We use affine arithmetic to improve both the performance and the robustness of genetic programming for symbolic regression. During evolution, we use affine arithmetic to analyze expressions generated by the genetic operators, estimating their output range given the ranges of their inputs over the training data. These estimated output ranges allow us to discard trees that contain asymptotes as well as those whose output is too far from the desired output range determined by the training instances. We also perform linear scaling of outputs before fitness evaluation. Experiments are performed on 15 problems, comparing the proposed system with a baseline genetic programming system with protected operators, and with a similar system based on interval arithmetic. Results show that integrating affine arithmetic with an implementation of standard genetic programming reduces the number of fitness evaluations during training and improves generalization performance, minimizes overfitting, and completely avoids extreme errors of unseen test data.

A novel approach, model-based clustering, is described foridentifying complex interactions between genes or gene-categories based on static gene expression data. The approach deals with categorical data, which consists of a set of gene expressionprofiles belonging to one category, and a set belonging to anothercategory. An evolutionary algorithm (Meta-Optimizing Semantic Evolutionary Search, or MOSES) is used to learn an ensemble of classification models distinguishing the two categories, based on inputs that are features corresponding to gene expression values. Each feature is associated with a model-based vector, which encodes quantitative information regarding the utilization of the feature across the ensembles of models. Two different ways of constructing these vectors are explored. These model-based vectors are then clustered using a variant of hierarchical clustering called Omniclust. The result is a set of model-based clusters, in which features are gathered together if they are often considered together by classification models -- which may be because they're co-expressed, or may be for subtler reasons involving multi-gene interactions. The method is illustrated by applying it to two datasets regarding human gene expression, one drawn from brain cells and pertinent to the neurogenetics of aging, and the other drawn from blood cells and relating to differentiating between types of lymphoma. We find that, compared to traditional expression-based clustering, the new method often yields clusters that have higher mathematical quality (in the sense of homogeneity and separation) and also yield novel and meaningful insights into the underlying biological processes.

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A novel method, MUTIC (model utilization-based clustering), is described for identifying complex interactions between genes or gene-categories based on gene expression data. The method deals with binary categorical data, which consists of a set of gene expression profiles divided into two biologically meaningful categories. It does not require data from multiple time points. Gene expression profiles are represented by feature vectors whose component features are either gene expression values, or averaged expression values corresponding to gene ontology or protein information resource categories. A supervised learning algorithm (genetic programming) is used to learn an ensemble of classification models distinguishing the two categories based on the feature vectors corresponding to their members. Each feature is associated with a "model utilization vector," which has an entry for each high-quality classification model found, indicating whether or not the feature was used in that model. These utilization vectors are then clustered using a variant of hierarchical clustering called Omniclust. The result is a set of model-utilization-based clusters, in which features are gathered together if they are often considered together by classification models - which may be because they're co-expressed, or may be for subtler reasons involving multi-gene interactions. The MUTIC method is illustrated via applying it to a dataset regarding gene expression in human brains of various ages. Compared to traditional expression-based clustering, MUTIC yields clusters that have higher mathematical quality (in the sense of homogeneity and separation) and also yield novel insights into the underlying biological processes.

We describe an extension of the Bayesian Optimization Algorithm (BOA), a probabilistic model building genetic algorithm, to the domain of program tree evolution. The new system, BOA programming (BOAP), improves significantly on previous probabilistic model building genetic programming (PMBGP) systems in terms of the articulacy and open-ended flexibility of the models learned, and hence control over the distribution of instances generated. Innovations include a novel tree representation and a generalized program evaluation scheme.