In this paper we present anaverage-case analysis of the Bayesian classifier, a simple induction algorithm that fares remarkably well on many learning tasks. Our analysis assumes a monotone conjunctive target concept, and independent, noise-free Boolean attributes. We calculate the probability that the algorithm will induce an arbitrary pair of concept descriptions and then use this to compute the probability of correct classification over the instance space. The analysis takes into account the number of training instances, the number of attributes, the distribution of these attributes, and the level of class noise. We also explore the behavioral implications of the analysis by presenting

We examine a graphical representation of uncertain knowledge called a Bayesian network. The representation is easy to construct and interpret, yet has formal probabilistic semantics making it suitable for statistical manipulation. We show how we can use the representation to learn new knowledge by combining domain knowledge with statistical data. 1 Introduction Many techniques for learning rely heavily on data. In contrast, the knowledge encoded in expert systems usually comes solely from an expert. In this paper, we examine a knowledge representation, called a Bayesian network, that lets us have the best of both worlds. Namely, the representation allows us to learn new knowledge by combining expert domain knowledge and statistical data. A Bayesian network is a graphical representation of uncertain knowledge that most people find easy to construct and interpret. In addition, the representation has formal probabilistic semantics, making it suitable for statistical manipulation (Howard,...

A new approach for learning Bayesian belief networks from raw data is presented. The approach is based on Rissanen's Minimal Description Length (MDL) principle, which is particularly well suited for this task. Our approach does not require any prior assumptions about the distribution being learned. In particular, our method can learn unrestricted multiply-connected belief networks. Furthermore, unlike other approaches our method allows us to tradeo accuracy and complexity in the learned model. This is important since if the learned model is very complex (highly connected) it can be conceptually and computationally intractable. In such a case it would be preferable to use a simpler model even if it is less accurate. The MDL principle o ers a reasoned method for making this tradeo. We also show that our method generalizes previous approaches based on Kullback cross-entropy. Experiments have been conducted to demonstrate the feasibility of the approach. Keywords: Knowledge Acquisition � Bayes Nets � Uncertainty Reasoning. 1

Approaches to learning Bayesian networks from data typically combine a scoring metric with a heuristic search procedure. Given aBayesian network structure, many of the scoring metrics derived in the literature return a score for the entire equivalence class to which the structure belongs. When using such a metric, it is appropriate for the heuristic search algorithm to searchover equivalence classes of Bayesian networks as opposed to individual structures. We present the general formulation of a search space for which the states of the search correspond to equivalence classes of structures. Using this space, anyoneofanumber of heuristic searchalgorithms can easily be applied. We compare greedy search performance in the proposed search space to greedy search performance in a search space for which the states correspond to individual Bayesian network structures. 1

A selective vision system sequentially collects evidence to support a specified hypothesis about a scene, as long as the additional evidence is worth the effort of obtaining it. Efficiency comes from processing the scene only where necessary, to the level of detail necessary, and with only the necessary operators. Knowledge representation and sequential decision-making are central issues for selective vision, which takes advantage of prior knowledge of a domain's abstract and geometrical structure and models for the expected performance and cost of visual operators. The TEA-1 selective vision system uses Bayes nets for representation and benefitcost analysis for control of visual and non-visual actions. It is the high-level control for an active vision system, enabling purposive behavior, the use of qualitative vision modules and a pointable multiresolution sensor. TEA-1 demonstrates that Bayes nets and decision theoretic techniques provide a general, re-usable framework for constructi...

This paper was partially presented at the 9th conference on Uncertainty in Artificial Intelligence, July 1993.

This paper surveys methods for representing and reasoning with imperfect information. It opens with an attempt to classify the different types of imperfection that may pervade data, and a discussion of the sources of such imperfections. The classification is then used as a framework for considering work that explicitly concerns the representation of imperfect information, and related work on how imperfect information may be used as a basis for reasoning. The work that is surveyed is drawn from both the field of databases and the field of artificial intelligence. Both of these areas have long been concerned with the problems caused by imperfect information, and this paper stresses the relationships between the approaches developed in each.

We describe a head-tracking system that harnesses Bayesian modality fusion, a technique for integrating the analyses of multiple visual tracking algorithms within a probabilistic framework. At the heart of the approach is a Bayesian network model that includes random variables that serve as context-sensitive indicators of reliability of the different tracking algorithms. Parameters of the Bayesian model are learned from data in an offline training phase using ground-truth data from a Polhemus tracking device. In our implementation for a real-time head tracking task, algorithms centering on color, motion, and background subtraction modalities are fused into a single estimate of head position in an image. Results demonstrate the effectiveness of Bayesian modality fusion in environments undergoing a variety of visual perturbances.

Probabilistic models based on directed acyclic graphs have a long and rich tradition, beginning with work by the geneticist Sewall Wright in the 1920s. Variants have appeared in many fields. Within statistics, such models are known as directed graphical models; within cognitive science and artificial intelligence, such models are known as Bayesian networks.

this paper, Rumelhart presented compelling evidence that text comprehension must be a distributed process that combines both top-down and bottom-up inferences. Strangely, this dual mode of inference, so characteristic of Bayesian analysis, did not match the capabilities of either the "certainty factors" calculus or the inference networks of PROSPECTOR -- the two major contenders for uncertainty management in the 1970s. I thus began to explore the possibility of achieving distributed computation in a "pure" Bayesian framework, so as not to compromise its basic capacity to combine bi-directional inferences (i.e., predictive and abductive) . Not caring much about generality at that point, I picked the simplest structure I could think of (i.e., a tree) and tried to see if anything useful can be computed by assigning each variable a simple processor, forced to communicate only with its neighbors. This gave rise to the tree-propagation algorithm reported in [15] and, a year later, the Kim-Pearl algorithm [12], which supported not only bi-directional inferences but also intercausal interactions, such as "explaining-away." These two algorithms were described in Section 2 of Fusion.