The naive Bayes classifier continues to be a popular learning algorithm for data mining applications due to its simplicity and linear run-time. Many enhancements to the basic algorithm have been proposed to help mitigate its primary weakness—the assumption that attributes are independent given the class. All of them improve the performance of naive Bayes at the expense (to a greater or lesser d...

Naive Bayes is a well-known and studied algorithm both in statistics and machine learning. Bayesian learning algorithms represent each concept with a single probabilistic summary. In this paper we present an iterative approach to naive Bayes. The Iterative Bayes begins with the distribution tables built by the naive Bayes. Those tables are iteratively updated in order to improve the probability...

Recent work in supervised learning has shown that a surprisingly simple Bayesian classifier with strong assumptions of independence among features, called naive Bayes, is competitive with state of the art classifiers such as C4.5. This fact raises the question of whether a classifier with less restrictive assumptions can perform even better. In this paper we examine and evaluate approaches for ...

Recent work in supervised learning has shown that a surprisingly simple Bayesian classifier with strong assumptions of independence among features, called naive Bayes, is competitive with state of the art classifiers such as C4.5. This fact raises the question of whether a classifier with less restrictive assumptions can perform even better. In this paper we examine and evaluate approaches for ...

Estimation procedures for nonstationary Markov chains appear to be relatively sparse. This work introduces empirical  Bayes estimators  for the transition probability  matrix of a finite nonstationary  Markov chain. The data are assumed to be of  a panel study type in which each data set consists of a sequence of observations on N>=2 independent and identically dis...

In singular statistical models, it was shown that Bayes learning is effective. However, on Bayes learning, calculation containing the Bayes posterior distribution requires huge computational costs. To overcome the problem, mean field approximation (or equally variational Bayes method) was proposed. Recently, the generalization error and stochastic complexity in mean field approximation have bee...

In this paper we illustrate a simple scheme for dividing a complex Bayes network into a system model and a collection of smaller evidence models. While the system model maintains a permanent record of the state of the system of interest, the evidence models are only used momentarily to absorb evidence from specific observations or findings and then discarded. This paper describes an implementat...

We investigate the theoretical performance of Bayes factor estimators in wavelet regression models with independent and identically distributed errors that are not necessarily normally distributed. We compare these estimators in terms of their frequentist optimality in Besov spaces for a wide variety of error and prior distributions. Furthermore, we provide sufficient conditions that determine ...

The problem of state estimation with stochastic uncertainties in the initial state, model noise, and measurement noise is approached using the restricted risk Bayes approach. It is assumed that the a priori distributions of these quantities are not perfectly known but that some a priori information may be available. While offering robustness, the restricted risk Bayes approach incorporates the ...