The global biodiversity crisis is one of humanity's most urgent problems, but even
quantifying biological diversity is a difficult mathematical and conceptual challenge. This …

We derive limit distributions for various empirical regularized optimal transport quantities
between probability distributions supported on a finite metric space and show their bootstrap …

We consider the “partial information decomposition”(PID) problem, which aims to
decompose the information that a set of source random variables provide about a target …

In many machine learning systems that jointly learn from multiple modalities, a core research
question is to understand the nature of multimodal interactions: the emergence of new task …

Given a set of discrete probability distributions, the minimum entropy coupling is the
minimum entropy joint distribution that has the input distributions as its marginals. This has …

This paper derives new bounds on the difference of the entropies of two discrete random
variables in terms of the local and total variation distances between their probability mass …

We consider the problem of communicating exogenous information by means of Markov
decision process trajectories. This setting, which we call a Markov coding game (MCG) …

Given two discrete random variables X and Y, with probability distributions p=(p 1,..., pn) and
q=(q 1,..., qm), respectively, let us denote by C (p, q) the set of all couplings of p and q, that …

It is well known that the entropy H (X) of a discrete random variable X is always greater than
or equal to the entropy H (f (X)) of a function f of X, with equality if and only if f is one-to-one …

This book brings new mathematical rigour to the ongoing vigorous debate on how to
quantify biological diversity. The question" what is diversity?" has surprising mathematical …