Related papers: Relating counting complexity to non-uniform probab…
Comparing clusterings is central to evaluating unsupervised models, yet the many existing similarity measures can produce widely divergent, sometimes contradictory, evaluations. Clustering similarity measures are typically organized into…
Markov chain Monte Carlo (MCMC) algorithms provide a very general recipe for estimating properties of complicated distributions. While their use has become commonplace and there is a large literature on MCMC theory and practice, MCMC users…
We propose a new type of approximate counting algorithms for the problems of enumerating the number of independent sets and proper colorings in low degree graphs with large girth. Our algorithms are not based on a commonly used Markov chain…
Normal variance mixtures are a class of multivariate distributions that generalize the multivariate normal by randomizing (or mixing) the covariance matrix via multiplication by a non-negative random variable W. The multivariate t…
Internet supercomputing is an approach to solving partitionable, computation-intensive problems by harnessing the power of a vast number of interconnected computers. For the problem of using network supercomputing to perform a large…
Prior to computing the Cholesky factorization of a sparse, symmetric positive definite matrix, a reordering of the rows and columns is computed so as to reduce both the number of fill elements in Cholesky factor and the number of arithmetic…
In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…
$ $In many optimization problems, a feasible solution induces a multi-dimensional cost vector. For example, in load-balancing a schedule induces a load vector across the machines. In $k$-clustering, opening $k$ facilities induces an…
We consider the problem of closeness testing for two discrete distributions in the practically relevant setting of \emph{unequal} sized samples drawn from each of them. Specifically, given a target error parameter $\varepsilon > 0$, $m_1$…
Markov chain Monte Carlo is a class of algorithms for drawing Markovian samples from high-dimensional target densities to approximate the numerical integration associated with computing statistical expectation, especially in Bayesian…
This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…
Adaptive importance sampling is a powerful tool to sample from complicated target densities, but its success depends sensitively on the initial proposal density. An algorithm is presented to automatically perform the initialization using…
Previously referred to as `miraculous' in the scientific literature because of its powerful properties and its wide application as optimal solution to the problem of induction/inference, (approximations to) Algorithmic Probability (AP) and…
We resolve a long-standing open question, about the existence of a constant-factor approximation algorithm for the average-case \textsc{Decision Tree} problem with uniform probability distribution over the hypotheses. We answer the question…
In this paper, we tackle the resolution of chance-constrained problems reformulated via Sample Average Approximation. The resulting data-driven deterministic reformulation takes the form of a large-scale mixed-integer program cursed with…
We introduce a new method for solving nonlinear continuous optimization problems with chance constraints. Our method is based on a reformulation of the probabilistic constraint as a quantile function. The quantile function is approximated…
In this paper, we consider the problem of counting and sampling structures in graphs. We define a class of "edge universal labeling problems"---which include proper $k$-colorings, independent sets, and downsets---and describe simple…
Model counting, or counting the satisfying assignments of a Boolean formula, is a fundamental problem with diverse applications. Given #P-hardness of the problem, developing algorithms for approximate counting is an important research area.…
Many problems in the physical sciences, machine learning, and statistical inference necessitate sampling from a high-dimensional, multi-modal probability distribution. Markov Chain Monte Carlo (MCMC) algorithms, the ubiquitous tool for this…
We explore a simple mathematical model of network computation, based on Markov chains. Similar models apply to a broad range of computational phenomena, arising in networks of computers, as well as in genetic, and neural nets, in social…