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Recently maximum pseudo-likelihood (MPL) inference method has been successfully applied to statistical physics models with intractable likelihoods. We use information theory to derive a relation between the pseudo-likelihood and likelihood…

Disordered Systems and Neural Networks · Physics 2015-06-18 Alexander Mozeika , Onur Dikmen , Joonas Piili

We present a distributional approach to theoretical analyses of reinforcement learning algorithms for constant step-sizes. We demonstrate its effectiveness by presenting simple and unified proofs of convergence for a variety of…

Machine Learning · Computer Science 2020-03-30 Philip Amortila , Doina Precup , Prakash Panangaden , Marc G. Bellemare

Probabilistic models based on continuous latent spaces, such as variational autoencoders, can be understood as uncountable mixture models where components depend continuously on the latent code. They have proven to be expressive tools for…

Machine Learning · Computer Science 2024-06-27 Alvaro H. C. Correia , Gennaro Gala , Erik Quaeghebeur , Cassio de Campos , Robert Peharz

We introduce a novel random integration algorithm that boasts both high convergence order and polynomial tractability for functions characterized by sparse frequencies or rapidly decaying Fourier coefficients. Specifically, for integration…

Numerical Analysis · Mathematics 2025-12-30 Liang Chen , Minqiang Xu , Haizhang Zhang

Measurement error is a pervasive issue which renders the results of an analysis unreliable. The measurement error literature contains numerous correction techniques, which can be broadly divided into those which aim to produce exactly…

Methodology · Statistics 2021-11-08 Dylan Spicker , Michael P Wallace , Grace Y Yi

We give a general method for rounding linear programs that combines the commonly used iterated rounding and randomized rounding techniques. In particular, we show that whenever iterated rounding can be applied to a problem with some slack,…

Data Structures and Algorithms · Computer Science 2019-07-19 Nikhil Bansal

Finite population inference is a central goal in survey sampling. Probability sampling is the main statistical approach to finite population inference. Challenges arise due to high cost and increasing non-response rates. Data integration…

Methodology · Statistics 2020-01-13 Shu Yang , Jae Kwang Kim

In this paper, we establish sublinear and linear convergence of fixed point iterations generated by averaged operators in a Hilbert space. Our results are achieved under a bounded H\"older regularity assumption which generalizes the…

Optimization and Control · Mathematics 2018-08-16 Jonathan M. Borwein , Guoyin Li , Matthew K. Tam

This paper is concerned with the study of the consistency of a variational method for probability measure quantization, deterministically realized by means of a minimizing principle, balancing power repulsion and attraction potentials. The…

Functional Analysis · Mathematics 2013-10-07 Massimo Fornasier , Jan-Christian Hütter

Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…

Methodology · Statistics 2023-05-26 Yanbo Tang

We consider estimating the proportion of random variables for two types of composite null hypotheses: (i) the means or medians of the random variables belonging to a non-empty, bounded interval; (ii) the means or medians of the random…

Statistics Theory · Mathematics 2025-03-24 Xiongzhi Chen

In this paper we develop randomized Krylov subspace methods for efficiently computing regularized solutions to large-scale linear inverse problems. Building on the recently developed randomized Gram-Schmidt process, where sketched inner…

Numerical Analysis · Mathematics 2025-08-29 Julianne Chung , Silvia Gazzola

This paper is devoted to the estimators of the mean that provide strong non-asymptotic guarantees under minimal assumptions on the underlying distribution. The main ideas behind proposed techniques are based on bridging the notions of…

Statistics Theory · Mathematics 2019-05-07 Stanislav Minsker

In this paper we study predictive mean matching mass imputation estimators to integrate data from probability and non-probability samples. We consider two approaches: matching predicted to predicted ($\hat{y}-\hat{y}$~matching; PMM A) and…

Methodology · Statistics 2024-06-18 Piotr Chlebicki , Łukasz Chrostowski , Maciej Beręsewicz

The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint…

Probability · Mathematics 2024-02-14 Johannes Heiny , Carolin Kleemann

The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio $s/d$, where $s$ and $d$ encode the…

Machine Learning · Statistics 2017-08-01 Francois-Xavier Briol , Chris J. Oates , Jon Cockayne , Wilson Ye Chen , Mark Girolami

The article is devoted to the estimation of the rate of convergence of integral functionals of a Markov process. Under the assumption that the given Markov process admits a transition probability density which is differentiable in $t$ and…

Probability · Mathematics 2015-08-03 I. Ganychenko , V. Knopova , A. Kulik

We present a convergence proof of the projective integration method for a class of deterministic multi-dimensional multi-scale systems which are amenable to centre manifold theory. The error is shown to contain contributions associated with…

Dynamical Systems · Mathematics 2013-02-01 John Maclean , Georg A. Gottwald

We introduce Lipschitz continuous and $C^{1,1}$ geometric approximation and interpolation methods for sampled bounded uniformly continuous functions over compact sets and over complements of bounded open sets in $\mathbb{R}^n$ by using…

Metric Geometry · Mathematics 2016-09-29 Kewei Zhang , Elaine Crooks , Antonio Orlando

In this paper, we provide strong $L_2$-rates of approximation of the integral-type functionals of Markov processes by integral sums. We improve the method developed in [2]. Under assumptions on the process formulated only in terms of its…

Probability · Mathematics 2015-08-13 Iurii Ganychenko