12 accepted papers
Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the problem of learning the best polytree is NP-hard, we study …
Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by performing a fixed number of a single type of these operation…
Expert knowledge can greatly reduce the complexity of Bayesian network structure learning by constraining the search space. These constraints can come in the form of ancestral constraints that relate to the existence of paths between nodes. When the constraints are compiled into a directed acyclic g…
We present a comprehensive classical and parameterized complexity analysis of decision tree pruning operations, extending recent research on the complexity of learning small decision trees. Thereby, we offer new insights into the computational challenges of decision tree simplification, a crucial as…
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…