Fitting Non-Parametric Mixture of Regressions: Introducing an EM-Type Algorithm to Address the Label-Switching Problem

The non-parametric Gaussian mixture of regressions (NPGMRs) model serves as a flexible approach for the determination latent heterogeneous regression relationships. This assumes that component means, variances and mixing proportions are smooth unknown functions covariates where error distribution each is assumed to be hence symmetric. These estimated over set grid points using Expectation-Maximization (EM) algorithm maximise local-likelihood functions. However, maximizing function separately does not guarantee local responsibilities corresponding labels, obtained at E-step EM algorithm, align point leading label-switching problem. results in non-smooth In this paper, we propose an estimation procedure account label switching by tracking roughness We use obtain global estimate which then used maximize function. performance proposed demonstrated simulation study through application real world data. case well-separated components, gives similar competitive methods. poorly separated outperforms