Spectrum-Based Kernel Length Estimation for Gaussian Process Classification

作     者：Wang, Liang Li, Chuan 

作者机构：Chinese Acad Sci Inst Automat Natl Lab Pattern Recognit Beijing 100190 Peoples R China Max Planck Inst Informat D-66123 Saarbrucken Germany 

出 版 物：《IEEE TRANSACTIONS ON CYBERNETICS》 (IEEE Trans. Cybern.)

年 卷 期：2014年第44卷第6期

页      面：805-816页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：National Basic Research Program of China [2012CB316300] Hundred Talents Program of the Chinese Academy of Sciences National Natural Science Foundation of China 

主　　题：Autocorrelation Gaussian process classification kernel length scale estimation spectrum analysis 

摘      要：Recent studies have shown that Gaussian process (GP) classification, a discriminative supervised learning approach, has achieved competitive performance in real applications compared with most state-of-the-art supervised learning methods. However, the problem of automatic model selection in GP classification, involving the kernel function form and the corresponding parameter values (which are unknown in advance), remains a challenge. To make GP classification a more practical tool, this paper presents a novel spectrum analysis-based approach for model selection by refining the GP kernel function to match the given input data. Specifically, we target the problem of GP kernel length scale estimation. Spectrums are first calculated analytically from the kernel function itself using the autocorrelation theorem as well as being estimated numerically from the training data themselves. Then, the kernel length scale is automatically estimated by equating the two spectrum values, i.e., the kernel function spectrum equals to the estimated training data spectrum. Compared with the classical Bayesian method for kernel length scale estimation via maximizing the marginal likelihood (which is time consuming and could suffer from multiple local optima), extensive experimental results on various data sets show that our proposed method is both efficient and accurate.