Optimization of the Smoothing Parameter of the Adaptive Kernel Estimator used in Bayes Classifier - Application to Microarray Data Analysis

다국어 초록 (Multilingual Abstract)

In this work, we focus on nonparametric kernel methods for estimating the probability density function (pdf). The convergence of a kernel estimator depends crucially on the choice of the smoothing parameter. We present in this paper, a new method for optimizing the bandwidth of an estimator of the probability density function: the adaptive kernel estimator. This optimized estimator is used to construct the Bayes classifier. In this sense, we have proposed a new approach to optimize the pdf based on the statistical properties of the probability distributions of random variables. We adopt the maximum entropy principle (MEP) in order to determine the optimal value of the smoothing parameter used in the estimator. In the proposed criterion, the estimated probability density function is called optimal in the sense of having a minimum error rate of classifying data. Finally, we illustrate the robustness of our optimization process of the kernel estimation methods by using a set of DNA microarray data showing that our approach effectively improves the performance of the classification process.

목차 (Table of Contents)

• Abstract
• 1. Introduction
• 2. Kernel based Density Estimation
• 2.1. K-nearest Neighbors Estimator
• 2.2. Parzen-Rosenblatt estimator
• 2.3. Adaptive Kernel Estimator
• 3. Bayes Classifier
• 4. Gene Selection Algorithm
• 4.1. Information Gain
• 4.2. ReliefF
• 4.3. Minimum Redundancy Maximum Relevance (mRMR)
• 5. Optimization of the Smoothing Parameter of the Kernel Estimator
• 5.1 Maximum Entropy Principle
• 5.2 Criterion based on the Maximum Entropy Principle
• 6. Experimental Results
• 6.1. Description of the Data Sets
• 6.2. Choice of Parameter k of Optimized Adaptive Kernel Estimator
• 6.3. Validation Indices
• 6.4. Experimental Results
• 7. Conclusion
• References