Evaluating Anytime Algorithms for Learning Optimal Bayesian Networks

Exact algorithms for learning Bayesian networks guarantee to find provably optimal networks. However, they may fail in difficult learning tasks due to limited time or memory. In this research we adapt several anytime heuristic search-based algorithms to learn Bayesian networks. These algorithms find high-quality solutions quickly, and continually improve the incumbent solution or prove its optimality before resources are exhausted. Empirical results show that the anytime window A* algorithm usually finds higher-quality, often optimal, networks more quickly than other approaches. The results also show that, surprisingly, while generating networks with few parents per variable are structurally simpler, they are harder to learn than complex generating networks with more parents per variable.Peer reviewe

Methods for evaluating Decision Problems with Limited Information

LImited Memory Influence Diagrams (LIMIDs) are general models of decision problems for representing limited memory policies (Lauritzen and Nilsson (2001)). The evaluation of LIMIDs can be done by Single Policy Updating that produces a local maximum strategy in which no single policy modification can increase the expected utility. This paper examines the quality of the obtained local maximum strategy and proposes three different methods for evaluating LIMIDs. The first algorithm, Temporal Policy Updating, resembles Single Policy Updating. The second algorithm, Greedy Search, successively updates the policy that gives the highest expected utility improvement. The final algorithm, Simulating Annealing, differs from the two preceeding by allowing the search to take some downhill steps to escape a local maximum. A careful comparison of the algorithms is provided both in terms of the quality of the obtained strategies, and in terms of implementation of the algorithms including some considerations of the computational complexity

Maximum a Posteriori Estimation by Search in Probabilistic Programs

We introduce an approximate search algorithm for fast maximum a posteriori probability estimation in probabilistic programs, which we call Bayesian ascent Monte Carlo (BaMC). Probabilistic programs represent probabilistic models with varying number of mutually dependent finite, countable, and continuous random variables. BaMC is an anytime MAP search algorithm applicable to any combination of random variables and dependencies. We compare BaMC to other MAP estimation algorithms and show that BaMC is faster and more robust on a range of probabilistic models.Comment: To appear in proceedings of SOCS1

Empirical Hardness of Finding Optimal Bayesian Network Structures: Algorithm Selection and Runtime Prediction

Various algorithms have been proposed for finding a Bayesian network structure that is guaranteed to maximize a given scoring function. Implementations of state-of-the-art algorithms, solvers, for this Bayesian network structure learning problem rely on adaptive search strategies, such as branch-and-bound and integer linear programming techniques. Thus, the time requirements of the solvers are not well characterized by simple functions of the instance size. Furthermore, no single solver dominates the others in speed. Given a problem instance, it is thus a priori unclear which solver will perform best and how fast it will solve the instance. We show that for a given solver the hardness of a problem instance can be efficiently predicted based on a collection of non-trivial features which go beyond the basic parameters of instance size. Specifically, we train and test statistical models on empirical data, based on the largest evaluation of state-of-the-art exact solvers to date. We demonstrate that we can predict the runtimes to a reasonable degree of accuracy. These predictions enable effective selection of solvers that perform well in terms of runtimes on a particular instance. Thus, this work contributes a highly efficient portfolio solver that makes use of several individual solvers.Peer reviewe