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The conditional independence assumption has recently appeared in a growing body of literature on the estimation of multivariate mixtures. We consider here conditionally independent multivariate mixtures of power series distributions with…

Statistics Theory · Mathematics 2025-09-09 Fadoua Balabdaoui , Harald Besdziek , Yong Wang

To get Bayesian neural networks to perform comparably to standard neural networks it is usually necessary to artificially reduce uncertainty using a "tempered" or "cold" posterior. This is extremely concerning: if the prior is accurate,…

Machine Learning · Statistics 2021-04-28 Laurence Aitchison

The asymptotic properties of Bayesian Neural Networks (BNNs) have been extensively studied, particularly regarding their approximations by Gaussian processes in the infinite-width limit. We extend these results by showing that posterior…

Machine Learning · Statistics 2025-02-07 Francesco Caporali , Stefano Favaro , Dario Trevisan

Maximum approximate Bernstein likelihood estimates of the baseline density function and the regression coefficients in the proportional hazard regression models based on interval-censored event time data are proposed. This results in not…

Methodology · Statistics 2020-12-25 Zhong Guan

It has long been known that for the comparison of pairwise nested models, a decision based on the Bayes factor produces a consistent model selector (in the frequentist sense). Here we go beyond the usual consistency for nested pairwise…

Statistics Theory · Mathematics 2009-04-21 George Casella , F. Javier Girón , M. Lina Martínez , Elías Moreno

We consider an infinite-dimensional Gaussian regression model, equipped with a high-dimensional Gaussian prior. We address the frequentist validity of posterior credible sets for a vector of linear functionals. We specify conditions for a…

Statistics Theory · Mathematics 2024-11-12 Gustav Rømer

In this paper the problem of learning appropriate bias for an environment of related tasks is examined from a Bayesian perspective. The environment of related tasks is shown to be naturally modelled by the concept of an {\em objective}…

Machine Learning · Computer Science 2019-11-15 Jonathan Baxter

We study posterior contraction rates for a class of deep Gaussian process priors applied to the nonparametric regression problem under a general composition assumption on the regression function. It is shown that the contraction rates can…

Statistics Theory · Mathematics 2022-08-16 Gianluca Finocchio , Johannes Schmidt-Hieber

We demonstrate that a prior influence on the posterior distribution of covariance matrix vanishes as sample size grows. The assumptions on a prior are explicit and mild. The results are valid for a finite sample and admit the dimension $p$…

Statistics Theory · Mathematics 2019-06-28 Igor Silin

Balanced representation learning methods have been applied successfully to counterfactual inference from observational data. However, approaches that account for survival outcomes are relatively limited. Survival data are frequently…

Machine Learning · Statistics 2021-03-04 Paidamoyo Chapfuwa , Serge Assaad , Shuxi Zeng , Michael J. Pencina , Lawrence Carin , Ricardo Henao

The martingale posterior framework is a generalization of Bayesian inference where one elicits a sequence of one-step ahead predictive densities instead of the likelihood and prior. Posterior sampling then involves the imputation of unseen…

Statistics Theory · Mathematics 2026-03-02 Edwin Fong , Andrew Yiu

We consider nonparametric Bayesian inference in a reflected diffusion model $dX_t = b (X_t)dt + \sigma(X_t) dW_t,$ with discretely sampled observations $X_0, X_\Delta, \dots, X_{n\Delta}$. We analyse the nonlinear inverse problem…

Statistics Theory · Mathematics 2020-05-26 Richard Nickl , Jakob Söhl

This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of…

Statistics Theory · Mathematics 2007-08-22 Stephen G. Walker , Antonio Lijoi , Igor Prünster

This article considers Bayesian model selection via mean-field (MF) variational approximation. Towards this goal, we study the non-asymptotic properties of MF inference under the Bayesian framework that allows latent variables and model…

Methodology · Statistics 2023-12-29 Yangfan Zhang , Yun Yang

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…

Machine Learning · Statistics 2020-12-29 Simón Rodríguez Santana , Daniel Hernández-Lobato

We derive posterior contraction rates (PCRs) and finite-sample Bernstein von Mises (BvM) results for non-parametric Bayesian models by extending the diffusion-based framework of Mou et al. (2024) to the infinite-dimensional setting. The…

Machine Learning · Statistics 2026-03-25 Enric Alberola-Boloix , Ioar Casado-Telletxea

Most NLP datasets are not annotated with protected attributes such as gender, making it difficult to measure classification bias using standard measures of fairness (e.g., equal opportunity). However, manually annotating a large dataset…

Computation and Language · Computer Science 2020-04-28 Kawin Ethayarajh

Given a Wiener process with unknown and unobservable drift, we try to estimate this drift as effectively but also as quickly as possible, in the presence of a quadratic penalty for the estimation error and of a fixed, positive cost per unit…

Statistics Theory · Mathematics 2019-05-24 Erik Ekström , Ioannis Karatzas , Juozas Vaicenavicius

This paper aims to examine the characteristics of the posterior distribution of covariance/precision matrices in a "large $p$, large $n$" scenario, where $p$ represents the number of variables and $n$ is the sample size. Our analysis…

Statistics Theory · Mathematics 2026-02-02 Partha Sarkar , Kshitij Khare , Malay Ghosh , Matt P. Wand

Deep learning methods continue to have a decided impact on machine learning, both in theory and in practice. Statistical theoretical developments have been mostly concerned with approximability or rates of estimation when recovering…

Statistics Theory · Mathematics 2021-04-07 Yuexi Wang , Veronika Ročková