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Operon C++: An efficient genetic programming framework for symbolic regression 20

Operon C++: An efficient genetic programming framework for s...

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2020 Genetic and evolutionary Computation Conference, GECCO 2020

作者： Burlacu, Bogdan Kronberger, Gabriel Kommenda, Michael Josef Ressel Centre for Symbolic Regression Heuristic and Evolutionary Algorithms Laboratory Hagenberg Austria

ISBN: (纸本)9781450371278

Genetic Programming (GP) is a dynamic field of research where empirical testing plays an important role in validating new ideas and algorithms. The ability to easily prototype new algorithms by reusing key components and quickly obtain results is therefore important for the researcher. In this paper we introduce Operon, a C++ GP framework focused on performance, modularity and usability, featuring an efficient linear tree encoding and a scalable concurrency model where each logical thread is responsible for generating a new individual. We model the GP evolutionary process around the concept of an offspring generator, a streaming operator that defines how new individuals are obtained. The approach allows different algorithmic variants to be expressed using high-level constructs within the same generational basic loop. The evaluation routine supports both scalar and dual numbers, making it possible to calculate model derivatives via automatic differentiation. This functionality allows seamless integration with gradient-based local search approaches. We discuss the design choices behind the proposed framework and compare against two other popular GP frameworks, DEAP and heuristiclab. We empirically show that Operon is competitive in terms of solution quality, while being able to generate results significantly faster. © 2020 ACM.

关键词： Genetic programming

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Data Aggregation for Reducing Training Data in symbolic regression 17th

Data Aggregation for Reducing Training Data in Symbolic Regr...

引用

17th International Conference on Computer Aided Systems Theory, EUROCAST 2019

作者： Kammerer, Lukas Kronberger, Gabriel Kommenda, Michael Josef Ressel Center for Symbolic Regression Heuristic and Evolutionary Algorithms Laboratory University of Applied Sciences Upper Austria Hagenberg Austria

ISBN: (纸本)9783030450922

The growing volume of data makes the use of computationally intense machine learning techniques such as symbolic regression with genetic programming more and more impractical. This work discusses methods to reduce the training data and thereby also the runtime of genetic programming. The data is aggregated in a preprocessing step before running the actual machine learning algorithm. K-means clustering and data binning is used for data aggregation and compared with random sampling as the simplest data reduction method. We analyze the achieved speed-up in training and the effects on the trained models’ test accuracy for every method on four real-world data sets. The performance of genetic programming is compared with random forests and linear regression. It is shown, that k-means and random sampling lead to very small loss in test accuracy when the data is reduced down to only 30% of the original data, while the speed-up is proportional to the size of the data set. Binning on the contrary, leads to models with very high test error. © 2020, Springer Nature Switzerland AG.

关键词： Genetic programming

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Shape-Constrained symbolic regression with NSGA-III 18th

Shape-Constrained Symbolic Regression with NSGA-III

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18th International Conference on Computer Aided Systems Theory, EUROCAST 2022

作者： Haider, Christian Kronberger, Gabriel Josef Ressel Center for Symbolic Regression Heuristic and Evolutionary Algorithms Laboratory University of Applied Sciences Upper Austria Hagenberg Austria

ISBN: (纸本)9783031253119

Shape-constrained symbolic regression (SCSR) allows to include prior knowledge into data-based modeling. This inclusion allows to ensure that certain expected behavior is reflected by the resulting models. This specific behavior is defined by constraints which restrict the functional form e.g. monotonicity, concavity or model image boundaries. That allows finding more robust and reliable models in the specific case of highly noisy data or in extrapolation domains. This paper presents a multi-objective approach to minimize the approximation error as well as the constraint violations. Explicitly the two algorithms NSGA-II and NSGA-III are implemented and compared against each other in terms of model quality and runtime. Both algorithms are executed on a selected set of benchmark instances from physics textbooks. The results indicate that both algorithms are able to generate mostly feasible solutions and NSGA-III provides slight improvements in terms of model quality. Moreover, an improvement in runtime can be observed when using NSGA-III. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Benchmarking

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Concept for a Technical Infrastructure for Management of Predictive Models in Industrial Applications 17th

Concept for a Technical Infrastructure for Management of Pre...

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17th International Conference on Computer Aided Systems Theory, EUROCAST 2019

作者： Bachinger, Florian Kronberger, Gabriel Josef Ressel Center for Symbolic Regression Heuristic and Evolutionary Algorithms Laboratory University of Applied Sciences Upper Austria Hagenberg Austria

ISBN: (纸本)9783030450922

With the increasing number of created and deployed prediction models and the complexity of machine learning workflows we require so called model management systems to support data scientists in their tasks. In this work we describe our technological concept for such a model management system. This concept includes versioned storage of data, support for different machine learning algorithms, fine tuning of models, subsequent deployment of models and monitoring of model performance after deployment. We describe this concept with a close focus on model lifecycle requirements stemming from our industry application cases, but generalize key features that are relevant for all applications of machine learning. © 2020, Springer Nature Switzerland AG.

关键词： Digital storage

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Comparing Shape-Constrained regression algorithms for Data Validation 18th

Comparing Shape-Constrained Regression Algorithms for Data ...

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18th International Conference on Computer Aided Systems Theory, EUROCAST 2022

ISBN: (纸本)9783031253119

Industrial and scientific applications handle large volumes of data that render manual validation by humans infeasible. Therefore, we require automated data validation approaches that are able to consider the prior knowledge of domain experts to produce dependable, trustworthy assessments of data quality. Prior knowledge is often available as rules that describe interactions of inputs with regard to the target e.g. the target must be monotonically decreasing and convex over increasing input values. Domain experts are able to validate multiple such interactions at a glance. However, existing rule-based data validation approaches are unable to consider these constraints. In this work, we compare different shape-constrained regression algorithms for the purpose of data validation based on their classification accuracy and runtime performance. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： regression analysis

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Identification of Dynamical Systems Using symbolic regression 17th

Identification of Dynamical Systems Using Symbolic Regressio...

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17th International Conference on Computer Aided Systems Theory, EUROCAST 2019

作者： Kronberger, Gabriel Kammerer, Lukas Kommenda, Michael Josef Ressel Centre for Symbolic Regression Heuristic and Evolutionary Algorithms Laboratory University of Applied Sciences Upper Austria Softwarepark 11 Hagenberg4232 Austria

ISBN: (纸本)9783030450922

We describe a method for the identification of models for dynamical systems from observational data. The method is based on the concept of symbolic regression and uses genetic programming to evolve a system of ordinary differential equations (ODE). The novelty is that we add a step of gradient-based optimization of the ODE parameters. For this we calculate the sensitivities of the solution to the initial value problem (IVP) using automatic differentiation. The proposed approach is tested on a set of 19 problem instances taken from the literature which includes datasets from simulated systems as well as datasets captured from mechanical systems. We find that gradient-based optimization of parameters improves predictive accuracy of the models. The best results are obtained when we first fit the individual equations to the numeric differences and then subsequently fine-tune the identified parameter values by fitting the IVP solution to the observed variable values. © 2020, Springer Nature Switzerland AG.

关键词： Initial value problems

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Empirical analysis of variance for genetic programming based symbolic regression 21

Empirical analysis of variance for genetic programming based...

引用

2021 Genetic and evolutionary Computation Conference, GECCO 2021

作者： Kammerer, Lukas Kronberger, Gabriel Winkler, Stephan Josef Ressel Center for Symbolic Regression Heuristic and Evolutionary Algorithms Laboratory University of Applied Sciences Upper Austria Campus Hagenberg Johannes Kepler University Department of Computer Science Linz Austria

ISBN: (纸本)9781450383516

Genetic programming (GP) based symbolic regression is a stochastic, high-variance algorithm. Its sensitivity to changes in training data is a drawback for practical applications. In this work, we analyze empirically the variance of GP models on the PennML benchmarks. We measure the spread of model predictions when models are trained on slightly perturbed data. We compare the spread of models from two GP variants as well as linear, polynomial and random forest regression models. The results show that the spread of models from GP with local optimization is significantly higher than that of all other algorithms. As a side effect of our analysis, we provide evidence that the PennML benchmark contains two groups of instances (Friedman and real-world problem instances) for which GP performs significantly different. © 2021 Owner/Author.

关键词： Genetic programming

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symbolic regression with Fast Function Extraction and Nonlinear Least Squares Optimization 18th

Symbolic Regression with Fast Function Extraction and Nonl...

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18th International Conference on Computer Aided Systems Theory, EUROCAST 2022

ISBN: (纸本)9783031253119

Fast Function Extraction (FFX) is a deterministic algorithm for solving symbolic regression problems. We improve the accuracy of FFX by adding parameters to the arguments of nonlinear functions. Instead of only optimizing linear parameters, we optimize these additional nonlinear parameters with separable nonlinear least squared optimization using a variable projection algorithm. Both FFX and our new algorithm is applied on the PennML benchmark suite. We show that the proposed extensions of FFX leads to higher accuracy while providing models of similar length and with only a small increase in runtime on the given data. Our results are compared to a large set of regression methods that were already published for the given benchmark suite. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Machine learning

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Identifying Differential Equations for the Prediction of Blood Glucose using Sparse Identification of Nonlinear Systems 18th

Identifying Differential Equations for the Prediction of ...

引用

18th International Conference on Computer Aided Systems Theory, EUROCAST 2022

作者： Joedicke, David Parra, Daniel Kronberger, Gabriel Winkler, Stephan M. Josef Ressel Centre for Symbolic Regression Heuristic and Evolutionary Algorithms Laboratory University of Applied Sciences Upper Austria Hagenberg Austria Universidad Complutense de Madrid Madrid Spain

ISBN: (纸本)9783031253119

Describing dynamic medical systems using machine learning is a challenging topic with a wide range of applications. In this work, the possibility of modeling the blood glucose level of diabetic patients purely on the basis of measured data is described. A combination of the influencing variables insulin and calories are used to find an interpretable model. The absorption speed of external substances in the human body depends strongly on external influences, which is why time-shifts are added for the influencing variables. The focus is put on identifying the best time-shifts that provide robust models with good prediction accuracy that are independent of other unknown external influences. The modeling is based purely on the measured data using Sparse Identification of Nonlinear Dynamics. A differential equation is determined which, starting from an initial value, simulates blood glucose dynamics. By applying the best model to test data, we can show that it is possible to simulate the long-term blood glucose dynamics using differential equations and few, influencing variables. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Differential equations

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Local Optimization Often is Ill-conditioned in Genetic Programming for symbolic regression

Local Optimization Often is Ill-conditioned in Genetic Progr...

引用

International Symposium on symbolic and Numeric algorithms for Scientific Computing (SYNASC)

作者： Gabriel Kronberger Josef Ressel Center for Symbolic Regression Heuristic and Evolutionary Algorithms Lab University of Applied Sciences Upper Austria

Gradient-based local optimization has been shown to improve results of genetic programming (GP) for symbolic regression. Several state-of-the-art GP implementations use iterative nonlinear least squares (NLS) algorithms such as the Levenberg-Marquardt algorithm for local optimization. The effectiveness of NLS algorithms depends on appropriate scaling and conditioning of the optimization problem. This has so far been ignored in symbolic regression and GP literature. In this study we use a singular value decomposition of NLS Jacobian matrices to determine the numeric rank and the condition number. We perform experiments with a GP implementation and six different benchmark datasets. Our results show that rank-deficient and ill-conditioned Jacobian matrices occur frequently and for all datasets. The issue is less extreme when restricting GP tree size and when using many non-linear functions in the function set.

关键词： Jacobian matrices Scientific computing Genetic programming Benchmark testing Approximation algorithms Iterative algorithms Optimization

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