Fast Partial Quantile Regression

TL;DR

This paper introduces fast partial quantile regression (fPQR), a robust and efficient extension of partial least squares that provides quantile-based estimates, improving robustness in high-dimensional, colinear, or heavy-tailed data scenarios.

Contribution

The paper extends multivariate PLS to the quantile regression framework, offering a new robust dimensionality reduction technique with a theoretical formulation and efficient implementation.

Findings

fPQR outperforms traditional methods in robustness to outliers

Simulation experiments demonstrate the efficiency of fPQR

Application to biscuit dough dataset shows practical effectiveness

Abstract

Partial least squares (PLS) is a dimensionality reduction technique used as an alternative to ordinary least squares (OLS) in situations where the data is colinear or high dimensional. Both PLS and OLS provide mean based estimates, which are extremely sensitive to the presence of outliers or heavy tailed distributions. In contrast, quantile regression is an alternative to OLS that computes robust quantile based estimates. In this work, the multivariate PLS is extended to the quantile regression framework, obtaining a theoretical formulation of the problem and a robust dimensionality reduction technique that we call fast partial quantile regression (fPQR), that provides quantile based estimates. An efficient implementation of fPQR is also derived, and its performance is studied through simulation experiments and the chemometrics well known biscuit dough dataset, a real high dimensional example.