Related papers: Toeplitz Inverse Eigenvalue Problem (ToIEP) and Ra…
Factor analysis, a classical multivariate statistical technique is popularly used as a fundamental tool for dimensionality reduction in statistics, econometrics and data science. Estimation is often carried out via the Maximum Likelihood…
In this paper, we address the problem of direction finding using coprime array, which is one of the most preferred sparse array configurations. Motivated by the fact that non-uniform element spacing hinders full utilization of the…
This manuscript presents an approach to perform generalized linear regression with multiple high dimensional covariance matrices as the outcome. Model parameters are proposed to be estimated by maximizing a pseudo-likelihood. When the data…
In this work, we propose a novel method for quantifying distances between Toeplitz structured covariance matrices. By exploiting the spectral representation of Toeplitz matrices, the proposed distance measure is defined based on an optimal…
Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…
We focus on \emph{row sampling} based approximations for matrix algorithms, in particular matrix multipication, sparse matrix reconstruction, and \math{\ell_2} regression. For \math{\matA\in\R^{m\times d}} (\math{m} points in \math{d\ll m}…
We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the…
The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential…
High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…
A new and an enriched JPEG algorithm is provided for identifying redundancies in a sequence of irregular noisy data points which also accommodates a reference-free criterion function. Our main contribution is by formulating analytically…
Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian…
This paper studies a machine learning regression problem as a multivariate approximation problem using the framework of the theory of random functions. An ab initio derivation of a regression method is proposed, starting from postulates of…
The Metropolis-Hastings algorithm allows one to sample asymptotically from any probability distribution $\pi$. There has been recently much work devoted to the development of variants of the MH update which can handle scenarios where such…
This paper revisits classical works of Rauch (1963, et al. 1965) and develops a novel method for maximum likelihood (ML) smoothing estimation from incomplete information/data of stochastic state-space systems. Score function and conditional…
A quasi-Toeplitz (QT) matrix is a semi-infinite matrix of the form $A=T(a)+E$ where $T(a)$ is the Toeplitz matrix with entries $(T(a))_{i,j}=a_{j-i}$, for $a_{j-i}\in\mathbb C$, $i,j\ge 1$, while $E$ is a matrix representing a compact…
While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…
In this paper, we consider robust system identification under sparse outliers and random noises. In our problem, system parameters are observed through a Toeplitz matrix. All observations are subject to random noises and a few are corrupted…
We prove localization with high probability on sets of size of order $N/\log N$ for the eigenvectors of non-Hermitian finitely banded $N\times N$ Toeplitz matrices $P_N$ subject to small random perturbations, in a very general setting. As…
The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either…
We provide an overview of recent progress in statistical inverse problems with random experimental design, covering both linear and nonlinear inverse problems. Different regularization schemes have been studied to produce robust and stable…