Sequential Symbolic Regression with Genetic Programming

This chapter describes the Sequential Symbolic Regression (SSR) method, a new strategy for function approximation in symbolic regression. The SSR method is inspired by the sequential covering strategy from machine learning, but instead of sequentially reducing the size of the problem being solved, it sequentially transforms the original problem into potentially simpler problems. This transformation is performed according to the semantic distances between the desired and obtained outputs and a geometric semantic operator. The rationale behind SSR is that, after generating a suboptimal function f via symbolic regression, the output errors can be approximated by another function in a subsequent iteration. The method was tested in eight polynomial functions, and compared with canonical genetic programming (GP) and geometric semantic genetic programming (SGP). Results showed that SSR significantly outperforms SGP and presents no statistical difference to GP. More importantly, they show the potential of the proposed strategy: an effective way of applying geometric semantic operators to combine different (partial) solutions, avoiding the exponential growth problem arising from the use of these operators

How Noisy Data Affects Geometric Semantic Genetic Programming

Noise is a consequence of acquiring and pre-processing data from the environment, and shows fluctuations from different sources---e.g., from sensors, signal processing technology or even human error. As a machine learning technique, Genetic Programming (GP) is not immune to this problem, which the field has frequently addressed. Recently, Geometric Semantic Genetic Programming (GSGP), a semantic-aware branch of GP, has shown robustness and high generalization capability. Researchers believe these characteristics may be associated with a lower sensibility to noisy data. However, there is no systematic study on this matter. This paper performs a deep analysis of the GSGP performance over the presence of noise. Using 15 synthetic datasets where noise can be controlled, we added different ratios of noise to the data and compared the results obtained with those of a canonical GP. The results show that, as we increase the percentage of noisy instances, the generalization performance degradation is more pronounced in GSGP than GP. However, in general, GSGP is more robust to noise than GP in the presence of up to 10% of noise, and presents no statistical difference for values higher than that in the test bed.Comment: 8 pages, In proceedings of Genetic and Evolutionary Computation Conference (GECCO 2017), Berlin, German

A Study of Geometric Semantic Genetic Programming with Linear Scaling

Dissertation presented as the partial requirement for obtaining a Master's degree in Data Science and Advanced Analytics, specialization in Data ScienceMachine Learning (ML) is a scientific discipline that endeavors to enable computers to learn without the need for explicit programming. Evolutionary Algorithms (EAs), a subset of ML algorithms, mimic Darwin’s Theory of Evolution by using natural selection mechanisms (i.e., survival of the fittest) to evolve a group of individuals (i.e., possible solutions to a given problem). Genetic Programming (GP) is the most recent type of EA and it evolves computer programs (i.e., individuals) to map a set of input data into known expected outputs. Geometric Semantic Genetic Programming (GSGP) extends this concept by allowing individuals to evolve and vary in the semantic space, where the output vectors are located, rather than being constrained by syntaxbased structures. Linear Scaling (LS) is a method that was introduced to facilitate the task of GP of searching for the best function matching a set of known data. GSGP and LS have both, independently, shown the ability to outperform standard GP for symbolic regression. GSGP uses Geometric Semantic Operators (GSOs), different from the standard ones, without altering the fitness, while LS modifies the fitness without altering the genetic operators. To the best of our knowledge, there has been no prior utilization of the combined methodology of GSGP and LS for classification problems. Furthermore, despite the fact that they have been used together in one practical regression application, a methodological evaluation of the advantages and disadvantages of integrating these methods for regression or classification problems has never been performed. In this dissertation, a study of a system that integrates both GSGP and LS (GSGP-LS) is presented. The performance of the proposed method, GSGPLS, was tested on six hand-tailored regression benchmarks, nine real-life regression problems and three real-life classification problems. The obtained results indicate that GSGP-LS outperforms GSGP in the majority of the cases, confirming the expected benefit of this integration. However, for some particularly hard regression datasets, GSGP-LS overfits training data, being outperformed by GSGP on unseen data. This contradicts the idea that LS is always beneficial for GP, warning the practitioners about its risk of overfitting in some specific cases.A Aprendizagem Automática (AA) é uma disciplina científica que se esforça por permitir que os computadores aprendam sem a necessidade de programação explícita. Algoritmos Evolutivos (AE),um subconjunto de algoritmos de ML, mimetizam a Teoria da Evolução de Darwin, usando a seleção natural e mecanismos de "sobrevivência dos mais aptos"para evoluir um grupo de indivíduos (ou seja, possíveis soluções para um problema dado). A Programação Genética (PG) é um processo algorítmico que evolui programas de computador (ou indivíduos) para ligar características de entrada e saída. A Programação Genética em Geometria Semântica (PGGS) estende esse conceito permitindo que os indivíduos evoluam e variem no espaço semântico, onde os vetores de saída estão localizados, em vez de serem limitados por estruturas baseadas em sintaxe. A Escala Linear (EL) é um método introduzido para facilitar a tarefa da PG de procurar a melhor função que corresponda a um conjunto de dados conhecidos. Tanto a PGGS quanto a EL demonstraram, independentemente, a capacidade de superar a PG padrão para regressão simbólica. A PGGS usa Operadores Semânticos Geométricos (OSGs), diferentes dos padrões, sem alterar o fitness, enquanto a EL modifica o fitness sem alterar os operadores genéticos. Até onde sabemos, não houve utilização prévia da metodologia combinada de PGGS e EL para problemas de classificação. Além disso, apesar de terem sido usados juntos em uma aplicação prática de regressão, nunca foi realizada uma avaliação metodológica das vantagens e desvantagens da integração desses métodos para problemas de regressão ou classificação. Nesta dissertação, é apresentado um estudo de um sistema que integra tanto a PGGS quanto a EL (PGGSEL). O desempenho do método proposto, PGGS-EL, foi testado em seis benchmarks de regressão personalizados, nove problemas de regressão da vida real e três problemas de classificação da vida real. Os resultados obtidos indicam que o PGGS-EL supera o PGGS na maioria dos casos, confirmando o benefício esperado desta integração. No entanto, para alguns conjuntos de dados de regressão particularmente difíceis, o PGGS-EL faz overfit aos dados de treino, obtendo piores resultados em comparação com PGGS em dados não vistos. Isso contradiz a ideia de que a EL é sempre benéfica para a PG, alertando os praticantes sobre o risco de overfitting em alguns casos específicos

Supporting medical decisions for treating rare diseases through genetic programming

Bakurov, I., Castelli, M., Vanneschi, L., & Freitas, M. J. (2019). Supporting medical decisions for treating rare diseases through genetic programming. In P. Kaufmann, & P. A. Castillo (Eds.), Applications of Evolutionary Computation: 22nd International Conference, EvoApplications 2019, Held as Part of EvoStar 2019, Proceedings (pp. 187-203). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11454 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-16692-2_13. ISBN: 978-3-030-16691-5; Online ISBN: 978-3-030-16692-2Casa dos Marcos is the largest specialized medical and residential center for rare diseases in the Iberian Peninsula. The large number of patients and the uniqueness of their diseases demand a considerable amount of diverse and highly personalized therapies, that are nowadays largely managed manually. This paper aims at catering for the emergent need of efficient and effective artificial intelligence systems for the support of the everyday activities of centers like Casa dos Marcos. We present six predictive data models developed with a genetic programming based system which, integrated into a web-application, enabled data-driven support for the therapists in Casa dos Marcos. The presented results clearly indicate the usefulness of the system in assisting complex therapeutic procedures for children suffering from rare diseases.authorsversionpublishe

Ensemble learning with GSGP

Dissertation presented as the partial requirement for obtaining a Master's degree in Data Science and Advanced AnalyticsThe purpose of this thesis is to conduct comparative research between Genetic Programming (GP) and Geometric Semantic Genetic Programming (GSGP), with different initialization (RHH and EDDA) and selection (Tournament and Epsilon-Lexicase) strategies, in the context of a model-ensemble in order to solve regression optimization problems. A model-ensemble is a combination of base learners used in different ways to solve a problem. The most common ensemble is the mean, where the base learners are combined in a linear fashion, all having the same weights. However, more sophisticated ensembles can be inferred, providing higher generalization ability. GSGP is a variant of GP using different genetic operators. No previous research has been conducted to see if GSGP can perform better than GP in model-ensemble learning. The evolutionary process of GP and GSGP should allow us to learn about the strength of each of those base models to provide a more accurate and robust solution. The base-models used for this analysis were Linear Regression, Random Forest, Support Vector Machine and Multi-Layer Perceptron. This analysis has been conducted using 7 different optimization problems and 4 real-world datasets. The results obtained with GSGP are statistically significantly better than GP for most cases.O objetivo desta tese é realizar pesquisas comparativas entre Programação Genética (GP) e Programação Genética Semântica Geométrica (GSGP), com diferentes estratégias de inicialização (RHH e EDDA) e seleção (Tournament e Epsilon-Lexicase), no contexto de um conjunto de modelos, a fim de resolver problemas de otimização de regressão. Um conjunto de modelos é uma combinação de alunos de base usados de diferentes maneiras para resolver um problema. O conjunto mais comum é a média, na qual os alunos da base são combinados de maneira linear, todos com os mesmos pesos. No entanto, conjuntos mais sofisticados podem ser inferidos, proporcionando maior capacidade de generalização. O GSGP é uma variante do GP usando diferentes operadores genéticos. Nenhuma pesquisa anterior foi realizada para verificar se o GSGP pode ter um desempenho melhor que o GP no aprendizado de modelos. O processo evolutivo do GP e GSGP deve permitir-nos aprender sobre a força de cada um desses modelos de base para fornecer uma solução mais precisa e robusta. Os modelos de base utilizados para esta análise foram: Regressão Linear, Floresta Aleatória, Máquina de Vetor de Suporte e Perceptron de Camadas Múltiplas. Essa análise foi realizada usando 7 problemas de otimização diferentes e 4 conjuntos de dados do mundo real. Os resultados obtidos com o GSGP são estatisticamente significativamente melhores que o GP na maioria dos casos

A multiple expression alignment framework for genetic programming

Vanneschi, L., Scott, K., & Castelli, M. (2018). A multiple expression alignment framework for genetic programming. In M. Castelli, L. Sekanina, M. Zhang, S. Cagnoni, & P. García-Sánchez (Eds.), Genetic Programming: 21st European Conference, EuroGP 2018, Proceedings, pp. 166-183. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10781 LNCS). Springer Verlag. DOI: 10.1007/978-3-319-77553-1_11Alignment in the error space is a recent idea to exploit semantic awareness in genetic programming. In a previous contribution, the concepts of optimally aligned and optimally coplanar individuals were introduced, and it was shown that given optimally aligned, or optimally coplanar, individuals, it is possible to construct a globally optimal solution analytically. As a consequence, genetic programming methods, aimed at searching for optimally aligned, or optimally coplanar, individuals were introduced. In this paper, we critically discuss those methods, analyzing their major limitations and we propose new genetic programming systems aimed at overcoming those limitations. The presented experimental results, conducted on four real-life symbolic regression problems, show that the proposed algorithms outperform not only the existing methods based on the concept of alignment in the error space, but also geometric semantic genetic programming and standard genetic programming.authorsversionpublishe

A multiple expression alignment framework for genetic programming

Dissertation presented as the partial requirement for obtaining a Master's degree in Data Science and Advanced AnalyticsAlignment in the error space is a recent idea to exploit semantic awareness in genetic programming. In a previous contribution, the concepts of optimally aligned and optimally coplanar individuals were introduced, and it was shown that given optimally aligned, or optimally coplanar, individuals, it is possible to construct a globally optimal solution analytically. Consequently, genetic programming methods, aimed at searching for optimally aligned, or optimally coplanar, individuals were introduced. This paper critically discusses those methods, analyzing their major limitations and introduces a new genetic programming system aimed at overcoming those limitations. The presented experimental results, conducted on five real-life symbolic regression problems, show that the proposed algorithms’ outperform not only the existing methods based on the concept of alignment in the error space, but also geometric semantic genetic programming and standard genetic programming

The influence of population size in geometric semantic GP

In this work, we study the influence of the population size on the learning ability of Geometric Semantic Genetic Programming for the task of symbolic regression. A large set of experiments, considering different population size values on different regression problems, has been performed. Results show that, on real-life problems, having small populations results in a better training fitness with respect to the use of large populations after the same number of fitness evaluations. However, performance on the test instances varies among the different problems: in datasets with a high number of features, models obtained with large populations present a better performance on unseen data, while in datasets characterized by a relative small number of variables a better generalization ability is achieved by using small population size values. When synthetic problems are taken into account, large population size values represent the best option for achieving good quality solutions on both training and test instances