A Bayesian Method for Causal Modeling and Discovery Under Selection

This paper describes a Bayesian method for learning causal networks using samples that were selected in a non-random manner from a population of interest. Examples of data obtained by non-random sampling include convenience samples and case-control data in which a fixed number of samples with and without some condition is collected; such data are not uncommon. The paper describes a method for combining data under selection with prior beliefs in order to derive a posterior probability for a model of the causal processes that are generating the data in the population of interest. The priors include beliefs about the nature of the non-random sampling procedure. Although exact application of the method would be computationally intractable for most realistic datasets, efficient special-case and approximation methods are discussed. Finally, the paper describes how to combine learning under selection with previous methods for learning from observational and experimental data that are obtained on random samples of the population of interest. The net result is a Bayesian methodology that supports causal modeling and discovery from a rich mixture of different types of data.Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000

A Method for Using Belief Networks as Influence Diagrams

This paper demonstrates a method for using belief-network algorithms to solve influence diagram problems. In particular, both exact and approximation belief-network algorithms may be applied to solve influence-diagram problems. More generally, knowing the relationship between belief-network and influence-diagram problems may be useful in the design and development of more efficient influence diagram algorithms.Comment: Appears in Proceedings of the Fourth Conference on Uncertainty in Artificial Intelligence (UAI1988

An Evaluation of an Algorithm for Inductive Learning of Bayesian Belief Networks Usin

Bayesian learning of belief networks (BLN) is a method for automatically constructing belief networks (BNs) from data using search and Bayesian scoring techniques. K2 is a particular instantiation of the method that implements a greedy search strategy. To evaluate the accuracy of K2, we randomly generated a number of BNs and for each of those we simulated data sets. K2 was then used to induce the generating BNs from the simulated data. We examine the performance of the program, and the factors that influence it. We also present a simple BN model, developed from our results, which predicts the accuracy of K2, when given various characteristics of the data set.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI1994

A Structurally and Temporally Extended Bayesian Belief Network Model: Definitions, Properties, and Modeling Techniques

We developed the language of Modifiable Temporal Belief Networks (MTBNs) as a structural and temporal extension of Bayesian Belief Networks (BNs) to facilitate normative temporal and causal modeling under uncertainty. In this paper we present definitions of the model, its components, and its fundamental properties. We also discuss how to represent various types of temporal knowledge, with an emphasis on hybrid temporal-explicit time modeling, dynamic structures, avoiding causal temporal inconsistencies, and dealing with models that involve simultaneously actions (decisions) and causal and non-causal associations. We examine the relationships among BNs, Modifiable Belief Networks, and MTBNs with a single temporal granularity, and suggest areas of application suitable to each one of them.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI1996

A Bayesian Network Scoring Metric That Is Based On Globally Uniform Parameter Priors

We introduce a new Bayesian network (BN) scoring metric called the Global Uniform (GU) metric. This metric is based on a particular type of default parameter prior. Such priors may be useful when a BN developer is not willing or able to specify domain-specific parameter priors. The GU parameter prior specifies that every prior joint probability distribution P consistent with a BN structure S is considered to be equally likely. Distribution P is consistent with S if P includes just the set of independence relations defined by S. We show that the GU metric addresses some undesirable behavior of the BDeu and K2 Bayesian network scoring metrics, which also use particular forms of default parameter priors. A closed form formula for computing GU for special classes of BNs is derived. Efficiently computing GU for an arbitrary BN remains an open problem.Comment: Appears in Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence (UAI2002

A Bayesian Network Classifier that Combines a Finite Mixture Model and a Naive Bayes Model

In this paper we present a new Bayesian network model for classification that combines the naive-Bayes (NB) classifier and the finite-mixture (FM) classifier. The resulting classifier aims at relaxing the strong assumptions on which the two component models are based, in an attempt to improve on their classification performance, both in terms of accuracy and in terms of calibration of the estimated probabilities. The proposed classifier is obtained by superimposing a finite mixture model on the set of feature variables of a naive Bayes model. We present experimental results that compare the predictive performance on real datasets of the new classifier with the predictive performance of the NB classifier and the FM classifier.Comment: Appears in Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI1999

Updating Probabilities in Multiply-Connected Belief Networks

This paper focuses on probability updates in multiply-connected belief networks. Pearl has designed the method of conditioning, which enables us to apply his algorithm for belief updates in singly-connected networks to multiply-connected belief networks by selecting a loop-cutset for the network and instantiating these loop-cutset nodes. We discuss conditions that need to be satisfied by the selected nodes. We present a heuristic algorithm for finding a loop-cutset that satisfies these conditions.Comment: Appears in Proceedings of the Fourth Conference on Uncertainty in Artificial Intelligence (UAI1988

A Multivariate Discretization Method for Learning Bayesian Networks from Mixed Data

In this paper we address the problem of discretization in the context of learning Bayesian networks (BNs) from data containing both continuous and discrete variables. We describe a new technique for multivariate discretization, whereby each continuous variable is discretized while taking into account its interaction with the other variables. The technique is based on the use of a Bayesian scoring metric that scores the discretization policy for a continuous variable given a BN structure and the observed data. Since the metric is relative to the BN structure currently being evaluated, the discretization of a variable needs to be dynamically adjusted as the BN structure changes.Comment: Appears in Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI1998

Causal Discovery from a Mixture of Experimental and Observational Data

This paper describes a Bayesian method for combining an arbitrary mixture of observational and experimental data in order to learn causal Bayesian networks. Observational data are passively observed. Experimental data, such as that produced by randomized controlled trials, result from the experimenter manipulating one or more variables (typically randomly) and observing the states of other variables. The paper presents a Bayesian method for learning the causal structure and parameters of the underlying causal process that is generating the data, given that (1) the data contains a mixture of observational and experimental case records, and (2) the causal process is modeled as a causal Bayesian network. This learning method was applied using as input various mixtures of experimental and observational data that were generated from the ALARM causal Bayesian network. In these experiments, the absolute and relative quantities of experimental and observational data were varied systematically. For each of these training datasets, the learning method was applied to predict the causal structure and to estimate the causal parameters that exist among randomly selected pairs of nodes in ALARM that are not confounded. The paper reports how these structure predictions and parameter estimates compare with the true causal structures and parameters as given by the ALARM network.Comment: Appears in Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI1999

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