Mixture of Quantile Regression

Abstract

Quantile Regression (QR) is a potent statistical technique enabling the estimation of conditional quantiles within a distribution. However, its application to dependent data units remains a challenging endeavor. In this paper, we introduce a novel approach aimed at extending the utility of quantile regression to correlated data structures. Leveraging the Ewens-Pitman Attraction (EPA) distribution, we propose a non-parametric mixture model of Quantile Regression, facilitating aplication of quantile regression to dependent / clustered data. Through experiments conducted on both synthetic and real-world datasets, we demonstrate the efficacy of our model in uncovering latent clusters embedded within the data while accommodating the fitting of adaptive quantiles to capture diverse patterns. Our findings underscore the versatility and effectiveness of the proposed framework, offering a promising avenue for the analysis of correlated data structures through quantile regression methodologies.