Related papers: Probabilistic constructions in continuous combinat…
We study a variant of the parallel Moser-Tardos Algorithm. We prove that if we restrict attention to a class of problems whose dependency graphs have subexponential growth, then the expected total number of random bits used by the algorithm…
Recently, Glasner, Tsankov, Weiss, and Zucker showed that if $\Gamma$ is an infinite discrete group, then every minimal $\Gamma$-flow is disjoint from the Bernoulli shift $2^\Gamma$. Their proof is somewhat involved; in particular, it…
Probabilistic Programming Languages (PPLs) are a powerful tool in machine learning, allowing highly expressive generative models to be expressed succinctly. They couple complex inference algorithms, implemented by the language, with an…
In this paper we solve two problems of Esperet, Kang and Thomasse as well as Li concerning (i) induced bipartite subgraphs in triangle-free graphs and (ii) van der Waerden numbers. Each time random greedy algorithms allow us to go beyond…
The van der Waerden number W(k,2) is the smallest integer n such that every 2-coloring of 1 to n has a monochromatic arithmetic progression of length k. The existence of such an n for any k is due to van der Waerden but known upper bounds…
It is known that the topology of a Polish group is uniquely determined by its Borel structure and group operations, but this does not give us a way to find the topology. In this article we expand on this theorem and give a criterion for a…
At the end, the house always wins! This simple truth holds for all public games of chance. Nevertheless, since lotteries have existed, people have tried everything to give luck a helping hand. This article compares objective scientific…
This note is an attempt to unconditionally prove the existence of weak one way functions (OWF). Starting from a provably intractable decision problem $L_D$ (whose existence is nonconstructively assured from the well-known discrete…
The field of statistical relational learning aims at unifying logic and probability to reason and learn from data. Perhaps the most successful paradigm in the field is probabilistic logic programming: the enabling of stochastic primitives…
We prove that the entropy compression method systematized by L. Esperet and A. Parreau [11] can be applied to any problem formulated in the variable version of the Lov\'asz Local Lemma. As an application, we prove the existence of…
The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…
In the general context of computable metric spaces and computable measures we prove a kind of constructive Borel-Cantelli lemma: given a sequence (constructive in some way) of sets $A_{i}$ with effectively summable measures, there are…
In many fields of science, generalized likelihood ratio tests are established tools for statistical inference. At the same time, it has become increasingly common that a simulator (or generative model) is used to describe complex processes…
We study connections between distributed local algorithms, finitary factors of iid processes, and descriptive combinatorics in the context of regular trees. We extend the Borel determinacy technique of Marks coming from descriptive…
Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…
Probabilistic programming languages allow programmers to write down conditional probability distributions that represent statistical and machine learning models as programs that use observe statements. These programs are run by accumulating…
We show that the log-likelihood of several probabilistic graphical models is Lipschitz continuous with respect to the lp-norm of the parameters. We discuss several implications of Lipschitz parametrization. We present an upper bound of the…
Probabilistic programming is an approach to reasoning under uncertainty by encoding inference problems as programs. In order to solve these inference problems, probabilistic programming languages (PPLs) employ different inference…
Combinatorics, in particular graph theory, has a rich history of being a domain of successful applications of tools from other areas of mathematics, including topological methods. Here, we survey the study of the Hom-complexes, and the ways…
Kim defined a very general combinatorial abstraction of the diameter of polytopes called subset partition graphs to study how certain combinatorial properties of such graphs may be achieved in lower bound constructions. Using Lov\'asz'…