14 accepted papers
The Bayesian network structure learning (BNSL) problem asks for a directed acyclic graph that maximizes a given score function. For networks with $n$ nodes, the fastest known algorithms run in time $O(2^n n^2)$ in the worst case, with no improvement in the asymptotic bound for two decades. Inspired
Sequential importance sampling (SIS) is one of the prominent methods for estimating high-dimensional integrals. For example, it is empirically the most efficient method known for estimating the permanent of nonnegative matrices, a notorious problem with numerous applications in computer science, sta…
Bayesian inference of a Bayesian network structure amounts to averaging over directed acyclic graphs (DAGs) on a given set of $n$ variables, each DAG weighted by its posterior probability. In practice, save some special inference tasks, one averages over a sample of DAGs generated perfectly or appro…
The permanent of a matrix has numerous applications but is notoriously hard to compute. While nonnegative matrices admit polynomial approximation schemes based on rapidly mixing Markov chains, the known practical estimators of the permanent rely on importance or rejection sampling. We advance the re…
Probabilistic generating circuits (PGCs) are economical representations of multivariate probability generating polynomials (PGPs). They unify and extend decomposable probabilistic circuits and determinantal point processes, admitting tractable computation of marginal probabilities. However, the need…
The problem of structure learning in Bayesian networks asks for a directed acyclic graph (DAG) that maximizes a given scoring function. Since the problem is NP-hard, research effort has been put into discovering restricted classes of DAGs for which the search problem can be solved in polynomial time…
Monte Carlo integration is a key technique for designing randomized approximation schemes for counting problems, with applications, e.g., in machine learning and statistical physics. The technique typically enables massively parallel computation, however, with the risk that some of the delegated com…
We present a randomized approximation scheme for the permanent of a matrix with nonnegative entries. Our scheme extends a recursive rejection sampling method of Huber and Law (SODA 2008) by replacing the permanent upper bound with a linear combination of the subproblem bounds at a moderately large d…
Bayesian inference of the Bayesian network structure requires averaging over all possible directed acyclic graphs, DAGs, each weighted by its posterior probability. For approximate averaging, the most popular method has been Markov chain Monte Carlo, MCMC. It was recently shown that collapsing the s…
We give methods for Bayesian inference of directed acyclic graphs, DAGs, and the induced causal effects from passively observed complete data. Our methods build on a recent Markov chain Monte Carlo scheme for learning Bayesian networks, which enables efficient approximate sampling from the graph post…
We consider the problem of sampling directed acyclic graphs (DAGs) from a given distribution. We assume the sampling distribution is modular, i.e., the probability of a DAG is a product of local factors, each of which only depends on a node and its parents in the DAG. Using inclusion–exclusion recur…
To learn a Bayesian network structure from data, one popular approach is to maximize a decomposable likelihood-based score. While various scores have been proposed, they usually assume a uniform prior, or “penalty,” over the possible directed acyclic graphs (DAGs); relatively little attention has be…
To compare learning algorithms that differ by the adopted statistical paradigm, model class, or search heuristic, it is common to evaluate the performance on training data of varying size. Measuring the performance is straightforward if the data are generated from a known model, the ground truth. Ho…
Context trees (CT) are a widely used tool in machine learning for representing context-specific independences in conditional probability distributions. Parsimonious context trees (PCTs) are a recently proposed generalization of CTs that can enable statistically more efficient learning due to a highe…