This paper presents a Bayesian method for constructing Bayesian belief networks from a database of cases. Potential applications include computer-assisted hypothesis testing, automated scientific discovery, and automated construction of probabilistic expert systems. Results are presented of a preliminary evaluation of an algorithm for constructing a belief network from a database of cases. We relate the methods in this paper to previous work, and we discuss open problems.

A series of monte carlo studies were performed to compare the behavior of some alternative procedures for reasoning under uncertainty. The behavior of several Bayesian, linear model and default reasoning procedures were examined in the context of increasing levels of calibration error. The most interesting result is that Bayesian procedures tended to output more extreme posterior belief values (posterior beliefs near 0.0 or 1.0) than other techniques, but the linear models were relatively less likely to output strong support for an erroneous conclusion. Also, accounting for the probabilistic dependencies between evidence items was important for both Bayesian and linear updating procedures.

Recent research on the Symbolic Probabilistic Inference (SPI) algorithm[2] has focused attention on the importance of resolving general queries in Bayesian networks. SPI applies the concept of dependency-directed backward search to probabilistic inference, and is incremental with respect to both queries and observations. In response to this research we have extended the evidence potential algorithm [3] with the same features. We call the extension symbolic evidence potential inference (SEPI). SEPI like SPI can handle generic queries and is incremental with respect to queries and observations. While in SPI, operations are done on a search tree constructed from the nodes of the original network, in SEPI, a clique-tree structure obtained from the evidence potential algorithm [3] is the basic framework for recursive query processing. In this paper, we describe the systematic query and caching procedure of SEPI. SEPI begins with finding a clique tree from a Bayesian network-the standard procedure of the evidence potential algorithm. With the clique tree, various probability distributions are computed and stored in each clique. This is the ?pre-processing? step of SEPI. Once this step is done, the query can then be computed. To process a query, a recursive process similar to the SPI algorithm is used. The queries are directed to the root clique and decomposed into queries for the clique's subtrees until a particular query can be answered at the clique at which it is directed. The algorithm and the computation are simple. The SEPI algorithm will be presented in this paper along with several examples.

This paper examines the interdependence generated between two parent nodes with a common instantiated child node, such as two hypotheses sharing common evidence. The relation so generated has been termed "intercausal." It is shown by construction that inter-causal independence is possible for binary distributions at one state of evidence. For such "CICI" distributions, the two measures of inter-causal effect, "multiplicative synergy" and "additive synergy" are equal. The well known "noisy-or" model is an example of such a distribution. This introduces novel semantics for the noisy-or, as a model of the degree of conflict among competing hypotheses of a common observation.

This paper proposes a new method for solving Bayesian decision problems. The method consists of representing a Bayesian decision problem as a valuation-based system and applying a fusion algorithm for solving it. The fusion algorithm is a hybrid of local computational methods for computation of marginals of joint probability distributions and the local computational methods for discrete optimization problems.

The belief network is a well-known graphical structure for representing independences in a joint probability distribution. The methods, which perform probabilistic inference in belief networks, often treat the conditional probabilities which are stored in the network as certain values. However, if one takes either a subjectivistic or a limiting frequency approach to probability, one can never be certain of probability values. An algorithm should not only be capable of reporting the probabilities of the alternatives of remaining nodes when other nodes are instantiated; it should also be capable of reporting the uncertainty in these probabilities relative to the uncertainty in the probabilities which are stored in the network. In this paper a method for determining the variances in inferred probabilities is obtained under the assumption that a posterior distribution on the uncertainty variables can be approximated by the prior distribution. It is shown that this assumption is plausible if their is a reasonable amount of confidence in the probabilities which are stored in the network. Furthermore in this paper, a surprising upper bound for the prior variances in the probabilities of the alternatives of all nodes is obtained in the case where the probability distributions of the probabilities of the alternatives are beta distributions. It is shown that the prior variance in the probability at an alternative of a node is bounded above by the largest variance in an element of the conditional probability distribution for that node.

In this paper, we consider several types of information and methods of combination associated with incomplete probabilistic systems. We discriminate between 'a priori' and evidential information. The former one is a description of the whole population, the latest is a restriction based on observations for a particular case. Then, we propose different combination methods for each one of them. We also consider conditioning as the heterogeneous combination of 'a priori' and evidential information. The evidential information is represented as a convex set of likelihood functions. These will have an associated possibility distribution with behavior according to classical Possibility Theory.

This paper presents a simple framework for Horn clause abduction, with probabilities associated with hypotheses. It is shown how this representation can represent any probabilistic knowledge representable in a Bayesian belief network. The main contributions are in finding a relationship between logical and probabilistic notions of evidential reasoning. This can be used as a basis for a new way to implement Bayesian Networks that allows for approximations to the value of the posterior probabilities, and also points to a way that Bayesian networks can be extended beyond a propositional language.

Since exact probabilistic inference is intractable in general for large multiply connected belief nets, approximate methods are required. A promising approach is to use heuristic search among hypotheses (instantiations of the network) to find the most probable ones, as in the TopN algorithm. Search is based on the relative probabilities of hypotheses which are efficient to compute. Given upper and lower bounds on the relative probability of partial hypotheses, it is possible to obtain bounds on the absolute probabilities of hypotheses. Best-first search aimed at reducing the maximum error progressively narrows the bounds as more hypotheses are examined. Here, qualitative probabilistic analysis is employed to obtain bounds on the relative probability of partial hypotheses for the BN20 class of networks networks and a generalization replacing the noisy OR assumption by negative synergy. The approach is illustrated by application to a very large belief network, QMR-BN, which is a reformulation of the Internist-1 system for diagnosis in internal medicine.

We present a generalization of the local expression language used in the Symbolic Probabilistic Inference (SPI) approach to inference in belief nets [1l, [8]. The local expression language in SPI is the language in which the dependence of a node on its antecedents is described. The original language represented the dependence as a single monolithic conditional probability distribution. The extended language provides a set of operators (*, +, and -) which can be used to specify methods for combining partial conditional distributions. As one instance of the utility of this extension, we show how this extended language can be used to capture the semantics, representational advantages, and inferential complexity advantages of the "noisy or" relationship.