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Stemming from information-theoretic learning, the correntropy criterion and its applications to machine learning tasks have been extensively explored and studied. Its application to regression problems leads to the robustness enhanced…

We consider two classes of linear kinetic equations: with constant collision frequency and constant mean free path of gas molecules (i.e., frequency of molecular collisions, proportional to the modulus molecular velocity). Based homogeneous…

We use a set of Schwinger-Dyson equations for the Ising Model to check several random number generators. For the model in two and three dimensions, it is shown that the equations are sensitive tests of bias originated by the random numbers.…

The aim of this article is to overview the problem of mean square optimal estimation of linear functionals which depend on unknown values of periodically correlated stochastic process. Estimates are based on observations of this process and…

Existing statistical learning guarantees for general kernel regressors often yield loose bounds when used with finite-rank kernels. Yet, finite-rank kernels naturally appear in several machine learning problems, e.g.\ when fine-tuning a…

The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…

This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or positioning of the vision sensors. It concentrates on the problem where images are encoded with compressed linear…

In the common linear regression model the problem of determining optimal designs for least squares estimation is considered in the case where the observations are correlated. A necessary condition for the optimality of a given design is…

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…

We suggest novel correlation coefficients which equal the maximum correlation for a class of bivariate Lancaster distributions while being only slightly smaller than maximum correlation for a variety of further bivariate distributions. In…

Previous papers have shown the impact of partial convergence of discretized PDE on the accuracy of tangent and adjoint linearizations. A series of papers suggested linearization of the fixed point iteration used in the solution process as a…

We study generalised linear regression and classification for a synthetically generated dataset encompassing different problems of interest, such as learning with random features, neural networks in the lazy training regime, and the hidden…

A general structural equation model is fitted on a panel data set that consists of $I$ correlated samples. The correlated samples could be data from correlated populations or correlated observations from occasions of panel data. We consider…

In this paper, we construct an estimator of an errors-in-variables linear regression model. The regression model leads to a constrained total least squares problems with row and column constraints. Although this problem can be numerically…

This paper characterizes the conditional distribution properties of the finite sample ridge regression estimator and uses that result to evaluate total regression and generalization errors that incorporate the inaccuracies committed at the…

Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…

This paper investigates the effect of quantization on the performance of the Neyman-Pearson test. It is assumed that a sensing unit observes samples of a correlated stationary ergodic multivariate process. Each sample is passed through an…

Scan line levelling, a ubiquitous and often necessary step in AFM data processing, can cause a severe bias on measured roughness parameters such as mean square roughness or correlation length. Although bias estimates have been formulated,…

For some estimations and predictions, we solve minimization problems with asymmetric loss functions. Usually, we estimate the coefficient of regression for these problems. In this paper, we do not make such the estimation, but rather give a…

An important unresolved challenge in the theory of regularization is to set the regularization coefficients of popular techniques like the ElasticNet with general provable guarantees. We consider the problem of tuning the regularization…