Bruce D'Ambrosio

Efficient inference in Bayes networks as a combinatorial optimization problem

Abstract A number of exact algorithms have been developed in recent years to perform probabilistic inference in Bayesian belief networks. The techniques used in these algorithms are closely related to network structures, and some of them are not easy to understand and implement. We consider the problem from the combinatorial optimization point of view and state that efficient probabilistic inference in a belief network is a problem of finding an optimal factoring given a set of probability distributions. From this viewpoint, previously developed algorithms can be seen as alternative factoring strategies. In this paper, we define a combinatorial optimization problem, the optimal factoring problem, and discuss application of this problem in belief networks. We show that optimal factoring provides insight into the key elements of efficient probabilistic inference, and demonstrate simple, easily implemented algorithms with excellent performance.

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.

Local expression languages for probabilistic dependence

Abstract A Bayesian belief net is a factored representation for a joint probability distribution over a set of variables. This factoring is made possible by the conditional independence relationships among variables made evident in the sparseness of the graphical level of the net. There is, however, another source of factoring available which cannot be directly represented in this graphical structure. This source is the microstructure within an individual marginal or conditional distribution. We present a representation capable of making this intradistribution structure explicit, and an extension to the SPI algorithm capable of utilizing this structural information to improve the efficiency of inference. We discuss the expressivity of the local expression language, and present early experimental results showing the efficacy of the approach.

Monitoring and diagnosis of a multistage manufacturing process using Bayesian networks

The application of Bayesian networks for monitoring and diagnosis of a multistage manufacturing process is described. Bayesian network “part models” were designed to represent individual parts in-process. These were combined to form a “process model,” a Bayesian network model of the entire manufacturing process. An efficient procedure is designed for managing the “process network.” Simulated data is used to test the validity of diagnosis made from this method. In addition, a critical analysis of this method is given, including computation speed concerns, accuracy of results, and ease of implementation. Finally, a discussion on future research in the area is given.

Taxonomy for classifying engineering decision problems and support systems

The design of even the simplest product requires thousands of decisions. Yet few of these decisions are supported with methods on paper or on computers. Is this because engineering design decisions do not need support or is it because techniques have yet to be developed that are usable on a wide basis ? In considering this question a wide range of decision problem characteristics need to be addressed. In engineering design some decisions are made by individuals, others by teams-some are about the product and others about the processes that support the product - some are based on complete, consistent, quantitative data and others on sparse, conflicting, qualitative discussions. To address the reasons why so little support is used and the characteristics of potentially useful decision support tools, a taxonomy of decision characteristics is proposed. This taxonomy is used to classify current techniques and to define the requirements for an ideal engineering design decision support system.

A hybrid approach to reasoning under uncertainty

Abstract A complete approach to reasoning under uncertainty requires support for both identification of the appropriate hypothesis space and ranking hypotheses based on available evidence. We present a hybrid reasoning scheme that combines symbolic and numerical methods for uncertainty management to provide efficient and effective support for both of these tasks. The hybrid is based on symbolic techniques adapted from assumption-based truth maintenance systems (ATMS), combined with numerical methods adapted from the Dempster/Shafer theory of evidence, as extended in Baldwins Support Logic Programming system. The hybridization is achieved by viewing an ATMS as a symbolic algebra system for uncertainty calculations. This technique has several major advantages over conventional methods for performing inference with numerical certainty estimates in addition to the ability to dynamically determine hypothesis spaces, including improved management of dependent and partially independent evidence, faster run-time evaluation of propositional certainties, and the ability to query the certainty value of a proposition from multiple perspectives.

An efficient approach for finding the MPE in belief networks

Given a belief network with evidence, the task of finding the l most probable explanations (MPE) in the belief network is that of identifying and ordering the l most probable instantiations of the nonevidence nodes of the belief network. Although many approaches have been proposed for solving this problem, most work only for restricted topologies (i.e., singly connected belief networks). In this paper, we will present a new approach for finding l MPEs in an arbitrary belief network. First, we will present an algorithm for finding the MPE in a belief network. Then, we will present a linear time algorithm for finding the next MPE after finding the first MPE. And finally, we will discuss the problem of finding the MPE for a subset of variables of a belief network, and show that the problem can be efficiently solved by this approach.

Real-time value-driven diagnosis

Abstract Diagnosis is often thought of as an isolated task in theoretical reasoning (reasoning with the goal of updating our beliefs about the world). We present a decision-theoretic interpretation of diagnosis as a task in practical reasoning (reasoning with the goal of acting in the world), and sketch components of our approach to this task. These components include an abstract problem description, a decision-theoretic model of the basic task, a set of inference methods suitable for evaluating the decision representation in real-time, and a control architecture to provide the needed continuing coordination between the agent and its environment. A principal contribution of this work is the representation and inference methods we have developed, which extend previously available probabilistic inference methods and narrow, somewhat, the gap between probabilistic and logical models of diagnosis.

Parallelizing probabilistic inference: some early explorations

We report on an experimental investigation into opportunities for parallelism in belief-net inference. Specifically, we report on a study performed of the available parallelism, on hypercube style machines, of a set of randomly generated belief nets, using factoring (SPI) style inference algorithms. Our results indicate that substantial speedup is available, but that it is available only through parallelization of individual conformal product operations, and depends critically on finding an appropriate factoring. We find negligible opportunity for parallelism at the topological, or clustering tree, level.

Symbolic probabilistic inference in large BN20 networks

A BN20 network is a two level belief net in which parent interactions are modeled using the noisy-or interaction model. In this paper we discuss application of the SPI local expression language [1] to efficient inference in large BN2O networks. In particular, we show that there is significant structure which can be exploited to improve over the Quickscore result. We further describe how symbolic techniques can provide information which can significantly reduce the computation required for computing all cause posterior marginals. Finally, we present a novel approximation technique with preliminary experimental results.