Real-world applications of machine learning tools in high-stakes domains are often
regulated to be fair, in the sense that the predicted target should satisfy some quantitative …

Given two probability measures, P and Q defined on a measurable space, S, the integral
probability metric (IPM) is defined as F (P, Q)=\sup\left {\left | S f\, d PS f\, d Q\right |\,:\, f ∈ …

A class of distance measures on probabilities--the integral probability metrics (IPMs)--is
addressed: these include the Wasserstein distance, Dudley metric, and Maximum Mean …

We report closed-form formula for calculating the Chi square and higher-order Chi distances
between statistical distributions belonging to the same exponential family with affine natural …

We unify f-divergences, Bregman divergences, surrogate regret bounds, proper scoring
rules, cost curves, ROC-curves and statistical information. We do this by systematically …

This paper presents a new approach to optimal sensor design for structural health
monitoring (SHM) applications using a modified f-divergence objective functional. One of the …

The families of f-divergences (eg the Kullback-Leibler divergence) and Integral Probability
Metrics (eg total variation distance or maximum mean discrepancies) are widely used to …

Clustering categorical distributions in the probability simplex is a fundamental task met in
many applications dealing with normalized histograms. Traditionally, differential-geometric …

Broadly speaking, an information measure is any function of one or more probability
distributions. An entropy is an information measure that have units of entropy—negative …

We generalise the classical Pinsker inequality which relates variational divergence to
Kullback-Liebler divergence in two ways: we consider arbitrary f-divergences in place of KL …