Probabilistic networks, which provide compact descriptions of complex stochastic relationships among several random variables, are rapidly becoming the tool of choice for uncertain reasoning in artificial intelligence. We show that networks with fixed structure containing hidden variables can be learned automatically from data using a gradient-descent mechanism similar to that used in neural networks. We also extend the method to networks with intensionally represented distributions, including networks with continuous variables and dynamic probabilistic networks. Because probabilistic networks provide explicit representations of causal structure, human experts can easily contribute prior knowledge to the training process, thereby significantly improving the learning rate. Adaptive probabilistic networks (APNs) may soon compete directly with neural networks as models in computational neuroscience as well as in industrial and financial applications. 1 Introduction Intelligent systems, ...

Incorporating prior knowledge into black-box classifiers is still much of an open problem. We propose a hybrid Bayesian methodology that consists in encoding prior knowledge in the form of a (Bayesian) belief network and then using this knowledge to estimate an informative prior for a blackbox model (e.g. a multilayer perceptron). Two technical approaches are proposed for the transformation of the belief network into an informative prior. The first one consists in generating samples according to the most probable parameterization of the Bayesian belief network and using them as virtual data together with the real data in the Bayesian learning of a multilayer perceptron. The second approach consists in transforming probability distributions over belief network parameters into distributions over multilayer perceptron parameters. The essential attribute of the hybrid methodology is that it combines prior knowledge and statistical data efficiently when prior knowledge is available and the sample is of small or medium size. Additionally, we describe how the Bayesian approach can provide uncertainty information about the predictions (e.g. for classification with rejection). We demonstrate these techniques on the medical task of predicting the malignancy of ovarian masses and summarize the practical advantages of the Bayesian approach. We compare the learning curves for the hybrid methodology with those of several belief networks and multilayer perceptrons. Furthermore, we report the performance of Bayesian belief networks when they are allowed to exclude hard cases based on various measures of prediction uncertainty.

Bayesian networks have become one of the most popular probabilistic techniques in AI, largely due to the development of several efficient inference algorithms. In this paper we describe a heuristic method for constructing Bayesian networks. Our construction method relies on the relationship between Bayesian networks and decomposable models, a special kind of graphical model. We explain this relationship and then show how it can be used to facilitate model construction. Finally, we describe an implemented computer program that illustrates these ideas. 1 Introduction Relationships among symptoms, evidence and diseases are often so complex that they can be described only by very general models. Such models can easily be constructed within the framework of probability theory. Several papers in defense of applying probability theory to AI appeared in the early 1980s (e.g. [2, 18]), and since then probability theory has been widely accepted as a framework for representing and reason...

The progress of medical informatics has been characterized by the development of a wide range of reasoning methods. These reasoning methods are based on organizing principles that make use of the various relations existing in medical domains: associations, probabilities, causality, functional relationships, temporal relations, locality, similarity, and clinical practice. Some, such as those based on associations and probabilities have been developed to the point where there are off-theshelf tools available for the researcher to develop new decision support tools. Others such as temporal relations require more effort to use effectively. Even so, we have learned the importance of a separate explicit representation of the domain knowledge and have considerable experience and an impressive armamentarium with which to face the new milieu provided by the Internet.