Mixture of warped Gaussian process functional regressions and its classification EM algorithm

Area of Science:

• Machine Learning
• Statistics
• Probabilistic Modeling

Background:

• Warped Gaussian processes (WGPs) excel at non-stationary regression but struggle with multimodal data and functional covariates.
• Existing methods lack the ability to adequately capture multimodal structures, nonlinear transformations, and functional dependencies simultaneously.

Purpose of the Study:

• To propose a unified framework, the mixture of warped Gaussian process functional regressions (MWGPFR), for handling multimodal data with functional covariates.
• To jointly model multimodal structures, nonlinear output transformations, and functional dependencies in probabilistic regression.

Main Methods:

• Each component of the MWGPFR framework is a warped Gaussian process functional regression (WGPFR) to capture local nonlinear variations.
• A classification expectation-maximization (CEM) algorithm is proposed for efficient parameter estimation.
• A split-and-merge CEM (SMCEM) algorithm is developed to enhance convergence quality and reduce sensitivity to initialization.

Main Results:

• The proposed MWGPFR method demonstrates improved predictive accuracy on both synthetic and real-world datasets.
• The approach shows competitive computational efficiency compared to conventional probabilistic regression techniques.
• The SMCEM algorithm ensures reliable convergence behavior, mitigating issues with local optima.

Conclusions:

• The MWGPFR framework offers a robust solution for multimodal probabilistic regression with functional covariates.
• The developed CEM and SMCEM algorithms provide efficient and reliable parameter estimation.
• This unified approach advances the capabilities of probabilistic regression for complex, non-stationary data patterns.