Backward Simulation in Bayesian Networks

Backward simulation is an approximate inference technique for Bayesian belief networks. It differs from existing simulation methods in that it starts simulation from the known evidence and works backward (i.e., contrary to the direction of the arcs). The technique's focus on the evidence leads to improved convergence in situations where the posterior beliefs are dominated by the evidence rather than by the prior probabilities. Since this class of situations is large, the technique may make practical the application of approximate inference in Bayesian belief networks to many real-world problems.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI1994

An Empirical Evaluation of a Randomized Algorithm for Probabilistic Inference

In recent years, researchers in decision analysis and artificial intelligence (Al) have used Bayesian belief networks to build models of expert opinion. Using standard methods drawn from the theory of computational complexity, workers in the field have shown that the problem of probabilistic inference in belief networks is difficult and almost certainly intractable. K N ET, a software environment for constructing knowledge-based systems within the axiomatic framework of decision theory, contains a randomized approximation scheme for probabilistic inference. The algorithm can, in many circumstances, perform efficient approximate inference in large and richly interconnected models of medical diagnosis. Unlike previously described stochastic algorithms for probabilistic inference, the randomized approximation scheme computes a priori bounds on running time by analyzing the structure and contents of the belief network. In this article, we describe a randomized algorithm for probabilistic inference and analyze its performance mathematically. Then, we devote the major portion of the paper to a discussion of the algorithm's empirical behavior. The results indicate that the generation of good trials (that is, trials whose distribution closely matches the true distribution), rather than the computation of numerous mediocre trials, dominates the performance of stochastic simulation. Key words: probabilistic inference, belief networks, stochastic simulation, computational complexity theory, randomized algorithms.Comment: Appears in Proceedings of the Fifth Conference on Uncertainty in Artificial Intelligence (UAI1989

Independence of Causal Influence and Clique Tree Propagation

This paper explores the role of independence of causal influence (ICI) in Bayesian network inference. ICI allows one to factorize a conditional probability table into smaller pieces. We describe a method for exploiting the factorization in clique tree propagation (CTP) - the state-of-the-art exact inference algorithm for Bayesian networks. We also present empirical results showing that the resulting algorithm is significantly more efficient than the combination of CTP and previous techniques for exploiting ICI.Comment: Appears in Proceedings of the Thirteenth Conference on Uncertainty in Artificial Intelligence (UAI1997

An Algorithm for Computing Probabilistic Propositions

A method for computing probabilistic propositions is presented. It assumes the availability of a single external routine for computing the probability of one instantiated variable, given a conjunction of other instantiated variables. In particular, the method allows belief network algorithms to calculate general probabilistic propositions over nodes in the network. Although in the worst case the time complexity of the method is exponential in the size of a query, it is polynomial in the size of a number of common types of queries.Comment: Appears in Proceedings of the Third Conference on Uncertainty in Artificial Intelligence (UAI1987

Improved Sampling for Diagnostic Reasoning in Bayesian Networks

Bayesian networks offer great potential for use in automating large scale diagnostic reasoning tasks. Gibbs sampling is the main technique used to perform diagnostic reasoning in large richly interconnected Bayesian networks. Unfortunately Gibbs sampling can take an excessive time to generate a representative sample. In this paper we describe and test a number of heuristic strategies for improving sampling in noisy-or Bayesian networks. The strategies include Monte Carlo Markov chain sampling techniques other than Gibbs sampling. Emphasis is put on strategies that can be implemented in distributed systems.Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995

Incremental Probabilistic Inference

Propositional representation services such as truth maintenance systems offer powerful support for incremental, interleaved, problem-model construction and evaluation. Probabilistic inference systems, in contrast, have lagged behind in supporting this incrementality typically demanded by problem solvers. The problem, we argue, is that the basic task of probabilistic inference is typically formulated at too large a grain-size. We show how a system built around a smaller grain-size inference task can have the desired incrementality and serve as the basis for a low-level (propositional) probabilistic representation service.Comment: Appears in Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (UAI1993

Ergo: A Graphical Environment for Constructing Bayesian

We describe an environment that considerably simplifies the process of generating Bayesian belief networks. The system has been implemented on readily available, inexpensive hardware, and provides clarity and high performance. We present an introduction to Bayesian belief networks, discuss algorithms for inference with these networks, and delineate the classes of problems that can be solved with this paradigm. We then describe the hardware and software that constitute the system, and illustrate Ergo's use with several exampleComment: Appears in Proceedings of the Sixth Conference on Uncertainty in Artificial Intelligence (UAI1990

Using Causal Information and Local Measures to Learn Bayesian Networks

In previous work we developed a method of learning Bayesian Network models from raw data. This method relies on the well known minimal description length (MDL) principle. The MDL principle is particularly well suited to this task as it allows us to tradeoff, in a principled way, the accuracy of the learned network against its practical usefulness. In this paper we present some new results that have arisen from our work. In particular, we present a new local way of computing the description length. This allows us to make significant improvements in our search algorithm. In addition, we modify our algorithm so that it can take into account partial domain information that might be provided by a domain expert. The local computation of description length also opens the door for local refinement of an existent network. The feasibility of our approach is demonstrated by experiments involving networks of a practical size.Comment: Appears in Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (UAI1993

Reasoning About Beliefs and Actions Under Computational Resource Constraints

Although many investigators affirm a desire to build reasoning systems that behave consistently with the axiomatic basis defined by probability theory and utility theory, limited resources for engineering and computation can make a complete normative analysis impossible. We attempt to move discussion beyond the debate over the scope of problems that can be handled effectively to cases where it is clear that there are insufficient computational resources to perform an analysis deemed as complete. Under these conditions, we stress the importance of considering the expected costs and benefits of applying alternative approximation procedures and heuristics for computation and knowledge acquisition. We discuss how knowledge about the structure of user utility can be used to control value tradeoffs for tailoring inference to alternative contexts. We address the notion of real-time rationality, focusing on the application of knowledge about the expected timewise-refinement abilities of reasoning strategies to balance the benefits of additional computation with the costs of acting with a partial result. We discuss the benefits of applying decision theory to control the solution of difficult problems given limitations and uncertainty in reasoning resources.Comment: Appears in Proceedings of the Third Conference on Uncertainty in Artificial Intelligence (UAI1987

Simulation Approaches to General Probabilistic Inference on Belief Networks

A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the graph structure is relatively sparse, and probabilistic sampling techniques which exploit the "conductance" of an embedded Markov chain when the conditional probabilities have non-extreme values. In this paper, we investigate a family of "forward" Monte Carlo sampling techniques similar to Logic Sampling [Henrion, 1988] which appear to perform well even in some multiply connected networks with extreme conditional probabilities, and thus would be generally applicable. We consider several enhancements which reduce the posterior variance using this approach and propose a framework and criteria for choosing when to use those enhancements.Comment: Appears in Proceedings of the Fifth Conference on Uncertainty in Artificial Intelligence (UAI1989