Related papers: Relating counting complexity to non-uniform probab…
#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of…
We consider training probabilistic classifiers in the case of a large number of classes. The number of classes is assumed too large to perform exact normalisation over all classes. To account for this we consider a simple approach that…
Rank regularized minimization problem is an ideal model for the low-rank matrix completion/recovery problem. The matrix factorization approach can transform the high-dimensional rank regularized problem to a low-dimensional factorized…
One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent…
Verification of infinite-state Markov chains is still a challenge despite several fruitful numerical or statistical approaches. For decisive Markov chains, there is a simple numerical algorithm that frames the reachability probability as…
Techniques for evaluating the normalization integral of the target density for Markov Chain Monte Carlo algorithms are described and tested numerically. It is assumed that the Markov Chain algorithm has converged to the target distribution…
Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…
This paper considers the problem of cardinality estimation in data stream applications. We present a statistical analysis of probabilistic counting algorithms, focusing on two techniques that use pseudo-random variates to form…
Given $m < n$, we consider the problem of ``best'' approximating an $n\text{-d}$ probability measure $\rho$ via an $m\text{-d}$ measure $\nu$ such that $\mathrm{supp}\ \nu$ has bounded total ``complexity.'' When $\rho$ is concentrated near…
Technology is a complex system, with technologies relating to each other in a space that can be mapped as a network. The technology network's structure can reveal properties of technologies and of human behavior, if it can be mapped…
Optimistic parallelization is a promising approach for the parallelization of irregular algorithms: potentially interfering tasks are launched dynamically, and the runtime system detects conflicts between concurrent activities, aborting and…
A typical computational geometry problem begins: Consider a set P of n points in R^d. However, many applications today work with input that is not precisely known, for example when the data is sensed and has some known error model. What if…
A new family of tree-structured Markov random fields for a vector of discrete counting random variables is introduced. According to the characteristics of the family, the marginal distributions of the Markov random fields are all Poisson…
We consider the problem of balancing load items (tokens) in networks. Starting with an arbitrary load distribution, we allow nodes to exchange tokens with their neighbors in each round. The goal is to achieve a distribution where all nodes…
In distribution compression, one aims to accurately summarize a probability distribution $\mathbb{P}$ using a small number of representative points. Near-optimal thinning procedures achieve this goal by sampling $n$ points from a Markov…
We use a Monte Carlo method to assemble finite element matrices for polynomial Chaos approximations of elliptic equations with random coefficients. In this approach, all required expectations are approximated by a Monte Carlo method. The…
Behavioral experiments on humans and animals suggest that the brain performs probabilistic inference to interpret its environment. Here we present a new general-purpose, biologically-plausible neural implementation of approximate inference.…
This paper considers a new approach to using Markov chain Monte Carlo (MCMC) in contexts where one may adopt multilevel (ML) Monte Carlo. The underlying problem is to approximate expectations w.r.t. an underlying probability measure that is…
Score matching is an approach to learning probability distributions parametrized up to a constant of proportionality (e.g. Energy-Based Models). The idea is to fit the score of the distribution, rather than the likelihood, thus avoiding the…
Chance-constrained programming (CCP) is one of the most difficult classes of optimization problems that has attracted the attention of researchers since the 1950s. In this survey, we focus on cases when only a limited information on the…