This paper considers the problem of optimum reconstruction in generalized sampling-reconstruction processes (GSRPs). We propose constrained GSRP, a novel framework that minimizes the reconstruction error for inputs in a subspace, subject to a constraint on the maximum regret-error for any other signal in the entire signal space. This framework addresses the primary limitation of existing GSRPs (consistent, subspace and minimax regret), namely, the assumption that the a priori subspace is either fully known or fully ignored. We formulate constrained GSRP as a constrained optimization problem, the solution to which turns out to be a convex combination of the subspace and the minimax regret samplings. Detailed theoretical analysis on the reconstruction error shows that constrained sampling achieves a reconstruction that is 1) (sub)optimal for signals in the input subspace, 2) robust for signals around the input subspace, and 3) reasonably bounded for any other signals with a simple choice of the constraint parameter. Experimental results on sampling-reconstruction of a Gaussian input and a speech signal demonstrate the effectiveness of the proposed scheme.
Under the frame assumption of @math , @math can be represented in terms of analysis and synthesis operators as @cite_17 where " @math " denotes the Moore-Penrose pseudoinverse.
@cite_17
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Motivated by online recommendation and advertising systems, we consider a causal model for stochastic contextual bandits with a latent low-dimensional confounder. In our model, there are @math observed contexts and @math arms of the bandit. The observed context influences the reward obtained through a latent confounder variable with cardinality @math ( @math ). The arm choice and the latent confounder causally determines the reward while the observed context is correlated with the confounder. Under this model, the @math mean reward matrix @math (for each context in @math and each arm in @math ) factorizes into non-negative factors @math ( @math ) and @math ( @math ). This insight enables us to propose an @math -greedy NMF-Bandit algorithm that designs a sequence of interventions (selecting specific arms), that achieves a balance between learning this low-dimensional structure and selecting the best arm to minimize regret. Our algorithm achieves a regret of @math at time @math , as compared to @math for conventional contextual bandits, assuming a constant gap between the best arm and the rest for each context. These guarantees are obtained under mild sufficiency conditions on the factors that are weaker versions of the well-known Statistical RIP condition. We further propose a class of generative models that satisfy our sufficient conditions, and derive a lower bound of @math . These are the first regret guarantees for online matrix completion with bandit feedback, when the rank is greater than one. We further compare the performance of our algorithm with the state of the art, on synthetic and real world data-sets. Let @math be a smooth scheme over an algebraically closed field @math of characteristic zero and @math a regular function, and write @math Crit @math , as a closed subscheme of @math . The motivic vanishing cycle @math is an element of the @math -equivariant motivic Grothendieck ring @math defined by Denef and Loeser math.AG 0006050 and Looijenga math.AG 0006220, and used in Kontsevich and Soibelman's theory of motivic Donaldson-Thomas invariants, arXiv:0811.2435. We prove three main results: (a) @math depends only on the third-order thickenings @math of @math . (b) If @math is another smooth scheme, @math is regular, @math Crit @math , and @math is an embedding with @math and @math an isomorphism, then @math equals @math "twisted" by a motive associated to a principal @math -bundle defined using @math , where now we work in a quotient ring @math of @math . (c) If @math is an "oriented algebraic d-critical locus" in the sense of Joyce arXiv:1304.4508, there is a natural motive @math , such that if @math is locally modelled on Crit @math , then @math is locally modelled on @math . Using results from arXiv:1305.6302, these imply the existence of natural motives on moduli schemes of coherent sheaves on a Calabi-Yau 3-fold equipped with "orientation data", as required in Kontsevich and Soibelman's motivic Donaldson-Thomas theory arXiv:0811.2435, and on intersections of oriented Lagrangians in an algebraic symplectic manifold. This paper is an analogue for motives of results on perverse sheaves of vanishing cycles proved in arXiv:1211.3259. We extend this paper to Artin stacks in arXiv:1312.0090. We develop a Bayesian nonparametric approach to a general family of latent class problems in which individuals can belong simultaneously to multiple classes and where each class can be exhibited multiple times by an individual. We introduce a combinatorial stochastic process known as the negative binomial process ( @math ) as an infinite-dimensional prior appropriate for such problems. We show that the @math is conjugate to the beta process, and we characterize the posterior distribution under the beta-negative binomial process ( @math ) and hierarchical models based on the @math (the @math ). We study the asymptotic properties of the @math and develop a three-parameter extension of the @math that exhibits power-law behavior. We derive MCMC algorithms for posterior inference under the @math , and we present experiments using these algorithms in the domains of image segmentation, object recognition, and document analysis. This paper proposes the novel Pose Guided Person Generation Network (PG @math ) that allows to synthesize person images in arbitrary poses, based on an image of that person and a novel pose. Our generation framework PG @math utilizes the pose information explicitly and consists of two key stages: pose integration and image refinement. In the first stage the condition image and the target pose are fed into a U-Net-like network to generate an initial but coarse image of the person with the target pose. The second stage then refines the initial and blurry result by training a U-Net-like generator in an adversarial way. Extensive experimental results on both 128 @math 64 re-identification images and 256 @math 256 fashion photos show that our model generates high-quality person images with convincing details.