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Nonparametric supervised learning by linear interpolation with maximum entropy

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3 Author(s)
Gupta, M.R. ; Dept. of Electr. Eng., Washington Univ., Seattle, WA, USA ; Gray, R.M. ; Olshen, R.A.

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.

Published in:

Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:28 ,  Issue: 5 )