Order of Nonlinearity as a Complexity Measure for Models Generated by Symbolic Regression via Pareto Genetic Programming

Vladislavleva, Ekaterina; Smits, Guido; Hertog, Dick den

doi:10.1109/tevc.2008.926486

Cited by 289 publications

(159 citation statements)

References 17 publications

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“…Recently, (Koo and Kil 2008) proposes a new model selection measure based on the modulus of continuity of a function (Lorentz 1986) and provide upper bounds for the modulus of continuity for different estimation functions. From Genetic Programming (GP), a new complexity measure is introduced in (Vladislavleva, Smits, and den Hertog 2009) that measures the order of non-linearity of a given GP tree. It is based on the degree of the best fitting polynomial of the symbolic equation represented by the tree.…”

Section: Related Workmentioning

confidence: 99%

An alternative approach to avoid overfitting for surrogate models

Nguyen¹,

Couckuyt²,

Knockaert³

et al. 2011

Proceedings of the 2011 Winter Simulation Conference (WSC)

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Surrogate models are data-driven models used to accurately mimic the complex behavior of a system. They are often used to approximate computationally expensive simulation code in order to speed up the exploration of design spaces. A crucial step in the building of surrogate models is finding a good set hyperparameters, which determine the behavior of the model. This is especially important when dealing with sparse data, as the models are in that case more prone to overfitting. Cross-validation is often used to optimize the hyperparameters of surrogate models, however it is computationally expensive and can still lead to overfitting or other erratic model behavior. This paper introduces a new auxiliary measure for the optimization of the hyperparameters of surrogate models which, when used in conjunction with a cheap accuracy measure, is fast and effective at avoiding unexplained model behavior.

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Section: Related Workmentioning

confidence: 99%

An alternative approach to avoid overfitting for surrogate models

Nguyen¹,

Couckuyt²,

Knockaert³

et al. 2011

Proceedings of the 2011 Winter Simulation Conference (WSC)

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“…We tested SCS on the following well known regression problems, Keijzer-6 [13], Nguyen-7 [22], Pagie-1 [21] and Vladislavleva-4 [26], proposed as good benchmarks by White et al [27]. Also only the training set was used for evaluation.…”

Section: Experimental Settingmentioning

confidence: 99%

Introducing Semantic-Clustering Selection in Grammatical Evolution

Forstenlechner

Nicolau

Fagan

et al. 2015

Proceedings of the Companion Publication of the 2015 Annual Conference on Genetic and Evolutionary Computation

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Semantics has gained much attention in the last few years and new advanced crossover and mutation operations have been created which use semantic information to improve the quality and generalisability of individuals in genetic programming. In this paper we present a new selection operator in grammatical evolution which uses semantic information of individuals instead of just the fitness value. The semantic traits of an individual are stored in a vector. An unsupervised learning technique is used to cluster individuals based on their semantic vector. Individuals are only allowed to reproduce with individuals from the same cluster to preserve semantic locality and intensify the search in a certain semantic area. At the same time, multiple semantic areas are covered by the search as there exist multiple clusters which cover different areas and therefore preserve semantic diversity. This new selection operator is tested on several symbolic regression benchmark problems and compared to grammatical evolution with tournament selection to analyse its performance.

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“…For instance, [15] proposed two measures. The first is to equate complexity with tree size, based on the assumption that bloated programs are also complex.…”

Section: Overfittingmentioning

confidence: 99%

“…The second addresses the complexity of the program output or functional complexity, measured as the degree of the Chebyshev polynomial that approximates the output. In [15] complexity is studied as an objective that should be optimized, not as an indicator of program overfitting, which could be studied in future work.…”

Section: Overfittingmentioning

confidence: 99%

An Empirical Study of Functional Complexity as an Indicator of Overfitting in Genetic Programming

Trujillo

Silva

Legrand

et al. 2011

Lecture Notes in Computer Science

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Abstract.Recently, it has been stated that the complexity of a solution is a good indicator of the amount of overfitting it incurs. However, measuring the complexity of a program, in Genetic Programming, is not a trivial task. In this paper, we study the functional complexity and how it relates with overfitting on symbolic regression problems. We consider two measures of complexity, Slope-based Functional Complexity, inspired by the concept of curvature, and Regularity-based Functional Complexity based on the concept of Hölderian regularity. In general, both complexity measures appear to be poor indicators of program overfitting. However, results suggest that Regularity-based Functional Complexity could provide a good indication of overfitting in extreme cases.

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Order of Nonlinearity as a Complexity Measure for Models Generated by Symbolic Regression via Pareto Genetic Programming

Cited by 289 publications

References 17 publications

An alternative approach to avoid overfitting for surrogate models

An alternative approach to avoid overfitting for surrogate models

Introducing Semantic-Clustering Selection in Grammatical Evolution

An Empirical Study of Functional Complexity as an Indicator of Overfitting in Genetic Programming

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