Related papers: Pseudorandomness, symmetry, smoothing: II

Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…

This paper derives non-asymptotic error bounds for nonlinear stochastic approximation algorithms in the Wasserstein-$p$ distance. To obtain explicit finite-sample guarantees for the last iterate, we develop a coupling argument that compares…

This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-gaussian and sub-gamma bounds previously studied in this context. The proof leverages a…

This article establishes novel strong uniform laws of large numbers for randomly weighted sums such as bootstrap means. By leveraging recent advances, these results extend previous work in their general applicability to a wide range of…

We study mean convergence results for weighted multiple ergodic averages defined by commuting transformations with iterates given by integer polynomials in several variables. Roughly speaking, we prove that a bounded sequence is a good…

We study weighted sums of free identically distributed self-adjoint random variables with weights chosen randomly from the unit sphere and show that the Kolmogorov distance between the distribution of such a weighted sum and Wigner's…

We propose a methodology for modeling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalized random measures, we consider a prior distribution for a collection of discrete random…

Mixtures of Gaussian (or normal) distributions arise in a variety of application areas. Many heuristics have been proposed for the task of finding the component Gaussians given samples from the mixture, such as the EM algorithm, a…

In this expository note, we give a modern proof of Hanson-Wright inequality for quadratic forms in sub-gaussian random variables. We deduce a useful concentration inequality for sub-gaussian random vectors. Two examples are given to…

We study the rates of convergence of the posterior distribution for Bayesian density estimation with Dirichlet mixtures of normal distributions as the prior. The true density is assumed to be twice continuously differentiable. The bandwidth…

We describe a framework to build distances by measuring the tightness of inequalities, and introduce the notion of proper statistical divergences and improper pseudo-divergences. We then consider the H\"older ordinary and reverse…

We discuss Bayesian inference for a known-mean Gaussian model with a compound symmetric variance-covariance matrix. Since the space of such matrices is a linear subspace of that of positive definite matrices, we utilize the methods of…

We propose a new method of histogram construction, providing a fully Bayesian approach to irregular histograms. Our procedure applies Bayesian model selection to a piecewise constant model of the underlying distribution, resulting in a…

Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior…

We establish concentration rates for estimation of treatment effects in experiments that incorporate prior sources of information -- such as past pilots, related studies, or expert assessments -- whose external validity is uncertain. Each…

We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…

Bayesian neural networks (BNNs) are a principled approach to modeling predictive uncertainties in deep learning, which are important in safety-critical applications. Since exact Bayesian inference over the weights in a BNN is intractable,…

We give a randomness-efficient homomorphism test in the low soundness regime for functions, $f: G\to \mathbb{U}_t$, from an arbitrary finite group $G$ to $t\times t$ unitary matrices. We show that if such a function passes a derandomized…

The goal of this article is two-fold: in a first part, we prove Azuma-Hoeffding type concentration inequalities around the drift for the displacement of non-elementary random walks on hyperbolic spaces. For a proper hyperbolic space $M$, we…

Let $Y$ be a nonnegative random variable with mean $\mu$ and finite positive variance $\sigma^2$, and let $Y^s$, defined on the same space as $Y$, have the $Y$ size biased distribution, that is, the distribution characterized by…