A flexible sequential Monte Carlo algorithm for parametric constrained regression

TL;DR

This paper introduces a flexible Sequential Monte Carlo algorithm that enforces complex shape constraints on regression models without requiring explicit constraint expressions or specific loss functions, demonstrated on rational and B-spline regressions.

Contribution

The paper presents a novel, adaptable SMC-based algorithm that applies shape constraints via indicator functions, enhancing regression modeling flexibility.

Findings

Successfully enforced monotonicity constraints on regression models.

Applicable to rational functions and B-splines.

Open-source implementation available in R.

Abstract

An algorithm is proposed that enables the imposition of shape constraints on regression curves, without requiring the constraints to be written as closed-form expressions, nor assuming the functional form of the loss function. This algorithm is based on Sequential Monte Carlo-Simulated Annealing and only relies on an indicator function that assesses whether or not the constraints are fulfilled, thus allowing the enforcement of various complex constraints by specifying an appropriate indicator function without altering other parts of the algorithm. The algorithm is illustrated by fitting rational function and B-spline regression models subject to a monotonicity constraint. An implementation of the algorithm using R is freely available on GitHub.