Related papers: On the sample complexity of parameter estimation i…

This paper develops a bias correction scheme for a multivariate normal model under a general parameterization. In the model, the mean vector and the covariance matrix share the same parameters. It includes many important regression models…

Aleatoric uncertainty captures the inherent randomness of the data, such as measurement noise. In Bayesian regression, we often use a Gaussian observation model, where we control the level of aleatoric uncertainty with a noise variance…

Sparsity-inducing penalties are useful tools for variable selection and they are also effective for regression settings where the data are functions. We consider the problem of selecting not only variables but also decision boundaries in…

We consider the problem of regression learning for deterministic design and independent random errors. We start by proving a sharp PAC-Bayesian type bound for the exponentially weighted aggregate (EWA) under the expected squared empirical…

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…

Building classification models that predict a binary class label on the basis of high dimensional multi-omics datasets poses several challenges, due to the typically widely differing characteristics of the data layers in terms of number of…

The problem of population recovery refers to estimating a distribution based on incomplete or corrupted samples. Consider a random poll of sample size $n$ conducted on a population of individuals, where each pollee is asked to answer $d$…

The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…

The inverse problem methodology is a commonly-used framework in the sciences for parameter estimation and inference. It is typically performed by fitting a mathematical model to noisy experimental data. There are two significant sources of…

We provide non-asymptotic excess risk guarantees for statistical learning in a setting where the population risk with respect to which we evaluate the target parameter depends on an unknown nuisance parameter that must be estimated from…

Logistic regression is one of the most popular methods in binary classification, wherein estimation of model parameters is carried out by solving the maximum likelihood (ML) optimization problem, and the ML estimator is defined to be the…

The paper introduces a new regression model designed for situations where both the response and covariates are non-stationary extremes. This method is specifically designed for situations where both the response variable and covariates are…

This paper investigates the asymptotic distribution of the maximum-likelihood estimate (MLE) in multinomial logistic models in the high-dimensional regime where dimension and sample size are of the same order. While classical large-sample…

Accurately quantifying the increased risks of climate extremes requires generating large ensembles of climate realization across a wide range of emissions scenarios, which is computationally challenging for conventional Earth System Models.…

We are motivated by problems that arise in a number of applications such as Online Marketing and explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…

Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…

Ensemble Kalman methods were initially developed to solve nonlinear data assimilation problems in oceanography, but are now popular in applications far beyond their original use cases. Of particular interest is climate model calibration. As…

Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically need to be estimated from the dataset. This article provides…

A new approach for signal parametrization, which consists of a specific regression model incorporating a discrete hidden logistic process, is proposed. The model parameters are estimated by the maximum likelihood method performed by a…

Most machine learning techniques are based upon statistical learning theory, often simplified for the sake of computing speed. This paper is focused on the uncertainty aspect of mathematical modeling in machine learning. Regression analysis…