Related papers: Componentwise condition numbers of random sparse m…
This paper considers the problem of detecting the support (sparsity pattern) of a sparse vector from random noisy measurements. Conditional power of a component of the sparse vector is defined as the energy conditioned on the component…
We represent the number of mxn non-negative integer matrices (contingency tables) with prescribed row sums and column sums as the expected value of the permanent of a non-negative random matrix with exponentially distributed entries. We…
In this paper we consider a system of quadratic equations |<z_j, x>|^2 = b_j, j = 1, ..., m, where x in R^n is unknown while normal random vectors z_j in R_n and quadratic measurements b_j in R are known. The system is assumed to be…
The performance of estimating the common support for jointly sparse signals based on their projections onto lower-dimensional space is analyzed. Support recovery is formulated as a multiple-hypothesis testing problem. Both upper and lower…
Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…
Matrix completion, i.e., the exact and provable recovery of a low-rank matrix from a small subset of its elements, is currently only known to be possible if the matrix satisfies a restrictive structural constraint---known as {\em…
In this paper, we present coherence-based performance guarantees of Orthogonal Matching Pursuit (OMP) for both support recovery and signal reconstruction of sparse signals when the measurements are corrupted by noise. In particular, two…
We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across…
Standard variational lower bounds used to train latent variable models produce biased estimates of most quantities of interest. We introduce an unbiased estimator of the log marginal likelihood and its gradients for latent variable models…
In this paper, we study the restricted isometry property of partial random circulant matrices. For a bounded subgaussian generator with independent entries, we prove that the partial random circulant matrices satisfy $s$-order RIP with high…
Recently there has been several works estimating the number of $n\times n$ matrices with elements from some finite sets $\mathcal X$ of arithmetic interest and of a given determinant. Typically such results are compared with the trivial…
We consider sparse matrix estimation where the goal is to estimate an $n\times n$ matrix from noisy observations of a small subset of its entries. We analyze the estimation error of the popularly utilized collaborative filtering algorithm…
We study various constraints and conditions on the true coefficient vector and on the design matrix to establish non-asymptotic oracle inequalities for the prediction error, estimation accuracy and variable selection for the Lasso estimator…
High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…
In this paper we derive tail bounds on the norms of random submatrices with non-uniformly distributed supports. We apply these results to sparse approximation and conduct an analysis of the average case performance of thresholding,…
We prove the existence of the limiting spectral distribution (LSD) of symmetric triangular patterned matrices and also establish the joint convergence of sequences of such matrices. For the particular case of the symmetric triangular Wigner…
In this paper, we adopt a componentwise perturbation analysis for $\star$-Sylvester equations. Based on the small condition estimation (SCE), we devise the algorithms to estimate normwise, mixed and componentwise condition numbers for…
We propose a general error analysis related to the low-rank approximation of a given real matrix in both the spectral and Frobenius norms. First, we derive deterministic error bounds that hold with some minimal assumptions. Second, we…
This paper is devoted to condition numbers of the total least squares problem with linear equality constraint (TLSE). With novel limit techniques, closed formulae for normwise, mixed and componentwise condition numbers of the TLSE problem…
For statistical modeling wherein the data regime is unfavorable in terms of dimensionality relative to the sample size, finding hidden sparsity in the ground truth can be critical in formulating an accurate statistical model. The so-called…