Iterative Bayes

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 class distribution associated with each training example. In this paper we argue that Iterative Bayes minimizes a quadratic loss function instead of the 0-1 loss function that usually applies to classification problems. Experimental evaluation of Iterative Bayes on 27 benchmark data sets shows consistent gains in accuracy. An interesting side effect of our algorithm is that it shows to be robust to attribute dependencies.

[1]  João Gama A Linear-Bayes Classifier , 2000, IBERAMIA-SBIA.

[2]  Charles Elkan,et al.  Boosting and Naive Bayesian learning , 1997 .

[3]  Pat Langley,et al.  Tractable Average-Case Analysis of Naive Bayesian Classifiers , 1999, ICML.

[4]  Yoshua Bengio,et al.  Pattern Recognition and Neural Networks , 1995 .

[5]  Ron Kohavi,et al.  Bias Plus Variance Decomposition for Zero-One Loss Functions , 1996, ICML.

[6]  Peter E. Hart,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[7]  Ron Kohavi,et al.  Scaling Up the Accuracy of Naive-Bayes Classifiers: A Decision-Tree Hybrid , 1996, KDD.

[8]  Ron Kohavi,et al.  Feature Selection for Knowledge Discovery and Data Mining , 1998 .

[9]  Ron Kohavi,et al.  Supervised and Unsupervised Discretization of Continuous Features , 1995, ICML.

[10]  Catherine Blake,et al.  UCI Repository of machine learning databases , 1998 .

[11]  Igor Kononenko,et al.  Semi-Naive Bayesian Classifier , 1991, EWSL.

[12]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[13]  Ron Kohavi,et al.  Irrelevant Features and the Subset Selection Problem , 1994, ICML.

[14]  George H. John Enhancements to the data mining process , 1997 .

[15]  Thomas G. Dietterich What is machine learning? , 2020, Archives of Disease in Childhood.

[16]  Pedro M. Domingos MetaCost: a general method for making classifiers cost-sensitive , 1999, KDD '99.

[17]  Thomas Richardson,et al.  Interpretable Boosted Naïve Bayes Classification , 1998, KDD.

[18]  Yoav Freund,et al.  Boosting the margin: A new explanation for the effectiveness of voting methods , 1997, ICML.

[19]  Geoffrey I. Webb,et al.  Adjusted Probability Naive Bayesian Induction , 1998, Australian Joint Conference on Artificial Intelligence.

[20]  M. Pazzani Constructive Induction of Cartesian Product Attributes , 1998 .

[21]  David J. Spiegelhalter,et al.  Machine Learning, Neural and Statistical Classification , 2009 .

[22]  Pat Langley,et al.  Induction of Recursive Bayesian Classifiers , 1993, ECML.