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Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kernel Hilbert Spaces (RKHSs), to compare…
Minimization of suitable statistical distances~(between the data and model densities) has proved to be a very useful technique in the field of robust inference. Apart from the class of $\phi$-divergences of \cite{a} and \cite{b}, the…
We consider Bayesian multiple statistical classification problem in the case where the unknown source distributions are estimated from the labeled training sequences, then the estimates are used as nominal distributions in a robust…
We are interested in the problem of robust parametric estimation of a density from $n$ i.i.d. observations. By using a practice-oriented procedure based on robust tests, we build an estimator for which we establish non-asymptotic risk…
In high-dimensional data, many sparse regression methods have been proposed. However, they may not be robust against outliers. Recently, the use of density power weight has been studied for robust parameter estimation and the corresponding…
Parametric hypothesis testing associated with two independent samples arises frequently in several applications in biology, medical sciences, epidemiology, reliability and many more. In this paper, we propose robust Wald-type tests for…
We introduce a generalized formulation of mutual information (MI) based on the extended Bregman divergence, a framework that subsumes the generalized S-Bregman (GSB) divergence family. The GSB divergence unifies two important classes of…
We propose a new density estimation algorithm. Given $n$ i.i.d. observations from a distribution belonging to a class of densities on $\mathbb{R}^d$, our estimator outputs any density in the class whose "perceptron discrepancy" with the…
This paper develops a robust dynamic mode decomposition (RDMD) method endowed with statistical and numerical robustness. Statistical robustness ensures estimation efficiency at the Gaussian and non-Gaussian probability distributions,…
Penalized logistic regression is extremely useful for binary classification with large number of covariates (higher than the sample size), having several real life applications, including genomic disease classification. However, the…
This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…
Gaussian processes constitute a very powerful and well-understood method for non-parametric regression and classification. In the classical framework, the training data consists of deterministic vector-valued inputs and the corresponding…
The Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter is an almost exact closed-form approximation to the Bayes-optimal multi-target tracking algorithm. Due to its optimality guarantees and ease of implementation, it has been…
Density-power-based divergences are known to provide robust inference procedures against outliers, and their extensions have been widely studied. A characteristic of successful divergences is that the estimation problem can be reduced to…
Confidence intervals based on penalized maximum likelihood estimators such as the LASSO, adaptive LASSO, and hard-thresholding are analyzed. In the known-variance case, the finite-sample coverage properties of such intervals are determined…
In real life we often deal with independent but not identically distributed observations (i.n.i.d.o), for which the most well-known statistical model is the multiple linear regression model (MLRM) without random covariates. While the…
We study the weak convergence (in the high-frequency limit) of the parameter estimators of power spectrum coefficients associated with Gaussian, spherical and isotropic random fields. In particular, we introduce a Whittle-type approximate…
This article extends the multivariate extreme value theory (MEVT) to discrete settings, focusing on the generalized Pareto distribution (GPD) as a foundational tool. The purpose of the study is to enhance the understanding of extreme…
We consider distributed estimation of a Gaussian vector with a linear observation model in an inhomogeneous wireless sensor network, where a fusion center (FC) reconstructs the unknown vector, using a linear estimator. Sensors employ…
We propose a function-valued evaluation metric for generative models based on the relative density ratio (RDR) designed to characterize distributional differences between real and generated samples. As an evaluation metric, the RDR function…