When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated by a single Gaussian. In this paper we abandon the normality assumption and instead use statistical methods for nonparametric density estimation. For a naive Bayesian classifier, we present experimental results on a variety of natural and artificial domains, comparing two methods of density estimation: assuming normality and modeling each conditional distribution with a single Gaussian; and using nonparametric kernel density estimation. We observe large reductions in error on several natural and artificial data sets, which suggests that kernel estimation is a useful tool for learning Bayesian models. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence, Morgan Kaufmann Publishers, San Mateo, 1995 1 Introduction In rec...

In the past decades Machine Learning tools have been successfully used in 11 several medical diagnostic problems. While they often significantly out- 12 perform expert physicians (in terms of diagnostic accuracy, sensitivity, and 13 specificity), they are mostly not being used in practice. One reason for this 14 is that it is difficult to obtain an unbiased estimation of diagnose's reliabil- 15 ity. We discuss how reliability of diagnoses is assessed in medical decision 16 making and propose a general framework for reliability estimation in Ma- 17 chine Learning, based on transductive inference. We compare our approach 18 with a usual (Machine Learning) probabilistic approach as well as with clas- 19 sical stepwise diagnostic process where reliability of diagnose is presented 20 as its post-test probability. The proposed transductive approach is evaluated 21 on several medical datasets from the UCI (University of California, Irvine) 22 repository as well as on a practical problem of clinical diagnosis of the coro- 23 nary artery disease. In all cases significant improvements over existing tech- 24 niques are achieved. 25 26 27 Keywords: transduction, machine learning, medical diagnosis, reliability 28 estimation, coronary artery disease. 29 1