# A flexible sequential Monte Carlo algorithm for parametric constrained regression

Research output: Contribution to journalArticle

### 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–SimulatedAnnealing 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.

Original language English 13-26 14 Computational Statistics and Data Analysis 138 26 Mar 2019 https://doi.org/10.1016/j.csda.2019.03.011 Published - 1 Oct 2019

### Fingerprint

Sequential Monte Carlo
Sequential Algorithm
Monte Carlo Algorithm
Regression
Indicator function
Shape Constraint
Rational functions
Loss Function
B-spline
Rational function
Splines
Monotonicity
Regression Model
Closed-form
Curve

### Cite this

@article{58c07307ba4d4f07b79c138067fb00bf,
title = "A flexible sequential Monte Carlo algorithm for parametric constrained regression",
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–SimulatedAnnealing 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.",
keywords = "B-splines, Constrained optimisation, Rational functions, Sequential Monte Carlo, Shape constraints, Simulated annealing",
author = "Kenyon Ng and Turlach, {Berwin A.} and Kevin Murray",
year = "2019",
month = "10",
day = "1",
doi = "10.1016/j.csda.2019.03.011",
language = "English",
volume = "138",
pages = "13--26",
journal = "Computational Statistics & Data Analysis",
issn = "0167-9473",
publisher = "Elsevier",

}

In: Computational Statistics and Data Analysis, Vol. 138, 01.10.2019, p. 13-26.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A flexible sequential Monte Carlo algorithm for parametric constrained regression

AU - Ng, Kenyon

AU - Turlach, Berwin A.

AU - Murray, Kevin

PY - 2019/10/1

Y1 - 2019/10/1

N2 - 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–SimulatedAnnealing 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.

AB - 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–SimulatedAnnealing 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.

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KW - Constrained optimisation

KW - Rational functions

KW - Sequential Monte Carlo

KW - Shape constraints

KW - Simulated annealing

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