Related papers: Cram\'er type moderate deviations for trimmed L-st…

In machine learning and statistical data analysis, we often run into objective function that is a summation: the number of terms in the summation possibly is equal to the sample size, which can be enormous. In such a setting, the stochastic…

Trimmed L-moments, were introduced by Elamir and Seheult(2003) to proposed a new estimation method for multi-parameter distributions when the mean doesn't exist or for heavy tailed distribution where the L-moments method which proposed by…

We develop a stabilized discrete Laplace-Beltrami operator that is used to compute an approximate mean curvature vector which enjoys convergence of order one in L2. The stabilization is of gradient jump type and we consider both standard…

We consider Markov chains which are polynomially mixing, in a weak sense expressed in terms of the space of functions on which the mixing speed is controlled. In this context, we prove polynomial large and moderate deviations inequalities.…

In many applications we seek to maximize an expectation with respect to a distribution over discrete variables. Estimating gradients of such objectives with respect to the distribution parameters is a challenging problem. We analyze…

This paper studies transfer learning for ridge-regularized robust linear regression in the moderate-dimensional regime, where the number of predictors is of the same order as the sample size and the regression coefficients are not assumed…

Fine-tuning over large pretrained language models (PLMs) has established many state-of-the-art results. Despite its superior performance, such fine-tuning can be unstable, resulting in significant variance in performance and potential risks…

We obtain large deviations estimates for both sequential and random compositions of intermittent maps. We also address the question of whether or not centering is necessary for the quenched central limit theorems (CLT) obtained by Nicol,…

We introduce the notion of the essential tangent bundle of a parametrized measure model and the notion of reduced Fisher metric on a (possibly singular) 2-integrable measure model. Using these notions and a new characterization of…

Trimmed (multi-patch) geometries are the state-of-the-art technology in computer-aided design for industrial applications such as automobile crashworthiness. In this context, fast solution techniques extensively rely on explicit time…

We establish large deviation type estimates for i.i.d. products of two dimensional random matrices with finitely supported probability distribution. The estimates are stable under perturbations and require no irreducibility assumptions. In…

The problem of f-divergence estimation is important in the fields of machine learning, information theory, and statistics. While several nonparametric divergence estimators exist, relatively few have known convergence properties. In…

We derive a large deviation principle for families of random variables in the basin of attraction of spectrally positive stable distributions by proving a uniform version of the Tauberian theorem for Laplace-Stieltjes transforms. The main…

In this paper we establish a large deviations type estimate for strongly mixing Markov chains with respect to the Lp norm. As applications we derive such estimates for the iterates of a locally constant random cocycle with mixed rank, as…

This paper is aimed to study the ergodic short-term behaviour of discretizations of circle expanding maps. More precisely, we prove some asymptotics of the distance between the $t$-th iterate of Lebesgue measure by the dynamics $f$ and the…

Numerical methods for SDEs with irregular coefficients are intensively studied in the literature, with different types of irregularities usually being attacked separately. In this paper we combine two different types of irregularities:…

A large class of non-smooth practical optimization problems can be written as minimization of a sum of smooth and partly smooth functions. We examine such structured problems which also depend on a parameter vector and study the problem of…

Due to the non-smoothness of optimization problems in Machine Learning, generalized smoothness assumptions have been gaining a lot of attention in recent years. One of the most popular assumptions of this type is $(L_0,L_1)$-smoothness…

The work of this paper is devoted to obtaining strong laws for intermediately trimmed sums of random variables with infinite means. Particularly, we provide conditions under which the intermediately trimmed sums of independent but not…

Linear mixed models (LMMs) are a popular class of methods for analyzing longitudinal and clustered data. However, such models can be sensitive to outliers, and this can lead to biased inference on model parameters and inaccurate prediction…