Related papers: Unbiased Risk Estimates for Singular Value Thresho…

Estimating a low rank matrix from its linear measurements is a problem of central importance in contemporary statistical analysis. The choice of tuning parameters for estimators remains an important challenge from a theoretical and…

In model-free deep reinforcement learning (RL) algorithms, using noisy value estimates to supervise policy evaluation and optimization is detrimental to the sample efficiency. As this noise is heteroscedastic, its effects can be mitigated…

Analysis and synthesis of safety-critical autonomous systems are carried out using models which are often dynamic. Two central features of these dynamic systems are parameters and unmodeled dynamics. This paper addresses the use of a…

The truncated singular value decomposition (SVD) of the measurement matrix is the optimal solution to the_representation_ problem of how to best approximate a noisy measurement matrix using a low-rank matrix. Here, we consider the…

We aim to analyze the behaviour of a finite-time stochastic system, whose model is not available, in the context of more rare and harmful outcomes. Standard estimators are not effective in making predictions about such outcomes due to their…

Many applications involve estimation of a signal matrix from a noisy data matrix. In such cases, it has been observed that estimators that shrink or truncate the singular values of the data matrix perform well when the signal matrix has…

This paper proposes a semiparametric stochastic volatility (SV) model that relaxes the restrictive Gaussian assumption in both the return and volatility error terms, allowing them to follow flexible, nonparametric distributions with…

Stein unbiased risk estimation is generalized twice, from the Gaussian shift model to nonparametric families of smooth densities, and from the quadratic risk to more general divergence type distances. The development relies on a connection…

Singular value thresholding (SVT) plays an important role in the well-known robust principal component analysis (RPCA) algorithms which have many applications in computer vision and recommendation systems. In this paper, we formulate and…

Stein's unbiased risk estimate (SURE) was proposed by Stein for the independent, identically distributed (iid) Gaussian model in order to derive estimates that dominate least-squares (LS). In recent years, the SURE criterion has been…

We consider the problem of estimating covariance and precision matrices, and their associated discriminant coefficients, from normal data when the rank of the covariance matrix is strictly smaller than its dimension and the available sample…

We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower…

Soft-thresholding is a sparse modeling method that is typically applied to wavelet denoising in statistical signal processing and analysis. It has a single parameter that controls a threshold level on wavelet coefficients and,…

In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear estimation techniques are widely used. These techniques have, however, some drawbacks.…

This article proposes numerically robust algorithms for Gaussian state estimation with singular observation noise. Our approach combines a series of basis changes with Bayes' rule, transforming the singular estimation problem into a…

The proposed smooth blockwise iterative thresholding estimator (SBITE) is a model selection technique defined as a fixed point reached by iterating a likelihood gradient-based thresholding function. The smooth James-Stein thresholding…

Noise is an unavoidable part of most measurements which can hinder a correct interpretation of the data. Uncertainties propagate in the data analysis and can lead to biased results even in basic descriptive statistics such as the central…

In this paper, we present a generalized estimating equations based estimation approach and a variable selection procedure for single-index models when the observed data are clustered. Unlike the case of independent observations,…

We consider estimating a matrix from noisy observations coming from an arbitrary additive bi-rotational invariant perturbation. We propose an estimator which is optimal among the class of rectangular rotational invariant estimators and can…

We address the problem of image denoising in additive white noise without placing restrictive assumptions on its statistical distribution. In the recent literature, specific noise distributions have been considered and correspondingly,…