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Uncertainty estimation is a key component in any deployed machine learning system. One way to evaluate uncertainty estimation is using "out-of-distribution" (OoD) detection, that is, distinguishing between the training data distribution and…

Machine Learning · Computer Science 2021-12-03 Haiwen Huang , Joost van Amersfoort , Yarin Gal

This paper is focused on derivations of data-processing and majorization inequalities for $f$-divergences, and their applications in information theory and statistics. For the accessibility of the material, the main results are first…

Information Theory · Computer Science 2020-01-08 Igal Sason

In this work we study the problem of inferring a discrete probability distribution using both expert knowledge and empirical data. This is an important issue for many applications where the scarcity of data prevents a purely empirical…

Machine Learning · Computer Science 2020-01-08 Rémi Besson , Erwan Le Pennec , Stéphanie Allassonnière

Distribution shift is an important concern in deep image classification, produced either by corruption of the source images, or a complete change, with the solution involving domain adaptation. While the primary goal is to improve accuracy…

Machine Learning · Statistics 2021-10-19 Tiago Salvador , Vikram Voleti , Alexander Iannantuono , Adam Oberman

We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…

Machine Learning · Computer Science 2013-05-15 Siu-On Chan , Ilias Diakonikolas , Rocco A. Servedio , Xiaorui Sun

Information divergence functions play a critical role in statistics and information theory. In this paper we show that a non-parametric f-divergence measure can be used to provide improved bounds on the minimum binary classification…

Information Theory · Computer Science 2015-02-11 Visar Berisha , Alan Wisler , Alfred O. Hero , Andreas Spanias

When some treatments are ordered according to the categories of an ordinal categorical variable (e.g., extent of side effects) in a monotone order, one might be interested in knowing wether the treatments are equally effective or not. One…

Methodology · Statistics 2014-02-24 Nirian Martín , Raquel Mata , Leandro Pardo

There are many applications that benefit from computing the exact divergence between 2 discrete probability measures, including machine learning. Unfortunately, in the absence of any assumptions on the structure or independencies within…

Machine Learning · Computer Science 2023-10-16 Loong Kuan Lee , Nico Piatkowski , François Petitjean , Geoffrey I. Webb

For testing goodness of fit it is very popular to use either the chi square statistic or G statistics (information divergence). Asymptotically both are chi square distributed so an obvious question is which of the two statistics that has a…

Statistics Theory · Mathematics 2012-06-19 Peter Harremoës , Gábor Tusnády

We describe a method for fitting distributions to data which only requires knowledge of the parametric form of either the signal or the background but not both. The unknown distribution is fit using a non-parametric kernel density…

Data Analysis, Statistics and Probability · Physics 2015-06-03 Wolfgang A. Rolke , Angel M. López

In computational histopathology algorithms now outperform humans on a range of tasks, but to date none are employed for automated diagnoses in the clinic. Before algorithms can be involved in such high-stakes decisions they need to "know…

Computer Vision and Pattern Recognition · Computer Science 2022-10-19 Lea Goetz

Decisions are often based on imprecise, uncertain or vague information. Likewise, the consequences of an action are often equally unpredictable, thus putting the decision maker into a twofold jeopardy. Assuming that the effects of an action…

General Economics · Economics 2022-05-03 Stefan Rass , Sandra König , Stefan Schauer

In this paper we establish lower bounds on information divergence of a distribution on the integers from a Poisson distribution. These lower bounds are tight and in the cases where a rate of convergence in the Law of Thin Numbers can be…

Probability · Mathematics 2016-01-19 Peter Harremoës , Oliver Johnson , Ioannis Kontoyiannis

Standard approaches for uncertainty quantification in deep learning and physics-informed learning have persistent limitations. Indicatively, strong assumptions regarding the data likelihood are required, the performance highly depends on…

Artificial Intelligence · Computer Science 2023-10-23 Qianli Shen , Wai Hoh Tang , Zhun Deng , Apostolos Psaros , Kenji Kawaguchi

Particle filtering is used to compute good nonlinear estimates of complex systems. It samples trajectories from a chosen distribution and computes the estimate as a weighted average. Easy-to-sample distributions often lead to degenerate…

Machine Learning · Computer Science 2021-10-07 Fernando Gama , Nicolas Zilberstein , Richard G. Baraniuk , Santiago Segarra

A method is described, which computes from an observed sample of events upper limits for production rates of particles, or, in case of appearance of a signal, the probability for an upwards fluctuation of the background. For any candidate,…

High Energy Physics - Experiment · Physics 2010-10-27 P. Bock

This paper studies the complexity of estimating Renyi divergences of discrete distributions: $p$ observed from samples and the baseline distribution $q$ known \emph{a priori}. Extending the results of Acharya et al. (SODA'15) on estimating…

Information Theory · Computer Science 2017-02-09 Maciej Skorski

When data do not conform to the hypothesis of a known sampling-variance, the fitting of a constant to the set of measured values is a long debated problem. Given the data, the fitting would require to find which measurand value is most…

Data Analysis, Statistics and Probability · Physics 2011-09-27 Giovanni Mana , Maria Mirabela Predescu

Consider a random sample $X_1 , X_2 , ..., X_n$ drawn independently and identically distributed from some known sampling distribution $P_X$. Let $X_{(1)} \le X_{(2)} \le ... \le X_{(n)}$ represent the order statistics of the sample. The…

Information Theory · Computer Science 2020-09-28 Alex Dytso , Martina Cardone , Cynthia Rush

The ratio between the probability that two distributions $R$ and $P$ give to points $x$ are known as importance weights or propensity scores and play a fundamental role in many different fields, most notably, statistics and machine…

Machine Learning · Computer Science 2021-03-11 Parikshit Gopalan , Omer Reingold , Vatsal Sharan , Udi Wieder