Pedro Larrañaga

Estimation of Distribution Algorithms

Partial abductive inference in Bayesian networks is intended as the process of generating the J( most probable configurations for a distinguished subset of the network variables (explanation set), given some observations (evidence). This problem, also known as the Maximum a Posteriori Problem, is known to be NP-hard, so exact computation is not always possible. As partial abductive inference in Bayesian networks can be viewed as a combinatorial optimization problem, Genetic Algorithms have been successfully applied to give an approximate algorithm for it (de Campos et al., 1999). In this work we approach the problem by means of Estimation of Distribution Algorithms, and an empirical comparison between the results obtained by Genetic Algorithms and Estimation of Distribution Algorithms is carried out.

An empirical comparison of four initialization methods for the K-Means algorithm

In this paper, we aim to compare empirically four initialization methods for the K-Means algorithm: random, Forgy, MacQueen and Kaufman. Although this algorithm is known for its robustness, it is widely reported in the literature that its performance depends upon two key points: initial clustering and instance order. We conduct a series of experiments to draw up (in terms of mean, maximum, minimum and standard deviation) the probability distribution of the square-error values of the final clusters returned by the K-Means algorithm independently on any initial clustering and on any instance order when each of the four initialization methods is used. The results of our experiments illustrate that the random and the Kaufman initialization methods outperform the rest of the compared methods as they make the K-Means more effective and more independent on initial clustering and on instance order. In addition, we compare the convergence speed of the K-Means algorithm when using each of the four initialization methods. Our results suggest that the Kaufman initialization method induces to the K-Means algorithm a more desirable behaviour with respect to the convergence speed than the random initialization method.

Genetic Algorithms for the Travelling Salesman Problem: A Review of Representations and Operators

This paper is the result of a literature study carried out by the authors. It is a review of the different attempts made to solve the Travelling Salesman Problem with Genetic Algorithms. We present crossover and mutation operators, developed to tackle the Travelling Salesman Problem with Genetic Algorithms with different representations such as: binary representation, path representation, adjacency representation, ordinal representation and matrix representation. Likewise, we show the experimental results obtained with different standard examples using combination of crossover and mutation operators in relation with path representation.

Filter versus wrapper gene selection approaches in DNA microarray domains

DNA microarray experiments generating thousands of gene expression measurements, are used to collect information from tissue and cell samples regarding gene expression differences that could be useful for diagnosis disease, distinction of the specific tumor type, etc. One important application of gene expression microarray data is the classification of samples into known categories. As DNA microarray technology measures the gene expression en masse, this has resulted in data with the number of features (genes) far exceeding the number of samples. As the predictive accuracy of supervised classifiers that try to discriminate between the classes of the problem decays with the existence of irrelevant and redundant features, the necessity of a dimensionality reduction process is essential. We propose the application of a gene selection process, which also enables the biology researcher to focus on promising gene candidates that actively contribute to classification in these large scale microarrays. Two basic approaches for feature selection appear in machine learning and pattern recognition literature: the filter and wrapper techniques. Filter procedures are used in most of the works in the area of DNA microarrays. In this work, a comparison between a group of different filter metrics and a wrapper sequential search procedure is carried out. The comparison is performed in two well-known DNA microarray datasets by the use of four classic supervised classifiers. The study is carried out over the original-continuous and three-intervals discretized gene expression data. While two well-known filter metrics are proposed for continuous data, four classic filter measures are used over discretized data. The same wrapper approach is used for both continuous and discretized data. The application of filter and wrapper gene selection procedures leads to considerably better accuracy results in comparison to the non-gene selection approach, coupled with interesting and notable dimensionality reductions. Although the wrapper approach mainly shows a more accurate behavior than filter metrics, this improvement is coupled with considerable computer-load necessities. We note that most of the genes selected by proposed filter and wrapper procedures in discrete and continuous microarray data appear in the lists of relevant-informative genes detected by previous studies over these datasets. The aim of this work is to make contributions in the field of the gene selection task in DNA microarray datasets. By an extensive comparison with more popular filter techniques, we would like to make contributions in the expansion and study of the wrapper approach in this type of domains.

Towards a New Evolutionary Computation

Linking Entropy to Estimation of Distribution Algorithms.- Entropy-based Convergence Measurement in Discrete Estimation of Distribution Algorithms.- Real-coded Bayesian Optimization Algorithm.- The CMA Evolution Strategy: A Comparing Review.- Estimation of Distribution Programming: EDA-based Approach to Program Generation.- Multi-objective Optimization with the Naive ID A.- A Parallel Island Model for Estimation of Distribution Algorithms.- GA-EDA: A New Hybrid Cooperative Search Evolutionary Algorithm.- Bayesian Classifiers in Optimization: An EDA-like Approach.- Feature Ranking Using an EDA-based Wrapper Approach.- Learning Linguistic Fuzzy Rules by Using Estimation of Distribution Algorithms as the Search Engine in the COR Methodology.- Estimation of Distribution Algorithm with 2-opt Local Search for the Quadratic Assignment Problem.

Learning Bayesian network structures by searching for the best ordering with genetic algorithms

Presents a new methodology for inducing Bayesian network structures from a database of cases. The methodology is based on searching for the best ordering of the system variables by means of genetic algorithms. Since this problem of finding an optimal ordering of variables resembles the traveling salesman problem, the authors use genetic operators that were developed for the latter problem. The quality of a variable ordering is evaluated with the structure-learning algorithm K2. The authors present empirical results that were obtained with a simulation of the ALARM network.

Protein Folding in Simplified Models With Estimation of Distribution Algorithms

Simplified lattice models have played an important role in protein structure prediction and protein folding problems. These models can be useful for an initial approximation of the protein structure, and for the investigation of the dynamics that govern the protein folding process. Estimation of distribution algorithms (EDAs) are efficient evolutionary algorithms that can learn and exploit the search space regularities in the form of probabilistic dependencies. This paper introduces the application of different variants of EDAs to the solution of the protein structure prediction problem in simplified models, and proposes their use as a simulation tool for the analysis of the protein folding process. We develop new ideas for the application of EDAs to the bidimensional and tridimensional (2-d and 3-d) simplified protein folding problems. This paper analyzes the rationale behind the application of EDAs to these problems, and elucidates the relationship between our proposal and other population-based approaches proposed for the protein folding problem. We argue that EDAs are an efficient alternative for many instances of the protein structure prediction problem and are indeed appropriate for a theoretical analysis of search procedures in lattice models. All the algorithms introduced are tested on a set of difficult 2-d and 3-d instances from lattice models. Some of the results obtained with EDAs are superior to the ones obtained with other well-known population-based optimization algorithms.

Inexact graph matching by means of estimation of distribution algorithms

Abstract Estimation of distribution algorithms (EDAs) are a quite recent topic in optimization techniques. They combine two technical disciplines of soft computing methodologies: probabilistic reasoning and evolutionary computing. Several algorithms and approaches have already been proposed by different authors, but up to now there are very few papers showing their potential and comparing them to other evolutionary computational methods and algorithms such as genetic algorithms (GAs). This paper focuses on the problem of inexact graph matching which is NP-hard and requires techniques to find an approximate acceptable solution. This problem arises when a nonbijective correspondence is searched between two graphs. A typical instance of this problem corresponds to the case where graphs are used for structural pattern recognition in images. EDA algorithms are well suited for this type of problems. This paper proposes to use EDA algorithms as a new approach for inexact graph matching. Also, two adaptations of the EDA approach to problems with constraints are described as two techniques to control the generation of individuals, and the performance of EDAs for inexact graph matching is compared with the one of GAs.

Decomposing Bayesian networks: triangulation of the moral graph with genetic algorithms

In this paper we consider the optimal decomposition of Bayesian networks. More concretely, we examine empirically the applicability of genetic algorithms to the problem of the triangulation of moral graphs. This problem constitutes the only difficult step in the evidence propagation algorithm of Lauritzen and Spiegelhalter (1988) and is known to be NP-hard (Wen, 1991). We carry out experiments with distinct crossover and mutation operators and with different population sizes, mutation rates and selection biasses. The results are analysed statistically. They turn out to improve the results obtained with most other known triangulation methods (Kjærulff, 1990) and are comparable to results obtained with simulated annealing (Kjærulff, 1990; Kjærulff, 1992).

A review on evolutionary algorithms in Bayesian network learning and inference tasks

Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Bayesian networks are one of the most widely used class of these models. Some of the inference and learning tasks in Bayesian networks involve complex optimization problems that require the use of meta-heuristic algorithms. Evolutionary algorithms, as successful problem solvers, are promising candidates for this purpose. This paper reviews the application of evolutionary algorithms for solving some NP-hard optimization tasks in Bayesian network inference and learning.