case of coverage functions, distributed constrained submodular maximization has also been the subject of recent research in the machine learning and data mining communities.


Next, we evaluated the performance of the same algorithms for different image features.

we used randomized tree (RT) features generated by [19], and PHOG features [5].


For halfspace classifiers, the set D B (H, x, c) is easily characterized.

when B is a bounded p ball, dim(V B ) = 0, giving AVC(H, R) = d + 1.


Proofs of the following theorems and corollary can be found in Appendix E, Appendix F, and Appendix G in the supplementary material.

then, the following holds with probability at least 1 − δ for every f ∈ F : where the following bound holds for the linear-in-parameter models.


These algorithms are built on an optimization technique called parametric programming [5][6][7], in which one solves a series of optimization problems parametrized by a single parameter.

one solves a solution path with respect to the coefficient parameter corresponding to the data point to be added or removed.


Before we discuss the discretization, we would like to discuss some properties of this regularizer.

its difference to the regularizer S ∆ (f ) using the Laplacian, proposed by Belkin and Niyogi [2] for semi-supervised classification and in the meantime also adopted for semi-supervised regression [12].


Then for any , η bounded above by some constant, and for any Note that the theorem requires a lower bound on the value of δ, and we now show why this bound is necessary.

we observe how the theorem does not hold if δ = o n −1/2 .


In most practical scenarios this is infeasible and we can only expect to have partial observations.

for some node pairs we know whether there exists an edge between them or not, whereas for the rest of the node pairs we do not have this knowledge.


However, our results highlight several issues and provide insights and rules of thumb that can help crowdsourcing practitioners make their own decisions.

we show that the optimal number of control items should be O( √ ) for the two-stage estimator and O( √ n t ) for the joint estimator.