Related papers: Determinantal Probability: Basic Properties and Co…
A new type of dependent thinning for point processes in continuous space is proposed, which leverages the advantages of determinantal point processes defined on finite spaces and, as such, is particularly amenable to statistical, numerical,…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
Adding a column of numbers produces "carries" along the way. We show that random digits produce a pattern of carries with a neat probabilistic description: the carries form a one-dependent determinantal point process. This makes it easy to…
Determinantal point processes (DPPs) are point process models that naturally encode diversity between the points of a given realization, through a positive definite kernel $K$. DPPs possess desirable properties, such as exact sampling or…
We define multideterminantal probability measures, a family of probability measures on $[k]^n$ where $[k]=\{1,2,\dots,k\}$, generalizing determinantal measures (which correspond to the case $k=2$). We give examples coming from the positive…
We explore the interplay between random and deterministic phenomena using a representation of uncertainty based on the measure-theoretic concept of outer measure. The meaning of the analogues of different probabilistic concepts is…
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…
Determinantal point processes (DPPs) offer an elegant tool for encoding probabilities over subsets of a ground set. Discrete DPPs are parametrized by a positive semidefinite matrix (called the DPP kernel), and estimating this kernel is key…
We provide elementary proofs of several results concerning the possible outcomes arising from a fixed profile within the class of positional voting systems. Our arguments enable a simple and explicit construction of paradoxical profiles,…
This is a detailed survey -- with rigorous and self-contained proofs -- of some of the basics of elementary combinatorics and algebra, including the properties of finite sums, binomial coefficients, permutations and determinants. It is…
We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on countable sets. We do this by constructing probability monads…
We provide a systematic, thorough treatment of the foundations of probability theory and stochastic processes along the lines of E. Bishop's constructive analysis. Every existence result presented shall be a construction; and the input…
Determinantal point processes (DPPs) are well-suited for modeling repulsion and have proven useful in many applications where diversity is desired. While DPPs have many appealing properties, such as efficient sampling, learning the…
When studying convergence of measures, an important issue is the choice of probability metric. In this review, we provide a summary and some new results concerning bounds among ten important probability metrics/distances that are used by…
The Determinantal Point Process (DPP) is a parameterized model for multivariate binary variables, characterized by a correlation kernel matrix. This paper proposes a closed form estimator of this kernel, which is particularly easy to…
The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…
We study a subclass of POMDPs, called Deterministic POMDPs, that is characterized by deterministic actions and observations. These models do not provide the same generality of POMDPs yet they capture a number of interesting and challenging…
In the footsteps of the book \textit{Measure Theory and Integration By and For the Learner} of our series in Probability Theory and Statistics, we intended to devote a special volume of the very probabilistic aspects of the first cited…
Probability metrics constitute an important tool in probability theory and statistics \cite{DKS91}, \cite{R91}, \cite{Z83} as they are specific metrics on spaces of random variables which, by satisfying an extra condition, concord well with…
We survey recent results on determinantal processes, random growth, random tilings and their relation to random matrix theory.