Using Genetic Programming with Prior Formula Knowledge to Solve Symbolic Regression Problem

Lü, Qiang; Ren, Jun

doi:10.1155/2016/1021378

Cited by 22 publications

(15 citation statements)

References 28 publications

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“…For convenience in generating and modifying equations algorithmically, they are typically represented as trees (see Figure S1 for an example of a function represented as a tree). Unfortunately, because it is not restricted to linear combinations of descriptors (which would be linear regression), symbolic regression poses an NP (as in Non-Polynomial time) -hard optimization problem 55 . Oftentimes, a genetic algorithm is used as the optimization algorithm in the case of symbolic regression.…”

Section: Genetic Programmingmentioning

confidence: 99%

Predicting Metal–Support Interactions in Oxide-Supported Single-Atom Catalysts

Tan

Dixit

Dean

et al. 2019

Ind. Eng. Chem. Res.

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Single-Atom Catalysts (SACs), containing under-coordinated single metal atoms bound on the surface of supports, have recently emerged as promising heterogeneous catalysts due to their intrinsic catalytic properties and efficient utilization (high dispersion) of noble metal atoms. Strong Metal-Support Interactions (MSIs) present in these catalysts can dictate the physicochemical properties, activity, and stability of SACs, which are significantly different from the conventional supported nanoscale metal catalysts. Although SACs exhibit unique catalytic behavior, their stability under catalytic operation is questioned due to the tendency of metals to sinter (aggregation). An optimal MSI can avoid metal aggregation and tune the stability and catalytic activity of SACs. Herein, we investigate MSIs of a series of transition metal atoms (Au, Cu, Ag,

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Section: Genetic Programmingmentioning

confidence: 99%

Predicting Metal–Support Interactions in Oxide-Supported Single-Atom Catalysts

Tan

Dixit

Dean

et al. 2019

Ind. Eng. Chem. Res.

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“…The search space grows exponentially with the length of the expression, rendering symbolic regression a challenging machine learning problem. It is generally believed to be NP-hard [Lu et al, 2016]; however, no formal proof exists. Given the 35th Conference on Neural Information Processing Systems (NeurIPS 2021), Sydney, Australia.…”

Section: Introductionmentioning

confidence: 99%

Symbolic Regression via Neural-Guided Genetic Programming Population Seeding

Mundhenk¹,

Landajuela²,

Glatt³

et al. 2021

Preprint

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Symbolic regression is the process of identifying mathematical expressions that fit observed output from a black-box process. It is a discrete optimization problem generally believed to be NP-hard. Prior approaches to solving the problem include neural-guided search (e.g. using reinforcement learning) and genetic programming. In this work, we introduce a hybrid neural-guided/genetic programming approach to symbolic regression and other combinatorial optimization problems. We propose a neural-guided component used to seed the starting population of a random restart genetic programming component, gradually learning better starting populations. On a number of common benchmark tasks to recover underlying expressions from a dataset, our method recovers 65% more expressions than a recently published top-performing model using the same experimental setup. We demonstrate that running many genetic programming generations without interdependence on the neural-guided component performs better for symbolic regression than alternative formulations where the two are more strongly coupled. Finally, we introduce a new set of 22 symbolic regression benchmark problems with increased difficulty over existing benchmarks. Source code is provided at www.github.com/brendenpetersen/deep-symbolic-optimization.

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“…Bagging is used in this paper, and classification and regression trees (CARTs) [23] are used as base learners. Subsequently, the optimal overproduction pool size H S ={ H 1 ,…, H T s } is estimated using the Pareto optimization algorithm.…”

Section: Methodsmentioning

confidence: 99%

Margin-Based Pareto Ensemble Pruning: An Ensemble Pruning Algorithm That Learns to Search Optimized Ensembles

Zhou

Liu

et al. 2019

Computational Intelligence and Neuroscience

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The ensemble pruning system is an effective machine learning framework that combines several learners as experts to classify a test set. Generally, ensemble pruning systems aim to define a region of competence based on the validation set to select the most competent ensembles from the ensemble pool with respect to the test set. However, the size of the ensemble pool is usually fixed, and the performance of an ensemble pool heavily depends on the definition of the region of competence. In this paper, a dynamic pruning framework called margin-based Pareto ensemble pruning is proposed for ensemble pruning systems. The framework explores the optimized ensemble pool size during the overproduction stage and finetunes the experts during the pruning stage. The Pareto optimization algorithm is used to explore the size of the overproduction ensemble pool that can result in better performance. Considering the information entropy of the learners in the indecision region, the marginal criterion for each learner in the ensemble pool is calculated using margin criterion pruning, which prunes the experts with respect to the test set. The effectiveness of the proposed method for classification tasks is assessed using datasets. The results show that margin-based Pareto ensemble pruning can achieve smaller ensemble sizes and better classification performance in most datasets when compared with state-of-the-art models.

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Using Genetic Programming with Prior Formula Knowledge to Solve Symbolic Regression Problem

Cited by 22 publications

References 28 publications

Predicting Metal–Support Interactions in Oxide-Supported Single-Atom Catalysts

Predicting Metal–Support Interactions in Oxide-Supported Single-Atom Catalysts

Symbolic Regression via Neural-Guided Genetic Programming Population Seeding

Margin-Based Pareto Ensemble Pruning: An Ensemble Pruning Algorithm That Learns to Search Optimized Ensembles

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