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We propose a new Bayesian strategy for adaptation to smoothness in nonparametric models based on heavy tailed series priors. We illustrate it in a variety of settings, showing in particular that the corresponding Bayesian posterior…

Statistics Theory · Mathematics 2024-05-30 Sergios Agapiou , Ismaël Castillo

Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations (Efron, 2013, Science). While it has…

Statistics Theory · Mathematics 2020-09-11 Abhik Ghosh , Tuhin Majumder , Ayanendranath Basu

Solutions of the bivariate, linear errors-in-variables estimation problem with unspecified errors are expected to be invariant under interchange and scaling of the coordinates. The appealing model of normally distributed true values and…

Statistics Theory · Mathematics 2012-02-07 David Leonard

The covariate shift is a challenging problem in supervised learning that results from the discrepancy between the training and test distributions. An effective approach which recently drew a considerable attention in the research community…

Machine Learning · Computer Science 2013-11-27 Yun-Qian Miao , Ahmed K. Farahat , Mohamed S. Kamel

Consider the communication-constrained problem of nonparametric function estimation, in which each distributed terminal holds multiple i.i.d. samples. Under certain regularity assumptions, we characterize the minimax optimal rates for all…

Machine Learning · Computer Science 2025-01-15 Deheng Yuan , Tao Guo , Zhongyi Huang

We address the regression problem under the constraint of demographic parity, a commonly used fairness definition. Recent studies have revealed fair minimax optimal regression algorithms, the most accurate algorithms that adhere to the…

Machine Learning · Statistics 2025-06-18 Kazuto Fukuchi

In this manuscript, we study the problem of scalar-on-distribution regression; that is, instances where subject-specific distributions or densities, or in practice, repeated measures from those distributions, are the covariates related to a…

Methodology · Statistics 2024-04-22 Bohao Tang , Sandipan Pramanik , Yi Zhao , Brian Caffo , Abhirup Datta

Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate…

Statistics Theory · Mathematics 2009-09-29 Anton Schick , Wolfgang Wefelmeyer

Probabilistic Regression refers to predicting a full probability density function for the target conditional on the features. We present a nonparametric approach to this problem which combines base classifiers (typically gradient boosted…

Machine Learning · Computer Science 2022-10-31 Brian Lucena

We offer a general Bayes theoretic framework to derive posterior contraction rates under a hierarchical prior design: the first-step prior serves to assess the model selection uncertainty, and the second-step prior quantifies the prior…

Statistics Theory · Mathematics 2021-02-12 Qiyang Han

The task of calibration is to retrospectively adjust the outputs from a machine learning model to provide better probability estimates on the target variable. While calibration has been investigated thoroughly in classification, it has not…

Machine Learning · Statistics 2018-06-21 Hao Song , Meelis Kull , Peter Flach

Smooth Estimation of probability density and distribution functions from its sample is an attractive and an important problem that has applications in several fields such as, business, medicine, and environment. This article introduces a…

Methodology · Statistics 2025-04-02 Elsayed A. H. Elamir

This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…

Statistics Theory · Mathematics 2010-01-13 Yuan Liao , Wenxin Jiang

In this paper, inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution is thoroughly investigated from the frequentist viewpoint. The higher-order validity of the profile…

Statistics Theory · Mathematics 2009-09-29 Guang Cheng , Michael R. Kosorok

This paper focuses on the problem of unbounded density ratio estimation -- an understudied yet critical challenge in statistical learning -- and its application to covariate shift adaptation. Much of the existing literature assumes that the…

Machine Learning · Statistics 2026-04-01 Ren-Rui Liu , Jun Fan , Lei Shi , Zheng-Chu Guo

We develop and analyze $M$-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variational characterization of $f$-divergences, which allows the…

Statistics Theory · Mathematics 2016-11-18 XuanLong Nguyen , Martin J. Wainwright , Michael I. Jordan

The class of Cressie-Read empirical likelihoods are constructed with weights derived at a minimum distance from the empirical distribution in the Cressie-Read family of divergences indexed by $\gamma$ under the constraint of an unbiased set…

Statistics Theory · Mathematics 2017-11-03 Laura Turbatu

We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite-dimensional dictionary. We propose a novel flexible composite…

Statistics Theory · Mathematics 2015-12-03 Patrick L. Combettes , Saverio Salzo , Silvia Villa

In the setting of dominated statistical models, we provide conditions yielding strong continuity of the posterior distribution with respect to the observed data. We show some applications, with special focus on exponential models.

Statistics Theory · Mathematics 2019-09-24 Emanuele Dolera , Edoardo Mainini

We focus on the increasingly important area of sparse regression problems where there are many variables and the effects of a large subset of these are negligible. This paper describes the construction of hierarchical prior distributions…

Methodology · Statistics 2014-07-23 Jim E. Griffin , Philip J. Brown