Wavelet-based Bayesian approximate kernel method for high-dimensional data analysis

• Published in: Computational statistics Vol. 39; no. 4; pp. 2323 - 2341
• Main Authors: Guo, Wenxing, Zhang, Xueying, Jiang, Bei, Kong, Linglong, Hu, Yaozhong
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2024; Springer Nature B.V
• Subjects: Bayesian analysis; Classification; Data analysis; Dimensional analysis; Economic Theory/Quantitative Economics/Mathematical Methods; Feature selection; Hilbert space; Kernel functions; Machine learning; Mathematical functions; Mathematics and Statistics; Methods; Original Paper; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Statistics; Support vector machines; Vector spaces; Wavelet analysis; Wavelet transforms; Bayesian kernel model; Wavelet transform; Randomized feature; Kernel method
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-023-01438-1

Kernel methods are often used for nonlinear regression and classification in statistics and machine learning because they are computationally cheap and accurate. The wavelet kernel functions based on wavelet analysis can efficiently approximate any nonlinear functions. In this article, we construct a novel wavelet kernel function in terms of random wavelet bases and define a linear vector space that captures nonlinear structures in reproducing kernel Hilbert spaces (RKHS). Based on the wavelet transform, the data are mapped into a low-dimensional randomized feature space and convert kernel function into operations of a linear machine. We then propose a new Bayesian approximate kernel model with the random wavelet expansion and use the Gibbs sampler to compute the model’s parameters. Finally, some simulation studies and two real datasets analyses are carried out to demonstrate that the proposed method displays good stability, prediction performance compared to some other existing methods.