Related papers: Using a Non-Commutative Bernstein Bound to Approxi…

Multiple rotation averaging plays a crucial role in computer vision and robotics domains. The conventional optimization-based methods optimize a nonlinear cost function based on certain noise assumptions, while most previous learning-based…

Multiple matrix sampling is a survey methodology technique that randomly chooses a relatively small subset of items to be presented to survey respondents for the purpose of reducing respondent burden. The data produced are missing…

This article provides an original understanding of the behavior of a class of graph-oriented semi-supervised learning algorithms in the limit of large and numerous data. It is demonstrated that the intuition at the root of these methods…

This paper proposes a CS scheme that exploits the representational power of restricted Boltzmann machines and deep learning architectures to model the prior distribution of the sparsity pattern of signals belonging to the same class. The…

The order of smoothness chosen in nonparametric estimation problems is critical. This choice balances the tradeoff between model parsimony and data overfitting. The most common approach used in this context is cross-validation. However,…

Matrix perturbation bounds play an essential role in the design and analysis of spectral algorithms. In this paper, we use a "contour bootstrapping" argument to derive several new perturbation bounds. As applications, we discuss new bounds…

We revisit the probabilistic construction of sparse random matrices where each column has a fixed number of nonzeros whose row indices are drawn uniformly at random with replacement. These matrices have a one-to-one correspondence with the…

Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…

Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information-theoretic…

A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…

We establish theoretical recovery guarantees of a family of Riemannian optimization algorithms for low rank matrix recovery, which is about recovering an $m\times n$ rank $r$ matrix from $p < mn$ number of linear measurements. The…

Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for…

We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…

We analyze randomized matrix-free quadrature algorithms for spectrum and spectral sum approximation. The algorithms studied include the kernel polynomial method and stochastic Lanczos quadrature, two widely used methods for these tasks. Our…

Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…

The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The…

We show both adaptive and non-adaptive minimax rates of convergence for a family of weighted Laplacian-Eigenmap based nonparametric regression methods, when the true regression function belongs to a Sobolev space and the sampling density is…

Modern statistical applications often involve minimizing an objective function that may be nonsmooth and/or nonconvex. This paper focuses on a broad Bregman-surrogate algorithm framework including the local linear approximation, mirror…

In this manuscript, we consider a finite multivariate nonparametric mixture model where the dependence between the marginal densities is modeled using the copula device. Pseudo EM stochastic algorithms were recently proposed to estimate all…

In recent years, a myriad of advanced results have been reported in the community of imitation learning, ranging from parametric to non-parametric, probabilistic to non-probabilistic and Bayesian to frequentist approaches. Meanwhile, ample…