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This article addresses online variational estimation in parametric state-space models. We propose a new procedure for efficiently computing the evidence lower bound and its gradient in a streaming-data setting, where observations arrive…

Methodology · Statistics 2026-02-09 Mathis Chagneux , Mathias Müller , Pierre Gloaguen , Sylvain Le Corff , Jimmy Olsson

We build on the formalism developed in [arXiv:1906.08372v1] to propose new representations of solutions to Stein equations. We provide new uniform and non uniform bounds on these solutions (a.k.a.\ Stein factors). We use these…

Probability · Mathematics 2019-11-14 Marie Ernst , Yvik Swan

We analyzed the effect of the deviation of the exact distribution of the p-values from the uniform distribution on the Kolmogorov-Smirnov (K-S) test that was implemented as the second-level randomness test. We derived an inequality that…

Methodology · Statistics 2021-10-18 Akihiro Yamaguchi , Asaki Saito

We consider parameter estimation in distributed networks, where each sensor in the network observes an independent sample from an underlying distribution and has $k$ bits to communicate its sample to a centralized processor which computes…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-07-23 Yanjun Han , Ayfer Özgür , Tsachy Weissman

Covariate shift occurs when the distribution of input features differs between the training and testing phases. In covariate shift, estimating an unknown function's moment is a classical problem that remains under-explored, despite its…

Machine Learning · Statistics 2025-07-01 Zhen Zhang , Xin Liu , Shaoli Wang , Jiaye Teng

I present an analytic method for estimating the errors in fitting a distribution. A well-known theorem from statistics gives the minimum variance bound (MVB) for the uncertainty in estimating a set of parameters $\l_i$, when a distribution…

Astrophysics · Physics 2009-10-22 Andrew Gould

This paper generalizes the notion of sufficiency for estimation problems beyond maximum likelihood. In particular, we consider estimation problems based on Jones et al. and Basu et al. likelihood functions that are popular among…

Statistics Theory · Mathematics 2024-02-29 Atin Gayen , M. Ashok Kumar

Power law distributions, in particular Pareto distributions, describe data across diverse areas of study. We have developed a package in R to estimate the tail index for such datasets focusing on speed (in particular with large datasets),…

Methodology · Statistics 2020-06-19 Ranjiva Munasinghe , Pathum Kossinna , Dovini Jayasinghe , Dilanka Wijeratne

We present a distribution optimization framework that significantly improves confidence bounds for various risk measures compared to previous methods. Our framework encompasses popular risk measures such as the entropic risk measure,…

Machine Learning · Computer Science 2023-06-13 Hao Liang , Zhi-quan Luo

Kolmogorov's exponential inequalities are basic tools for studying the strong limit theorems such as the classical laws of the iterated logarithm for both independent and dependent random variables. This paper establishes the Kolmogorov…

Probability · Mathematics 2020-05-08 Li-Xin Zhang

Power-law distributions have been widely observed in different areas of scientific research. Practical estimation issues include how to select a threshold above which observations follow a power-law distribution and then how to estimate the…

Statistics Theory · Mathematics 2020-02-13 Holger Drees , Anja Janßen , Sidney I. Resnick , Tiandong Wang

We review a finite-sampling exponential bound due to Serfling and discuss related exponential bounds for the hypergeometric distribution. We then discuss how such bounds motivate some new results for two-sample empirical processes. Our…

Statistics Theory · Mathematics 2017-02-20 Evan Greene , Jon A. Wellner

Data representation techniques have made a substantial contribution to advancing data processing and machine learning (ML). Improving predictive power was the focus of previous representation techniques, which unfortunately perform rather…

Machine Learning · Computer Science 2022-05-24 Qiyou Duan , Hadi Ghauch , Taejoon Kim

In the numerical treatment of large-scale Sylvester and Lyapunov equations, projection methods require solving a reduced problem to check convergence. As the approximation space expands, this solution takes an increasing portion of the…

Numerical Analysis · Mathematics 2017-02-03 Davide Palitta , Valeria Simoncini

Here I present the analytic form of two common distance metrics, the symmetrised Kullback-Leibler Divergence and the Kolmogorov-Smirnov statistic, as well as an extension of the Kolmogorov-Smirnov statistic for comparing theoretical gamma…

Statistics Theory · Mathematics 2018-02-06 Colin M. McCrimmon

We present a general method for deriving collapsed variational inference algo- rithms for probabilistic models in the conjugate exponential family. Our method unifies many existing approaches to collapsed variational inference. Our…

Machine Learning · Computer Science 2012-12-05 James Hensman , Magnus Rattray , Neil D. Lawrence

Decision making under uncertainty is at the heart of any autonomous system acting with imperfect information. The cost of solving the decision making problem is exponential in the action and observation spaces, thus rendering it unfeasible…

Artificial Intelligence · Computer Science 2024-06-18 Tom Yotam , Vadim Indelman

Markov decision processes are useful models of concurrency optimisation problems, but are often intractable for exhaustive verification methods. Recent work has introduced lightweight approximative techniques that sample directly from…

Logic in Computer Science · Computer Science 2015-03-24 Axel Legay , Sean Sedwards , Louis-Marie Traonouez

We propose an adaptive randomized truncation estimator for Krylov subspace methods that optimizes the trade-off between the solution variance and the computational cost, while remaining unbiased. The estimator solves a constrained…

Numerical Analysis · Mathematics 2025-04-08 Qi Luo , Florian Schäfer

A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…

Methodology · Statistics 2015-11-24 Rong Zhu , Ping Ma , Michael W. Mahoney , Bin Yu