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

Warped Gaussian processes (WGPs) are effective for non-stationary probabilistic regression but cannot handle multimodal data with functional covariates adequately. To address this limitation, we propose a mixture of warped Gaussian process functional regressions (MWGPFR), a unified framework that jointly captures multimodal structures, nonlinear output transformations and functional dependencies. In MWGPFR, each mixture component is modeled as a warped Gaussian process functional regression (WGPFR), enabling the capture of local nonlinear variations while representing shared global trends. For efficient parameter estimation, we propose a classification expectation-maximization (CEM) algorithm. To reduce sensitivity to initialization and mitigate convergence to poor local optima, we further develop a split-and-merge CEM (SMCEM) algorithm that improves convergence quality. Experimental results on synthetic and real-world datasets demonstrate that the proposed method achieves improved predictive accuracy, competitive computational efficiency and reliable convergence behavior compared with conventional probabilistic regression approaches.