Related papers: Unbiased Bregman-Risk Estimators: Application to R…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
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,…
Debiased estimation has long been an area of research in the group testing literature. This has led to the development of several estimators with the goal of bias minimization and, recently, an unbiased estimator based on sequential…
In this article, we consider computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time…
Recommender systems are seen as an effective tool to address information overload, but it is widely known that the presence of various biases makes direct training on large-scale observational data result in sub-optimal prediction…
This paper explores Bayesian estimation for categorical data, focusing on simple yet effective models that provide a foundation for applying more advanced methods accurately and reliably in real-world applications. We begin by revisiting…
The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…
A bias-reduced estimator is proposed for the mean absolute deviation parameter of a median regression model. A workaround is devised for the lack of smoothness in the sense conventionally required in general bias-reduced estimation. A local…
Focus of this work is solving a non-smooth constraint minimization problem by a primal-dual splitting algorithm involving proximity operators. The problem is penalized by the Bregman divergence associated with the non-smooth total variation…
The bias of an estimator is defined as the difference of its expected value from the parameter to be estimated, where the expectation is with respect to the model. Loosely speaking, small bias reflects the desire that if an experiment is…
We consider the estimation of a sparse parameter vector from measurements corrupted by white Gaussian noise. Our focus is on unbiased estimation as a setting under which the difficulty of the problem can be quantified analytically. We show…
Recent deep learning approaches focus on improving quantitative scores of dedicated benchmarks, and therefore only reduce the observation-related (aleatoric) uncertainty. However, the model-immanent (epistemic) uncertainty is less…
In this paper a new family of minimum divergence estimators based on the Bregman divergence is proposed, where the defining convex function has an exponential nature. These estimators avoid the necessity of using an intermediate kernel…
We characterize the squared prediction risk of ensemble estimators obtained through subagging (subsample bootstrap aggregating) regularized M-estimators and construct a consistent estimator for the risk. Specifically, we consider a…
Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…
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.…
Statistical inference, a central tool of science, revolves around the study and the usage of statistical estimators: functions that map finite samples to predictions about unknown distribution parameters. In the frequentist framework,…
We consider the problem of estimating the inverse covariance matrix by maximizing the likelihood function with a penalty added to encourage the sparsity of the resulting matrix. We propose a new approach based on the split Bregman method to…
The aim of this paper is to introduce an adaptive penalized estimator for identifying the true reduced parametric model under the sparsity assumption. In particular, we deal with the framework where the unpenalized estimator of the…
In the framework of matrix valued observables with low rank means, Stein's unbiased risk estimate (SURE) can be useful for risk estimation and for tuning the amount of shrinkage towards low rank matrices. This was demonstrated by Cand\`es…