A Statistical Learning Theory Approach of Bloat

Code bloat, the excessive increase of code size, is an important is- sue in Genetic Programming (GP). This paper proposes a theoreti- cal analysis of code bloat in the framework of symbolic regression in GP, from the viewpoint of Statistical Learning Theory, a well grounded mathematical toolbox for Machine Learning. Two kinds of bloat must be distinguished in that context, depending whether the target function lies in the search space or not. Then, important mathematical results are proved using classical results from Sta- tistical Learning. Namely, the Vapnik-Cervonenkis dimension of programs is computed, and further results from Statistical Learn- ing allow to prove that a parsimonious fitness ensures Universal Consistency (the solution minimizing the empirical error does con- verge to the best possible error when the number of samples goes to infinity). However, it is proved that the standard method consisting in choosing a maximal program size depending on the number of samples might still result in programs of infinitely increasing size whith their accuracy; a more complicated modification of the fit- ness is proposed that theoretically avoids unnecessary bloat while nevertheless preserving the Universal Consistency

Apprentissage statistique et programmation génétique: la croissance du code est-elle inévitable ?

Universal Consistency, the convergence to the minimum possible error rate in learning through genetic programming (GP), and Code bloat, the excessive increase of code size, are important issues in GP. This paper proposes a theoretical analysis of universal consistency and code bloat in the framework of symbolic regression in GP, from the viewpoint of Statistical Learning Theory, a well grounded mathematical toolbox for Machine Learning. Two kinds of bloat must be distinguished in that context, depending whether the target function has finite description length or not. Then, the Vapnik-Chervonenkis dimension of programs is computed, and we prove that a parsimonious fitness ensures Universal Consistency (i.e. the fact that the solution minimizing the empirical error does converge to the best possible error when the number of examples goes to infinity). However, it is proved that the standard method consisting in choosing a maximal program size depending on the number of examples might still result in programs of infinitely increasing size with their accuracy; a fitness biased by parsimony pressure is proposed. This fitness avoids unnecessary bloat while nevertheless preserving the Universal Consistency

Universal Consistency and Bloat in GP

In this paper, we provide an analysis of Genetic Programming (GP) from the Statistical Learning Theory viewpoint in the scope of symbolic regression. Firstly, we are interested in Universal Consistency, i.e. the fact that the solution minimizing the empirical error does converge to the best possible error when the number of examples goes to infinity, and secondly, we focus our attention on the uncontrolled growth of program length (i.e. bloat), which is a well-known problem in GP. Results show that (1) several kinds of code bloats may be identified and that (2) Universal consistency can be obtained as well as avoiding bloat under some con- ditions. We conclude by describing an ad hoc method that makes it possible simultaneously to avoid bloat and to ensure universal consistency

A Field Guide to Genetic Programming

xiv, 233 p. : il. ; 23 cm.Libro ElectrónicoA Field Guide to Genetic Programming (ISBN 978-1-4092-0073-4) is an introduction to genetic programming (GP). GP is a systematic, domain-independent method for getting computers to solve problems automatically starting from a high-level statement of what needs to be done. Using ideas from natural evolution, GP starts from an ooze of random computer programs, and progressively refines them through processes of mutation and sexual recombination, until solutions emerge. All this without the user having to know or specify the form or structure of solutions in advance. GP has generated a plethora of human-competitive results and applications, including novel scientific discoveries and patentable inventions. The authorsIntroduction -- Representation, initialisation and operators in Tree-based GP -- Getting ready to run genetic programming -- Example genetic programming run -- Alternative initialisations and operators in Tree-based GP -- Modular, grammatical and developmental Tree-based GP -- Linear and graph genetic programming -- Probalistic genetic programming -- Multi-objective genetic programming -- Fast and distributed genetic programming -- GP theory and its applications -- Applications -- Troubleshooting GP -- Conclusions.Contents xi 1 Introduction 1.1 Genetic Programming in a Nutshell 1.2 Getting Started 1.3 Prerequisites 1.4 Overview of this Field Guide I Basics 2 Representation, Initialisation and GP 2.1 Representation 2.2 Initialising the Population 2.3 Selection 2.4 Recombination and Mutation Operators in Tree-based 3 Getting Ready to Run Genetic Programming 19 3.1 Step 1: Terminal Set 19 3.2 Step 2: Function Set 20 3.2.1 Closure 21 3.2.2 Sufficiency 23 3.2.3 Evolving Structures other than Programs 23 3.3 Step 3: Fitness Function 24 3.4 Step 4: GP Parameters 26 3.5 Step 5: Termination and solution designation 27 4 Example Genetic Programming Run 4.1 Preparatory Steps 29 4.2 Step-by-Step Sample Run 31 4.2.1 Initialisation 31 4.2.2 Fitness Evaluation Selection, Crossover and Mutation Termination and Solution Designation Advanced Genetic Programming 5 Alternative Initialisations and Operators in 5.1 Constructing the Initial Population 5.1.1 Uniform Initialisation 5.1.2 Initialisation may Affect Bloat 5.1.3 Seeding 5.2 GP Mutation 5.2.1 Is Mutation Necessary? 5.2.2 Mutation Cookbook 5.3 GP Crossover 5.4 Other Techniques 32 5.5 Tree-based GP 39 6 Modular, Grammatical and Developmental Tree-based GP 47 6.1 Evolving Modular and Hierarchical Structures 47 6.1.1 Automatically Defined Functions 48 6.1.2 Program Architecture and Architecture-Altering 50 6.2 Constraining Structures 51 6.2.1 Enforcing Particular Structures 52 6.2.2 Strongly Typed GP 52 6.2.3 Grammar-based Constraints 53 6.2.4 Constraints and Bias 55 6.3 Developmental Genetic Programming 57 6.4 Strongly Typed Autoconstructive GP with PushGP 59 7 Linear and Graph Genetic Programming 61 7.1 Linear Genetic Programming 61 7.1.1 Motivations 61 7.1.2 Linear GP Representations 62 7.1.3 Linear GP Operators 64 7.2 Graph-Based Genetic Programming 65 7.2.1 Parallel Distributed GP (PDGP) 65 7.2.2 PADO 67 7.2.3 Cartesian GP 67 7.2.4 Evolving Parallel Programs using Indirect Encodings 68 8 Probabilistic Genetic Programming 8.1 Estimation of Distribution Algorithms 69 8.2 Pure EDA GP 71 8.3 Mixing Grammars and Probabilities 74 9 Multi-objective Genetic Programming 75 9.1 Combining Multiple Objectives into a Scalar Fitness Function 75 9.2 Keeping the Objectives Separate 76 9.2.1 Multi-objective Bloat and Complexity Control 77 9.2.2 Other Objectives 78 9.2.3 Non-Pareto Criteria 80 9.3 Multiple Objectives via Dynamic and Staged Fitness Functions 80 9.4 Multi-objective Optimisation via Operator Bias 81 10 Fast and Distributed Genetic Programming 83 10.1 Reducing Fitness Evaluations/Increasing their Effectiveness 83 10.2 Reducing Cost of Fitness with Caches 86 10.3 Parallel and Distributed GP are Not Equivalent 88 10.4 Running GP on Parallel Hardware 89 10.4.1 Master–slave GP 89 10.4.2 GP Running on GPUs 90 10.4.3 GP on FPGAs 92 10.4.4 Sub-machine-code GP 93 10.5 Geographically Distributed GP 93 11 GP Theory and its Applications 97 11.1 Mathematical Models 98 11.2 Search Spaces 99 11.3 Bloat 101 11.3.1 Bloat in Theory 101 11.3.2 Bloat Control in Practice 104 III Practical Genetic Programming 12 Applications 12.1 Where GP has Done Well 12.2 Curve Fitting, Data Modelling and Symbolic Regression 12.3 Human Competitive Results – the Humies 12.4 Image and Signal Processing 12.5 Financial Trading, Time Series, and Economic Modelling 12.6 Industrial Process Control 12.7 Medicine, Biology and Bioinformatics 12.8 GP to Create Searchers and Solvers – Hyper-heuristics xiii 12.9 Entertainment and Computer Games 127 12.10The Arts 127 12.11Compression 128 13 Troubleshooting GP 13.1 Is there a Bug in the Code? 13.2 Can you Trust your Results? 13.3 There are No Silver Bullets 13.4 Small Changes can have Big Effects 13.5 Big Changes can have No Effect 13.6 Study your Populations 13.7 Encourage Diversity 13.8 Embrace Approximation 13.9 Control Bloat 13.10 Checkpoint Results 13.11 Report Well 13.12 Convince your Customers 14 Conclusions Tricks of the Trade A Resources A.1 Key Books A.2 Key Journals A.3 Key International Meetings A.4 GP Implementations A.5 On-Line Resources 145 B TinyGP 151 B.1 Overview of TinyGP 151 B.2 Input Data Files for TinyGP 153 B.3 Source Code 154 B.4 Compiling and Running TinyGP 162 Bibliography 167 Inde

Cognition-based approaches for high-precision text mining

This research improves the precision of information extraction from free-form text via the use of cognitive-based approaches to natural language processing (NLP). Cognitive-based approaches are an important, and relatively new, area of research in NLP and search, as well as linguistics. Cognitive approaches enable significant improvements in both the breadth and depth of knowledge extracted from text. This research has made contributions in the areas of a cognitive approach to automated concept recognition in. Cognitive approaches to search, also called concept-based search, have been shown to improve search precision. Given the tremendous amount of electronic text generated in our digital and connected world, cognitive approaches enable substantial opportunities in knowledge discovery. The generation and storage of electronic text is ubiquitous, hence opportunities for improved knowledge discovery span virtually all knowledge domains. While cognition-based search offers superior approaches, challenges exist due to the need to mimic, even in the most rudimentary way, the extraordinary powers of human cognition. This research addresses these challenges in the key area of a cognition-based approach to automated concept recognition. In addition it resulted in a semantic processing system framework for use in applications in any knowledge domain. Confabulation theory was applied to the problem of automated concept recognition. This is a relatively new theory of cognition using a non-Bayesian measure, called cogency, for predicting the results of human cognition. An innovative distance measure derived from cogent confabulation and called inverse cogency, to rank order candidate concepts during the recognition process. When used with a multilayer perceptron, it improved the precision of concept recognition by 5% over published benchmarks. Additional precision improvements are anticipated. These research steps build a foundation for cognition-based, high-precision text mining. Long-term it is anticipated that this foundation enables a cognitive-based approach to automated ontology learning. Such automated ontology learning will mimic human language cognition, and will, in turn, enable the practical use of cognitive-based approaches in virtually any knowledge domain --Abstract, page iii

Digital ecosystems

We view Digital Ecosystems to be the digital counterparts of biological ecosystems, which are considered to be robust, self-organising and scalable architectures that can automatically solve complex, dynamic problems. So, this work is concerned with the creation, investigation, and optimisation of Digital Ecosystems, exploiting the self-organising properties of biological ecosystems. First, we created the Digital Ecosystem, a novel optimisation technique inspired by biological ecosystems, where the optimisation works at two levels: a first optimisation, migration of agents which are distributed in a decentralised peer-to-peer network, operating continuously in time; this process feeds a second optimisation based on evolutionary computing that operates locally on single peers and is aimed at finding solutions to satisfy locally relevant constraints. We then investigated its self-organising aspects, starting with an extension to the definition of Physical Complexity to include the evolving agent populations of our Digital Ecosystem. Next, we established stability of evolving agent populations over time, by extending the Chli-DeWilde definition of agent stability to include evolutionary dynamics. Further, we evaluated the diversity of the software agents within evolving agent populations, relative to the environment provided by the user base. To conclude, we considered alternative augmentations to optimise and accelerate our Digital Ecosystem, by studying the accelerating effect of a clustering catalyst on the evolutionary dynamics of our Digital Ecosystem, through the direct acceleration of the evolutionary processes. We also studied the optimising effect of targeted migration on the ecological dynamics of our Digital Ecosystem, through the indirect and emergent optimisation of the agent migration patterns. Overall, we have advanced the understanding of creating Digital Ecosystems, the self-organisation that occurs within them, and the optimisation of their Ecosystem-Oriented Architecture

A meta-language for systems architecting

Thesis (Ph. D.)--Massachusetts Institute of Technology, Engineering Systems Division, 2005.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (leaves 164-168).(cont.) To demonstrate its practical value in large-scale engineering systems, the research applied OPN to two space exploration programs and one aircraft design problem. In our experiments, OPN was able to significantly change the modeling and architectural reasoning process by automating a number of manual model construction, manipulation, and simulation tasks.The aim of this research is to design an executable meta-language that supports system architects' modeling process by automating certain model construction, manipulation and simulation tasks. This language specifically addresses the needs in systematically communicating architects' intent with a wide range of stakeholders and to organize knowledge from various domains. Our investigation into existing architecting approaches and technologies has pointed out the need to develop a simple and intuitive, yet formal language, that expresses multiple layers of abstractions, provides reflexive knowledge about the models, mechanizes data exchange and manipulation, while allowing integration with legacy infrastructures. A small set of linguistic primitives, stateful objects and processes that transform them were identified as both required and sufficient building blocks of the meta-language, specified as an Object-Process Network (OPN). To demonstrate the applicability of OPN, a software environment has been developed and applied to define meta-models of large-scale complex system architectures such as space transportation systems. OPN provides three supporting aspects of architectural modeling. As a declarative language, OPN provides a diagrammatic formal language to help architects specify the space of architectural options. As an imperative language, OPN automates the process of creating architectural option instances and computes associated performance metrics for those instances. As a simulation language, OPN uses a function-algebraic model to subsume and compose discrete, continuous, and probabilistic events within one unified execution engine.by Hsueh-Yung Benjamin Koo.Ph.D