Symbolic regression /

"Symbolic regression (SR) is one of the most powerful machine learning techniques that produces transparent models, searching the space of mathematical expressions for a model that represents the relationship between the predictors and the dependent variable without the need of taking assumptio...

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Bibliographic Details
Main Authors:	Kronberger, Gabriel (Author), Burlacu, Bogdan (Author), Kommenda, Michael (Author), Winkler, Stephan M. (Author), Affenzeller, Michael (Author)
Corporate Author:	Taylor & Francis
Format:	eBook
Language:	English
Published:	Boca Raton, FL : CRC Press, 2025.
Edition:	First edition.
Subjects:	Genetic programming (Computer science) Machine learning > Mathematics. Mathematical models. Logic, Symbolic and mathematical. Regression analysis. Engineering mathematics. Programmation génétique (Informatique) Apprentissage automatique > Mathématiques. Logique symbolique et mathématique. Analyse de régression. Mathématiques de l'ingénieur. COMPUTERS / Computer Graphics / Game Programming & Design COMPUTERS / Database Management / Data Mining COMPUTERS / Machine Theory Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

Cover
Half Title
Title Page
Copyright Page
Contents
Preface
Symbols and Notation
1. Introduction
2. Basics of Supervised Learning
2.1. Introduction
2.2. Regression
2.2.1. Linear Models
2.2.2. Nonlinear Models
2.2.3. Error Measures
2.3. Classification
2.4. Time Series Prediction
2.5. Model Selection
2.6. Cross-validation
2.7. Further Reading
3. Basics of Symbolic Regression
3.1. Example: Identification of a Polynomial
3.1.1. Data Collection and Preprocessing
3.1.2. Establishing a Baseline
3.1.3. Modeling Approach
3.1.4. Modeling Results
3.2. Example: Discovery of Laws of Physics from Data
3.3. Example: Approximation of the Gamma Function
3.4. Extending Symbolic Regression to Classification
3.4.1. Model Structures for Symbolic Classification
3.4.2. Evaluation of Symbolic Classification Models
3.5. Further Reading
4. Evolutionary Computation and Genetic Programming
4.1. General Concepts
4.1.1. Genotype, Phenotype, and Semantics
4.1.2. Diversity and Evolvability
4.1.3. Buffering, Redundancy, and Neutrality
4.2. Population Initialization
4.2.1. Operators
4.3. Fitness Calculation
4.4. Parent Selection
4.4.1. Operators
4.4.2. Selection Pressure
4.5. Bloat and Introns
4.6. Crossover and Mutation
4.7. Power of the Hypothesis Space
4.8. GP Dynamics
4.8.1. Fitness
4.8.2. Variable Relevance
4.8.3. Model Complexity
4.8.4. Diversity
4.9. Algorithmic Extensions
4.9.1. Brood Selection and Offspring Selection
4.9.2. Age-layered Population Structures
4.9.3. Multi-objective GP
4.9.4. Alternative Encodings: Linear and Graph GP
4.9.5. Restricting Expressions: Syntax and Types
4.9.6. Semantics-aware GP
4.10. Conclusions
4.11. Further Reading
5. Model Validation, Inspection, Simplification, and Selection
5.1. Model Validation
5.1.1. Visual Tools
5.1.2. Explaining Models
5.1.3. Model Interpretability
5.2. Model Selection
5.2.1. Criteria for Model Selection
5.2.2. Hold-out Set for Validation
5.2.3. Cross-validation
5.2.4. Akaike's Information Criterion
5.2.5. Bayesian Information Criterion
5.2.6. Minimum Description Length Principle
5.2.7. Comparison of Model Selection Criteria
5.3. Model Simplification
5.3.1. Nested Models
5.3.2. Removal of Subexpressions
5.4. Example: Boston Housing
5.4.1. Data Preprocessing
5.4.2. Model Generation and Selection for Median Values of Homes
5.4.3. Model Generation and Selection for NOX Concentrations
5.5. Conclusions
5.6. Further Reading
6. Advanced Techniques
6.1. Integration of Knowledge
6.1.1. Example Applications
6.1.2. Knowledge Integration Methods
6.1.3. Knowledge Integration via Customized Fitness Evaluation
6.1.4. Shape Constraints
6.1.5. Knowledge Integration via the Hypothesis Space
6.2. Optimization of Coefficients