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Growth in both size and complexity of modern data challenges the applicability of traditional likelihood-based inference. Composite likelihood (CL) methods address the difficulties related to model selection and computational intractability…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
The hypergraph container lemma is a powerful tool in probabilistic combinatorics that has found many applications since it was first proved a decade ago. Roughly speaking, it asserts that the family of independent sets of every uniform…
We study the relationship between hyperfiniteness and problems in Borel graph combinatorics by adapting game-theoretic techniques introduced by Marks to the hyperfinite setting. We compute the possible Borel chromatic numbers and edge…
The aim of this paper is to extend probability theory from the classical to the product t-norm fuzzy logic setting. More precisely, we axiomatize a generalized notion of finitely additive probability for product logic formulas, called…
We generalize Brooks's theorem to show that if $G$ is a Borel graph on a standard Borel space $X$ of degree bounded by $d \geq 3$ which contains no $(d+1)$-cliques, then $G$ admits a $\mu$-measurable $d$-coloring with respect to any Borel…
The goal of this paper is to apply the collection of mathematical tools known as the "method of arbitrary functions" to analyze how probability arises from quantum dynamics. We argue that in a toy model of quantum measurement the Born rule…
Likelihood-free methods perform parameter inference in stochastic simulator models where evaluating the likelihood is intractable but sampling synthetic data is possible. One class of methods for this likelihood-free problem uses a…
The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…
Whereas the semantics of probabilistic languages has been extensively studied, specification languages for their properties have received less attention -- with the notable exception of recent and on-going efforts by Joost-Pieter Katoen and…
We investigate the practical aspects of computing the necessary and possible winners in elections over incomplete voter preferences. In the case of the necessary winners, we show how to implement and accelerate the polynomial-time algorithm…
Two representations theorems are presented: 1. Any Borel action of a second countable locally compact group $G$ on a standard Borel space $X$ admits an injective $G$-equivariant Borel map into the shift space of $1$-Lipschitz functions from…
Local algorithms on graphs are algorithms that run in parallel on the nodes of a graph to compute some global structural feature of the graph. Such algorithms use only local information available at nodes to determine local aspects of the…
In the last ten years, the employment of symbolic methods has substantially extended both the theory and the applications of statistics and probability. This survey reviews the development of a symbolic technique arising from classical…
Programs using random values can either make all choices in advance (eagerly) or sample as needed (lazily). In formal proofs, we focus on indistinguishability between two lazy programs, a common requirement in the random oracle model (ROM).…
We establish a Sewing lemma in the regime $\gamma \in \left( 0, 1 \right]$, constructing a Sewing map which is neither unique nor canonical, but which is nonetheless continuous with respect to the standard norms. Two immediate corollaries…
Random projections are random linear maps, sampled from appropriate distributions, that approx- imately preserve certain geometrical invariants so that the approximation improves as the dimension of the space grows. The well-known…
We prove a pointwise ergodic theorem for quasi-probability-measure-preserving (quasi-pmp) locally countable measurable graphs, equivalently, Schreier graphs of quasi-pmp actions of countable groups. For ergodic graphs, the theorem gives an…
Shared randomness is a valuable resource in distributed computing, allowing some form of coordination between processors without explicit communication. But what happens when the shared random string can affect the inputs to the system?…
The interest in the combination of probability with logics for modeling the world has rapidly increased in the last few years. One of the most effective approaches is the Distribution Semantics which was adopted by many logic programming…