Mixture of partially linear experts

TL;DR

This paper introduces a partially linear mixture of experts model that captures nonlinear relationships in data, improving upon traditional linear assumptions with theoretical guarantees and practical estimation methods.

Contribution

It proposes a novel partially linear structure for mixture of experts models, with proven identifiability and an effective estimation algorithm.

Findings

Model successfully captures nonlinear relationships.

Numerical studies demonstrate improved estimation accuracy.

Real data analysis confirms practical applicability.

Abstract

In the mixture of experts model, a common assumption is the linearity between a response variable and covariates. While this assumption has theoretical and computational benefits, it may lead to suboptimal estimates by overlooking potential nonlinear relationships among the variables. To address 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.