Nonparametric supervised learning by linear interpolation with maximum entropy
Gupta, M.R.; Gray, R.M.; Olshen, R.A.
Pattern Analysis and Machine Intelligence, IEEE Transactions on
Volume 28, Issue 5, May 2006 Page(s):766 - 781
Digital Object Identifier 10.1109/TPAMI.2006.101
Summary:Nonparametric neighborhood methods for learning entail estimation of class conditional probabilities based on relative frequencies of samples that are "near-neighbors" of a test point. We propose and explore the behavior of a learning algorithm that uses linear interpolation and the principle of maximum entropy (LIME). We consider some theoretical properties of the LIME algorithm: LIME weights have exponential form; the estimates are consistent; and the estimates are robust to additive noise. In relation to bias reduction, we show that near-neighbors contain a test point in their convex hull asymptotically. The common linear interpolation solution used for regression on grids or look-up-tables is shown to solve a related maximum entropy problem. LIME simulation results support use of the method, and performance on a pipeline integrity classification problem demonstrates that the proposed algorithm has practical value.
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