Mixture of Partially Linear Experts

ABSTRACT The mixture of experts framework is widely used in machine learning to model data with latent clusters. However, the conventional assumption of linearity between response variables and covariates may overlook inherent nonlinear relationships, potentially yielding suboptimal estimates. To overcome this limitation, we propose a partially linear structure that incorporates unspecified functions to capture nonlinear relationships. We establish the identifiability of the proposed model under mild conditions and introduce a practical estimation algorithm. We present the performance of our approach through numerical studies, including simulations and real data analysis.