Related papers: Sufficient conditions for convergence of the Sum-P…
We establish two new direct product theorems for the randomized query complexity of Boolean functions. The first shows that computing $n$ copies of a function $f$, even with a small success probability of $\gamma^n$, requires $\Theta(n)$…
We study propagation algorithms for the conjunction of two AllDifferent constraints. Solutions of an AllDifferent constraint can be seen as perfect matchings on the variable/value bipartite graph. Therefore, we investigate the problem of…
Factor graphs are important models for succinctly representing probability distributions in machine learning, coding theory, and statistical physics. Several computational problems, such as computing marginals and partition functions, arise…
The sum-product or belief propagation (BP) algorithm is a widely used message-passing technique for computing approximate marginals in graphical models. We introduce a new technique, called stochastic orthogonal series message-passing…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
In second-order uncertain Bayesian networks, the conditional probabilities are only known within distributions, i.e., probabilities over probabilities. The delta-method has been applied to extend exact first-order inference methods to…
Undirected graphical models are a widely used class of probabilistic models in machine learning that capture prior knowledge or putative pairwise interactions between variables. Those interactions are encoded in a graph for pairwise…
In this work, we consider the fundamental problem of deriving quantitative bounds on the probability that a given assertion is violated in a probabilistic program. We provide automated algorithms that obtain both lower and upper bounds on…
Probabilistic graphical models are a powerful concept for modeling high-dimensional distributions. Besides modeling distributions, probabilistic graphical models also provide an elegant framework for performing statistical inference;…
Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as conditional distributions of a single probability measure on…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
We study hypothesis testing under communication constraints, where each sample is quantized before being revealed to a statistician. Without communication constraints, it is well known that the sample complexity of simple binary hypothesis…
Exploiting the indistinguishability of objects in a probabilistic graphical model such as a factor graph is key to lifted probabilistic inference algorithms and allows for tractable probabilistic inference problems with respect to domain…
Belief propagation (BP) algorithm is a widely used message-passing method for inference in graphical models. BP on loop-free graphs converges in linear time. But for graphs with loops, BP's performance is uncertain, and the understanding of…
The sum-product algorithm for decoding of binary codes is analyzed for bipartite graphs in which the check nodes all have degree $2$. The algorithm simplifies dramatically and may be expressed using linear algebra. Exact results about the…
The Robbins-Siegmund theorem establishes the convergence of stochastic processes that are almost supermartingales and is one of the most commonly used approaches for analyzing stochastic iterative algorithms in stochastic approximation and…
A strong direct product theorem states that if we want to compute $k$ independent instances of a function, using less than $k$ times the resources needed for one instance, then the overall success probability will be exponentially small in…
We study the problem of bounding the posterior distribution of discrete probabilistic programs with unbounded support, loops, and conditioning. Loops pose the main difficulty in this setting: even if exact Bayesian inference is possible,…
When causal quantities cannot be point identified, researchers often pursue partial identification to quantify the range of possible values. However, the peculiarities of applied research conditions can make this analytically intractable.…