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We compute the expected value of the Kullback-Leibler divergence to various fundamental statistical models with respect to canonical priors on the probability simplex. We obtain closed formulas for the expected model approximation errors,…

Machine Learning · Statistics 2014-06-18 Guido F. Montufar , Johannes Rauh

We propose an algorithm to estimate the path-gradient of both the reverse and forward Kullback-Leibler divergence for an arbitrary manifestly invertible normalizing flow. The resulting path-gradient estimators are straightforward to…

Machine Learning · Computer Science 2022-07-19 Lorenz Vaitl , Kim A. Nicoli , Shinichi Nakajima , Pan Kessel

We give a comprehensive theoretical characterization of a nonparametric estimator for the $L_2^2$ divergence between two continuous distributions. We first bound the rate of convergence of our estimator, showing that it is…

Machine Learning · Statistics 2014-10-31 Akshay Krishnamurthy , Kirthevasan Kandasamy , Barnabas Poczos , Larry Wasserman

In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the…

Numerical Analysis · Mathematics 2014-08-11 Frank J. Pinski , Gideon Simpson , Andrew M. Stuart , Hendrik Weber

In this paper, we discuss a property of the Kullback--Leibler divergence measured between two models of the family of the location-scale distributions. We show that, if model $M_1$ and model $M_2$ are represented by location-scale…

Statistics Theory · Mathematics 2016-04-08 Cristiano Villa

This paper addresses the problem of distributed detection in fixed and switching networks. A network of agents observe partially informative signals about the unknown state of the world. Hence, they collaborate with each other to identify…

Systems and Control · Computer Science 2016-01-01 Shahin Shahrampour , Alexander Rakhlin , Ali Jadbabaie

Universal hypothesis testing refers to the problem of deciding whether samples come from a nominal distribution or an unknown distribution that is different from the nominal distribution. Hoeffding's test, whose test statistic is equivalent…

Information Theory · Computer Science 2017-11-15 Pengfei Yang , Biao Chen

This study tackles the efficient estimation of Kullback-Leibler (KL) Divergence in Dirichlet Mixture Models (DMM), crucial for clustering compositional data. Despite the significance of DMMs, obtaining an analytically tractable solution for…

Machine Learning · Statistics 2024-03-20 Samyajoy Pal , Christian Heumann

We consider the problem of estimating the mean of a distribution supported by the $k$-dimensional probability simplex in the setting where an $\varepsilon$ fraction of observations are subject to adversarial corruption. A simple particular…

Statistics Theory · Mathematics 2020-02-04 Amir-Hossein Bateni , Arnak S. Dalalyan

This letter provides an adaptive resampling method. It determines the number of particles to resample so that the Kullback-Leibler distance (KLD) between distribution of particles before resampling and after resampling does not exceed a…

Applications · Statistics 2017-07-31 Tiancheng Li , Shudong Sun , Tariq Pervez Sattar

We study the problem of model selection type aggregation with respect to the Kullback-Leibler divergence for various probabilistic models. Rather than considering a convex combination of the initial estimators $f_1, \ldots, f_N$, our…

Statistics Theory · Mathematics 2016-01-22 Cristina Butucea , Jean-François Delmas , Anne Dutfoy , Richard Fischer

We study the gradient flow for a relaxed approximation to the Kullback-Leibler (KL) divergence between a moving source and a fixed target distribution. This approximation, termed the KALE (KL approximate lower-bound estimator), solves a…

Machine Learning · Statistics 2021-11-01 Pierre Glaser , Michael Arbel , Arthur Gretton

This paper introduces two new robust methods for estimation of parameters in a given parametric family. The first method is that of `minimum weighted L2', effectively minimising an estimate of the integrated (and possibly weighted) squared…

Methodology · Statistics 2026-02-23 Nils Lid Hjort

Good robust estimators can be tuned to combine a high breakdown point and a specified asymptotic efficiency at a central model. This happens in regression with MM- and tau-estimators among others. However, the finite-sample efficiency of…

Statistics Theory · Mathematics 2013-11-21 Ricardo Maronna , Víctor Yohai

In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…

Probability · Mathematics 2016-06-02 Frank Pinski , Gideon Simpson , Andrew Stuart , Hendrik Weber

In this paper we derive lower bounds in minimax sense for estimation of the instantaneous volatility if the diffusion type part cannot be observed directly but under some additional Gaussian noise. Three different models are considered. Our…

Statistics Theory · Mathematics 2010-02-17 Axel Munk , Johannes Schmidt-Hieber

Bayesian neural networks (BNNs) are state-of-the-art machine learning methods that can naturally regularize and systematically quantify uncertainties using their stochastic parameters. Kullback-Leibler (KL) divergence-based variational…

Machine Learning · Computer Science 2024-12-10 Ponkrshnan Thiagarajan , Susanta Ghosh

We study the problem of closeness testing for continuous distributions and its implications for causal discovery. Specifically, we analyze the sample complexity of distinguishing whether two multidimensional continuous distributions are…

Machine Learning · Computer Science 2025-03-11 Fateme Jamshidi , Sina Akbari , Negar Kiyavash

We pose the Kantorovich optimal transport problem as a min-max problem with a Nash equilibrium that can be obtained dynamically via a two-player game, providing a framework for approximating optimal couplings. We prove convergence of the…

Optimization and Control · Mathematics 2025-05-28 Lauren Conger , Franca Hoffmann , Ricardo Baptista , Eric Mazumdar

We study a worst-case approach to measure the sensitivity to model misspecification in the performance analysis of stochastic systems. The situation of interest is when only minimal parametric information is available on the form of the…

Probability · Mathematics 2015-07-14 Henry Lam
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