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

A Stratified Simulation Scheme for Inference in Bayesian Belief Networks

Simulation schemes for probabilistic inference in Bayesian belief networks offer many advantages over exact algorithms; for example, these schemes have a linear and thus predictable runtime while exact algorithms have exponential runtime. Experiments have shown that likelihood weighting is one of the most promising simulation schemes. In this paper, we present a new simulation scheme that generates samples more evenly spread in the sample space than the likelihood weighting scheme. We show both theoretically and experimentally that the stratified scheme outperforms likelihood weighting in average runtime and error in estimates of beliefs.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI1994

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

Forecasting Sleep Apnea with Dynamic Network Models

Dynamic network models (DNMs) are belief networks for temporal reasoning. The DNM methodology combines techniques from time series analysis and probabilistic reasoning to provide (1) a knowledge representation that integrates noncontemporaneous and contemporaneous dependencies and (2) methods for iteratively refining these dependencies in response to the effects of exogenous influences. We use belief-network inference algorithms to perform forecasting, control, and discrete event simulation on DNMs. The belief network formulation allows us to move beyond the traditional assumptions of linearity in the relationships among time-dependent variables and of normality in their probability distributions. We demonstrate the DNM methodology on an important forecasting problem in medicine. We conclude with a discussion of how the methodology addresses several limitations found in traditional time series analyses.Comment: Appears in Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (UAI1993

Importance Sampling via Variational Optimization

Computing the exact likelihood of data in large Bayesian networks consisting of thousands of vertices is often a difficult task. When these models contain many deterministic conditional probability tables and when the observed values are extremely unlikely even alternative algorithms such as variational methods and stochastic sampling often perform poorly. We present a new importance sampling algorithm for Bayesian networks which is based on variational techniques. We use the updates of the importance function to predict whether the stochastic sampling converged above or below the true likelihood, and change the proposal distribution accordingly. The validity of the method and its contribution to convergence is demonstrated on hard networks of large genetic linkage analysis tasks.Comment: Appears in Proceedings of the Twenty-Third Conference on Uncertainty in Artificial Intelligence (UAI2007

IDEAL: A Software Package for Analysis of Influence Diagrams

IDEAL (Influence Diagram Evaluation and Analysis in Lisp) is a software environment for creation and evaluation of belief networks and influence diagrams. IDEAL is primarily a research tool and provides an implementation of many of the latest developments in belief network and influence diagram evaluation in a unified framework. This paper describes IDEAL and some lessons learned during its development.Comment: Appears in Proceedings of the Sixth Conference on Uncertainty in Artificial Intelligence (UAI1990

Loopy Belief Propagation for Approximate Inference: An Empirical Study

Recently, researchers have demonstrated that loopy belief propagation - the use of Pearls polytree algorithm IN a Bayesian network WITH loops OF error- correcting codes.The most dramatic instance OF this IS the near Shannon - limit performance OF Turbo Codes codes whose decoding algorithm IS equivalent TO loopy belief propagation IN a chain - structured Bayesian network. IN this paper we ask : IS there something special about the error - correcting code context, OR does loopy propagation WORK AS an approximate inference schemeIN a more general setting? We compare the marginals computed using loopy propagation TO the exact ones IN four Bayesian network architectures, including two real - world networks : ALARM AND QMR.We find that the loopy beliefs often converge AND WHEN they do, they give a good approximation TO the correct marginals.However,ON the QMR network, the loopy beliefs oscillated AND had no obvious relationship TO the correct posteriors. We present SOME initial investigations INTO the cause OF these oscillations, AND show that SOME simple methods OF preventing them lead TO the wrong results.Comment: Appears in Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI1999

Error Estimation in Approximate Bayesian Belief Network Inference

We can perform inference in Bayesian belief networks by enumerating instantiations with high probability thus approximating the marginals. In this paper, we present a method for determining the fraction of instantiations that has to be considered such that the absolute error in the marginals does not exceed a predefined value. The method is based on extreme value theory. Essentially, the proposed method uses the reversed generalized Pareto distribution to model probabilities of instantiations below a given threshold. Based on this distribution, an estimate of the maximal absolute error if instantiations with probability smaller than u are disregarded can be made.Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995

Incremental Dynamic Construction of Layered Polytree Networks

Certain classes of problems, including perceptual data understanding, robotics, discovery, and learning, can be represented as incremental, dynamically constructed belief networks. These automatically constructed networks can be dynamically extended and modified as evidence of new individuals becomes available. The main result of this paper is the incremental extension of the singly connected polytree network in such a way that the network retains its singly connected polytree structure after the changes. The algorithm is deterministic and is guaranteed to have a complexity of single node addition that is at most of order proportional to the number of nodes (or size) of the network. Additional speed-up can be achieved by maintaining the path information. Despite its incremental and dynamic nature, the algorithm can also be used for probabilistic inference in belief networks in a fashion similar to other exact inference algorithms.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI1994

Fast Belief Update Using Order-of-Magnitude Probabilities

We present an algorithm, called Predict, for updating beliefs in causal networks quantified with order-of-magnitude probabilities. The algorithm takes advantage of both the structure and the quantification of the network and presents a polynomial asymptotic complexity. Predict exhibits a conservative behavior in that it is always sound but not always complete. We provide sufficient conditions for completeness and present algorithms for testing these conditions and for computing a complete set of plausible values. We propose Predict as an efficient method to estimate probabilistic values and illustrate its use in conjunction with two known algorithms for probabilistic inference. Finally, we describe an application of Predict to plan evaluation, present experimental results, and discuss issues regarding its use with conditional logics of belief, and in the characterization of irrelevance.Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995