Shape-constrained multi-objective genetic programming for symbolic regression

Haider, Christian; França, Fabrício Olivetti de; Burlacu, Bogdan; Kronberger, Gabriel

doi:10.1016/j.asoc.2022.109855

Cited by 9 publications

(4 citation statements)

References 25 publications

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“…These issues, as well as a concise review of the advantages and challenges of symbolic regression, are presented by Smits and Kotanchek (2005). Recently, Haider et al (2023) continued improving symbolic regression algorithms, in particular by focusing on issues with the shape the regression functions and including prior knowledge about it.…”

Section: Forecasting Methods Challengesmentioning

confidence: 99%

Forecasting Selected Commodities’ Prices with the Bayesian Symbolic Regression

Drachal,

Pawłowski

2024

IJFS

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This study firstly applied a Bayesian symbolic regression (BSR) to the forecasting of numerous commodities’ prices (spot-based ones). Moreover, some features and an initial specification of the parameters of the BSR were analysed. The conventional approach to symbolic regression, based on genetic programming, was also used as a benchmark tool. Secondly, various other econometric methods dealing with variable uncertainty were estimated including Bayesian Model Averaging, Dynamic Model Averaging, LASSO, ridge, elastic net, and least-angle regressions, etc. Therefore, this study reports a concise and uniform comparison of an application of several popular econometric models to forecasting the prices of numerous commodities. Robustness checks and statistical tests were performed to strengthen the obtained conclusions. Monthly data beginning from January 1988 and ending in August 2021 were analysed.

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Section: Forecasting Methods Challengesmentioning

confidence: 99%

Forecasting Selected Commodities’ Prices with the Bayesian Symbolic Regression

Drachal,

Pawłowski

2024

IJFS

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“…A number of other approaches exist in the literature that narrow down the equation search space of SR for analyzing scientific data. One is the shape-constrained SR [14,15], which incorporates constraints on function shape (such as partial derivatives and monotonicity) using an efficient application of integer arithmetic. Additionally, other variations of SR direct the search for unit correctness [16][17][18], conserve physical properties [17,[19][20][21], and guide using predefined forms derived from the dataset [19,[22][23][24].…”

Section: Incorporating Background Knowledge Into Srmentioning

confidence: 99%

“…Consequently, we impose these as 'soft' constraints, penalizing expressions for constraint violation, without outright rejecting them. References [14,15] also found soft constraints to be more effective than hard constraints. This approach (as implemented in PySR) is detailed in algorithm 1 (in SI).…”

Section: Checking Thermodynamic Constraintsmentioning

confidence: 99%

Incorporating background knowledge in symbolic regression using a computer algebra system

Fox,

Tran,

Nacion

et al. 2024

Mach. Learn.: Sci. Technol.

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Symbolic Regression (SR) can generate interpretable, concise expressions that fit a given dataset, allowing for more human understanding of the structure than black-box approaches. The addition of background knowledge (in the form of symbolic mathematical constraints) allows for the generation of expressions that are meaningful with respect to theory while also being consistent with data. We specifically examine the addition of constraints to traditional genetic algorithm (GA) based SR (PySR) as well as a Markov-chain Monte Carlo (MCMC) based Bayesian SR architecture (Bayesian Machine Scientist), and apply these to rediscovering adsorption equations from experimental, historical datasets.We find that, while hard constraints prevent GA and MCMC SR from searching, soft constraints can lead to improved performance both in terms of search effectiveness and model meaningfulness, with computational costs increasing by about an order of magnitude. If the constraints do not correlate well with the dataset or expected models, they can hinder the search of expressions. We find incorporating these constraints in Bayesian SR (as the Bayesian prior) is better than by modifying the fitness function in the GA.

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“…This strategy, also known as automated knowledge discovery or symbolic regression, maintains the benefits of mechanistic models while eliminating some of their drawbacks, such as the need for background knowledge and time-consuming construction. 27 The methodology presented in this work follows this paradigm.…”

Section: Introductionmentioning

confidence: 99%