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Beyond Independence: Conditions for the Optimality of the Simple Bayesian Classifier (1996) [234 citations — 8 self]

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@INPROCEEDINGS{Domingos96beyondindependence:,
    author = {Pedro Domingos and Michael Pazzani},
    title = {Beyond Independence: Conditions for the Optimality of the Simple Bayesian Classifier},
    booktitle = {Machine Learning},
    year = {1996},
    pages = {105--112},
    publisher = {Morgan Kaufmann}
}

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Abstract:

The simple Bayesian classifier (SBC) is commonly thought to assume that attributes are independent given the class, but this is apparently contradicted by the surprisingly good performance it exhibits in many domains that contain clear attribute dependences. No explanation for this has been proposed so far. In this paper we show that the SBC does not in fact assume attribute independence, and can be optimal even when this assumption is violated by a wide margin. The key to this finding lies in the distinction between classification and probability estimation: correct classification can be achieved even when the probability estimates used contain large errors. We show that the previously-assumed region of optimality of the SBC is a second-order infinitesimal fraction of the actual one. This is followed by the derivation of several necessary and several sufficient conditions for the optimality of the SBC. For example, the SBC is optimal for learning arbitrary conjunctions and disjunction...

Citations

3356	C4.5: Programs for Machine Learning – Quinlan - 1993
3011	Pattern Classification and Scene Analysis – Duda, Hart - 1973
638	UCI repository of machine learning databases. For information contact ml-repository@ics.uci.edu – Murphy, Aha - 1994
620	The CN2 induction algorithm – Clark, Niblett - 1989
330	Very simple classification rules perform well on most commonly used datasets – Holte - 1993
304	Supervised and unsupervised discretization of continuous features – Dougherty, Kohavi, et al. - 1995
251	Rule induction with CN2: Some recent improvements – Clark, Boswell - 1991
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238	A Weighted Nearest Neighbor Algorithm for Learning with Symbolic Features – Cost, Salzberg - 1993
216	Pattern Classi cation and Scene Analysis – Duda, Hart - 1973
163	Induction of selective Bayesian classifiers – Langley, Sage - 1994
99	Semi-naive Bayesian classifier – Kononenko - 1991
87	Wrappers for performance enhancement and oblivious decision graphs – Kohavi - 1995
40	Induction of recursive Bayesian classifiers – Langley - 1993
30	Towards a better understanding of memory-based reasoning systems – Rachlin, Kasif, et al. - 1994
21	Very simple classi cation rules perform well on most commonly used datasets – Holte - 1993
13	An analysis of Bayesian classi ers – Langley, Iba, et al. - 1992
10	Induction of selective Bayesian classi ers – Langley, Sage - 1994
9	Searching for attribute dependencies in Bayesian classi ers – Pazzani - 1995
5	Semi-naive Bayesian classier – Kononenko - 1991
5	Induction of recursive Bayesian classi ers – Langley - 1993