Complexity of probabilistic reasoning in (directedpath) singly connected (not polytree!) Bayes networks. submitted for publication

2003 Abstract Directed-path singly connected Bayesian networks are an interesting special case that, in particular, includes both polytrees and two-level networks. We analyze the computational complexity of these networks. The prediction problem is shown to be easy, as standard message passing can perform correct updating. However, diagnostic reasoning is hard even for directed-path singly connected networks. In addition, finding the most-probable explanation (MPE) is hard, even without evidence. Finally, complexity of nearly directed-path singly-connected networks is analyzed

Exploiting Case-Based Independence for Approximating Marginal Probabilities

Computing marginal probabilities in Bayes networks is a hard problem. Deterministic anytime approximation schemes accumulate the probability mass in a small number of value assignments to the network variables. Under certain assumptions, the probability mass in the assignments is sufficient to obtain a good approximation. Such methods are especially useful for highly connected networks, where the topology makes the exact algorithms intractable. Bayes networks often possess a fine independence structure not evident from the topology, but apparent in local conditional distributions. Independence-based (IB) assignments, originally proposed as a theory of abduction, take advantage of such independence, and thus contain fewer assigned variables-and more probability mass. We present several algorithms that use IB assignments for approximating marginal probabilities. Experimental results suggest that this approach is feasible for highly connected belief networks. Abstract © Elsevie

Prioritizing Point-Based POMDP Solvers ⋆

Abstract. Recent scaling up of POMDP solvers towards realistic applications is largely due to point-based methods such as PBVI, Perseus, and HSVI, which quickly converge to an approximate solution for medium-sized problems. These algorithms improve a value function by using backup operations over a single belief point. In the simpler domain of MDP solvers, prioritizing the order of equivalent backup operations on states is well known to speed up convergence. We generalize the notion of prioritized backups to the POMDP framework, and show that the ordering of backup operations on belief points is important. We also present a new algorithm, Prioritized Value Iteration (PVI), and show empirically that it outperforms current point-based algorithms. Finally, a new empirical evaluation measure, based on the number of backups and the number of belief points, is proposed, in order to provide more accurate benchmark comparisons.

Hybrid Algorithms for Approximate Belief Updating in Bayes Nets

Belief updating in Bayes nets, a well-known computationally hard problem, has recently been approximated by several deterministic algorithms and by various randomized approximation algorithms. Deterministic algorithms usually provide probability bounds, but have an exponential runtime. Some randomized schemes have a polynomial runtime, but provide only probability estimates. Randomized algorithms that accumulate high-probability partial instantiations, resulting in probability bounds, are presented. Some of these algorithms are also sampling algorithms. Specifically, a variant of backward sampling, used both as a sampling algorithm and as a randomized enumeration algorithm, is introduced and evaluated. An implicit assumption made in prior work, for both sampling and accumulation algorithms, that query nodes must be instantiated in all the samples, is relaxed. Genetic algorithms can be used as an alternate search component for high-probability instantiations; several methods of applying them to belief updating are presented. Abstract © Elsevie

Metareasoning for Interleaved Planning and Execution

Agents that plan and act in the real world must deal with the fact that time passes as they are planning. In the presence of tight deadlines, there may be insufficient time to complete the search for a plan before it is time to act. One can gain additional time to search by starting to act before a complete plan is found, incurring the risk of making incorrect action choices. This tradeoff between opportunity and risk, inherent in interleaving planning and execution, is a non-trivial metareasoning problem addressed in this paper