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Increasing and Decreasing Returns and Losses in Mutual Information Feature Subset Selection
Laboratorium voor Neuro- en Psychofysiologie, Computational Neuroscience Research Group, Katholieke Universiteit Leuven, O&N II Herestraat 49 - bus 1021, 3000 Leuven, Belgium
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Received: 28 August 2010; Accepted: 19 September 2010 / Published: 11 October 2010
Abstract: Mutual information between a target variable and a feature subset is extensively used as a feature subset selection criterion. This work contributes to a more thorough understanding of the evolution of the mutual information as a function of the number of features selected. We describe decreasing returns and increasing returns behavior in sequential forward search and increasing losses and decreasing losses behavior in sequential backward search. We derive conditions under which the decreasing returns and the increasing losses behavior hold and prove the occurrence of this behavior in some Bayesian networks. The decreasing returns behavior implies that the mutual information is concave as a function of the number of features selected, whereas the increasing returns behavior implies this function is convex. The increasing returns and decreasing losses behavior are proven to occur in an XOR hypercube.
Keywords: Bayesian networks; bit parity; conditional entropy; conditional mutual information; decreasing losses; decreasing returns; feature subset selection; increasing losses; increasing returns
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Van Dijck, G.; Van Hulle, M.M. Increasing and Decreasing Returns and Losses in Mutual Information Feature Subset Selection. Entropy 2010, 12, 2144-2170.
Van Dijck G, Van Hulle MM. Increasing and Decreasing Returns and Losses in Mutual Information Feature Subset Selection. Entropy. 2010; 12(10):2144-2170.
Van Dijck, Gert; Van Hulle, Marc M. 2010. "Increasing and Decreasing Returns and Losses in Mutual Information Feature Subset Selection." Entropy 12, no. 10: 2144-2170.