556 research outputs found
Genetic Programming is Naturally Suited to Evolve Bagging Ensembles
Learning ensembles by bagging can substantially improve the generalization
performance of low-bias, high-variance estimators, including those evolved by
Genetic Programming (GP). To be efficient, modern GP algorithms for evolving
(bagging) ensembles typically rely on several (often inter-connected)
mechanisms and respective hyper-parameters, ultimately compromising ease of
use. In this paper, we provide experimental evidence that such complexity might
not be warranted. We show that minor changes to fitness evaluation and
selection are sufficient to make a simple and otherwise-traditional GP
algorithm evolve ensembles efficiently. The key to our proposal is to exploit
the way bagging works to compute, for each individual in the population,
multiple fitness values (instead of one) at a cost that is only marginally
higher than the one of a normal fitness evaluation. Experimental comparisons on
classification and regression tasks taken and reproduced from prior studies
show that our algorithm fares very well against state-of-the-art ensemble and
non-ensemble GP algorithms. We further provide insights into the proposed
approach by (i) scaling the ensemble size, (ii) ablating the changes to
selection, (iii) observing the evolvability induced by traditional subtree
variation. Code: https://github.com/marcovirgolin/2SEGP.Comment: Added interquartile range in tables 1, 2, and 3; improved Fig. 3 and
its analysis, improved experiment design of section 7.
A Neural-Guided Dynamic Symbolic Network for Exploring Mathematical Expressions from Data
Symbolic regression (SR) is a powerful technique for discovering the
underlying mathematical expressions from observed data. Inspired by the success
of deep learning, recent efforts have focused on two categories for SR methods.
One is using a neural network or genetic programming to search the expression
tree directly. Although this has shown promising results, the large search
space poses difficulties in learning constant factors and processing
high-dimensional problems. Another approach is leveraging a transformer-based
model training on synthetic data and offers advantages in inference speed.
However, this method is limited to fixed small numbers of dimensions and may
encounter inference problems when given data is out-of-distribution compared to
the synthetic data. In this work, we propose DySymNet, a novel neural-guided
Dynamic Symbolic Network for SR. Instead of searching for expressions within a
large search space, we explore DySymNet with various structures and optimize
them to identify expressions that better-fitting the data. With a topology
structure like neural networks, DySymNet not only tackles the challenge of
high-dimensional problems but also proves effective in optimizing constants.
Based on extensive numerical experiments using low-dimensional public standard
benchmarks and the well-known SRBench with more variables, our method achieves
state-of-the-art performance in terms of fitting accuracy and robustness to
noise
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
Local Search is Underused in Genetic Programming
Trujillo, L., Z-Flores, E., Juárez-Smith, P. S., Legrand, P., Silva, S., Castelli, M., ... Muñoz, L. (2018). Local Search is Underused in Genetic Programming. In R. Riolo, B. Worzel, B. Goldman, & B. Tozier (Eds.), Genetic Programming Theory and Practice XIV (pp. 119-137). [8] (Genetic and Evolutionary Computation). Springer. https://doi.org/10.1007/978-3-319-97088-2_8There are two important limitations of standard tree-based genetic programming (GP). First, GP tends to evolve unnecessarily large programs, what is referred to as bloat. Second, GP uses inefficient search operators that focus on modifying program syntax. The first problem has been studied extensively, with many works proposing bloat control methods. Regarding the second problem, one approach is to use alternative search operators, for instance geometric semantic operators, to improve convergence. In this work, our goal is to experimentally show that both problems can be effectively addressed by incorporating a local search optimizer as an additional search operator. Using real-world problems, we show that this rather simple strategy can improve the convergence and performance of tree-based GP, while also reducing program size. Given these results, a question arises: Why are local search strategies so uncommon in GP? A small survey of popular GP libraries suggests to us that local search is underused in GP systems. We conclude by outlining plausible answers for this question and highlighting future work.authorsversionpublishe
Predicting Ordinary Differential Equations with Transformers
We develop a transformer-based sequence-to-sequence model that recovers
scalar ordinary differential equations (ODEs) in symbolic form from irregularly
sampled and noisy observations of a single solution trajectory. We demonstrate
in extensive empirical evaluations that our model performs better or on par
with existing methods in terms of accurate recovery across various settings.
Moreover, our method is efficiently scalable: after one-time pretraining on a
large set of ODEs, we can infer the governing law of a new observed solution in
a few forward passes of the model.Comment: Published at ICML 202
Information Fusion via Symbolic Regression: A Tutorial in the Context of Human Health
This tutorial paper provides a general overview of symbolic regression (SR)
with specific focus on standards of interpretability. We posit that
interpretable modeling, although its definition is still disputed in the
literature, is a practical way to support the evaluation of successful
information fusion. In order to convey the benefits of SR as a modeling
technique, we demonstrate an application within the field of health and
nutrition using publicly available National Health and Nutrition Examination
Survey (NHANES) data from the Centers for Disease Control and Prevention (CDC),
fusing together anthropometric markers into a simple mathematical expression to
estimate body fat percentage. We discuss the advantages and challenges
associated with SR modeling and provide qualitative and quantitative analyses
of the learned models
Mini-Batching, Gradient-Clipping, first-versus second-order: What works in Gradient-Based coefficient optimisation for Symbolic Regression'
The aim of Symbolic Regression (SR) is to discover interpretable expressions that accurately describe data. The accuracy of an expression depends on both its structure and coefficients. To keep the structure simple enough to be interpretable, effective coefficient optimisation becomes key. Gradient-based optimisation is clearly effective at training neural networks in Deep Learning (DL), which can essentially be viewed as large, over-parameterised expressions: in this paper, we study how gradient-based optimisation techniques as often used in DL transfer to SR. In particular, we first assess what techniques work well across random SR expressions, independent of any specific SR algorithm. We find that mini-batching and gradient-clipping can be helpful (similar to DL), while second-order optimisers outperform first-order ones (different from DL). Next, we consider whether including gradient-based optimisation in Genetic Programming (GP), a classic SR algorithm, is beneficial. On five real-world datasets, in a generation-based comparison, we find that second-order optimisation outperforms coefficient mutation (or no optimisation). However, in time-based comparisons, performance gaps shrink substantially because the computational expensiveness of second-order optimisation causes GP to perform fewer generations. The interplay of computational costs between the optimisation of structure and coefficients is thus a critical aspect to consider
Mining Explicit and Implicit Relationships in Data Using Symbolic Regression
Identification of implicit and explicit relations within observed data is a generic problem commonly encountered in several domains including science, engineering, finance, and more. It forms the core component of data analytics, a process of discovering useful information from data sets that are potentially huge and otherwise incomprehensible. In industries, such information is often instrumental for profitable decision making, whereas in science and engineering it is used to build empirical models, propose new or verify existing theories and explain natural phenomena. In recent times, digital and internet based technologies have proliferated, making it viable to generate and collect large amount of data at low cost. This inturn has resulted in an ever growing need for methods to analyse and draw interpretations from such data quickly and reliably. With this overarching goal, this thesis attempts to make contributions towards developing accurate and efficient methods for discovering such relations through evolutionary search, a method commonly referred to as Symbolic Regression (SR).
A data set of input variables x and a corresponding observed response y is given. The aim is to find an explicit function y = f (x) or an implicit function f (x, y) = 0, which represents the data set. While seemingly simple, the problem is challenging for several reasons. Some of the conventional regression methods try to “guess” a functional form such as linear/quadratic/polynomial, and attempt to do a curve-fitting of the data to the equation, which may limit the possibility of discovering more complex relations, if they exist. On the other hand, there are meta-modelling techniques such as response surface method, Kriging, etc., that model the given data accurately, but provide a “black-box” predictor instead of an expression. Such approximations convey little or no insights about how the variables and responses are dependent on each other, or their relative contribution to the output. SR attempts to alleviate the above two extremes by providing a structure which evolves mathematical expressions instead of assuming them. Thus, it is flexible enough to represent the data, but at the same time provides useful insights instead of a black-box predictor. SR can be categorized as part of Explainable Artificial Intelligence and can contribute to Trustworthy Artificial Intelligence.
The works proposed in this thesis aims to integrate the concept of “semantics” deeper into Genetic Programming (GP) and Evolutionary Feature Synthesis, which are the two algorithms usually employed for conducting SR. The semantics will be integrated into well-known components of the algorithms such as compactness, diversity, recombination, constant optimization, etc. The main contribution of this thesis is the proposal of two novel operators to generate expressions based on Linear Programming and Mixed Integer Programming with the aim of controlling the length of the discovered expressions without compromising on the accuracy. In the experiments, these operators are proven to be able to discover expressions with better accuracy and interpretability on many explicit and implicit benchmarks. Moreover, some applications of SR on real-world data sets are shown to demonstrate the practicality of the proposed approaches. Besides, in related to practical problems, how GP can be applied to effectively solve the Resource Constrained Scheduling Problems is also presented
Prediction of high-performance concrete compressive strength through a comparison of machine learning techniques
Dissertation presented as the partial requirement for obtaining a Master's degree in Data Science and Advanced Analytics, specialization in Data ScienceHigh-performance concrete (HPC) is a highly complex composite material whose characteristics are extremely difficult to model. One of those characteristics is the concrete compressive strength, a nonlinear function of the same ingredients that compose HPC: cement, fly ash, blast furnace slag, water, superplasticizer, age, and coarse and fine aggregates. Research has shown time and time again that concrete strength is not determined just by the water-to-cement ratio, which was for years the go to metric. In addition, traditional methods that attempt to model HPC, such as regression analysis, do not provide sufficient prediction power due to nonlinear proprieties of the mixture. Therefore, this study attempts to optimize the prediction and modeling of the compressive strength of HPC by analyzing seven different machine learning (ML) algorithms: three regularization algorithms (Lasso, Ridge and Elastic Net), three ensemble algorithms (Random Forest, Gradient Boost and AdaBoost), and Artificial Neural Networks. All techniques were built and tested with a dataset composed of data from 17 different concrete strength test laboratories, under the same experimental conditions, which enabled a fair comparison amongst them and between different previous studies in the field. Feature importance analysis and outlier analysis were also performed, and all models were subject to a
Wilcoxon Signed-Ranks Test to ensure statistically significant results. The final results show that the
more complex ML algorithms provided greater accuracy than the regularization techniques, with Gradient Boost being the superior model amongst them, providing more accurate predictions than the sate-of-the-art. Better results were achieved using all variables and without removing outlier observations
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