Nonlocal prior mixture-based Bayesian wavelet regression

2025-01-30

AI Summary

This paper addresses the challenge in Bayesian wavelet regression of simultaneously achieving sparsity and preserving large-magnitude wavelet coefficients, arising from the high dispersion of multiscale coefficients. We propose a novel three-component spike-and-slab prior that integrates a point mass at zero (spike), the moment prior (MOM), and the inverse moment prior (IMOM), introducing for the first time an IMOM/MOM synergistic modeling framework. To flexibly control mixture weights, we incorporate generalized logistic, hyperbolic secant, and generalized normal decay functions; scale parameters are adaptively tuned via double-exponential decay. The method employs empirical Bayes hyperparameter estimation and wavelet transforms, enabling robust inference through nonlocal prior modeling. Extensive simulations and real-world applications—including EEG and noisy audio data—demonstrate substantial improvements in estimation accuracy and sparse signal recovery over classical MOM and IMOM approaches. The accompanying R package, NLPwavelet, is publicly available.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Mining multimedia, multimodal, multilingual, cross-lingual Web data
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

We propose a novel Bayesian wavelet regression approach using a three-component spike-and-slab prior for wavelet coefficients, combining a point mass at zero, a moment (MOM) prior, and an inverse moment (IMOM) prior. This flexible prior supports small and large coefficients differently, offering advantages for highly dispersed data where wavelet coefficients span multiple scales. The IMOM prior's heavy tails capture large coefficients, while the MOM prior is better suited for smaller non-zero coefficients. Further, our method introduces innovative hyperparameter specifications for mixture probabilities and scale parameters, including generalized logit, hyperbolic secant, and generalized normal decay for probabilities, and double exponential decay for scaling. Hyperparameters are estimated via an empirical Bayes approach, enabling posterior inference tailored to the data. Extensive simulations demonstrate significant performance gains over two-component wavelet methods. Applications to electroencephalography and noisy audio data illustrate the method's utility in capturing complex signal characteristics. We implement our method in an R package NLPwavelet.

Problem

• Develops Bayesian wavelet regression with three-component prior
• Improves handling of highly dispersed wavelet coefficients
• Enhances signal extraction in noisy data applications

Innovation

• Three-component spike-and-slab prior for coefficients
• Empirical Bayes hyperparameter estimation approach
• Generalized logit and double exponential decay specifications