Sparse Volterra and Polynomial Regression Models: Recoverability and Estimation

Volterra and polynomial regression models play a major role in nonlinear system identification and inference tasks. Exciting applications ranging from neuroscience to genome-wide association analysis build on these models with the additional requirement of parsimony. This requirement has high interpretative value, but unfortunately cannot be met by least-squares based or kernel regression methods. To this end, compressed sampling (CS) approaches, already successful in linear regression settings, can offer a viable alternative. The viability of CS for sparse Volterra and polynomial models is the core theme of this work. A common sparse regression task is initially posed for the two models. Building on (weighted) Lasso-based schemes, an adaptive RLS-type algorithm is developed for sparse polynomial regressions. The identifiability of polynomial models is critically challenged by dimensionality. However, following the CS principle, when these models are sparse, they could be recovered by far fewer measurements. To quantify the sufficient number of measurements for a given level of sparsity, restricted isometry properties (RIP) are investigated in commonly met polynomial regression settings, generalizing known results for their linear counterparts. The merits of the novel (weighted) adaptive CS algorithms to sparse polynomial modeling are verified through synthetic as well as real data tests for genotype-phenotype analysis.Comment: 20 pages, to appear in IEEE Trans. on Signal Processin

Efficient graph-based genetic programming representation with multiple outputs

In this work, we explore and study the implication of having more than one output on a genetic programming (GP) graph-representation. This approach, called multiple interactive outputs in a single tree (MIOST), is based on two ideas. First, we defined an approach, called interactivity within an individual (IWI), which is based on a graph-GP representation. Second, we add to the individuals created with the IWI approach multiple outputs in their structures and as a result of this, we have MIOST. As a first step, we analyze the effects of IWI by using only mutations and analyze its implications (i.e., presence of neutrality). Then, we continue testing the effectiveness of IWI by allowing mutations and the standard GP crossover in the evolutionary process. Finally, we tested the effectiveness of MIOST by using mutations and crossover and conducted extensive empirical results on different evolvable problems of different complexity taken from the literature. The results reported in this paper indicate that the proposed approach has a better overall performance in terms of consistency reaching feasible solutions

A stepwise evolution of functions

A Genotype-Phenotype mapping in most Genetic Programming (GP) systems uses a predefined and rigid grammar definition. This method has been successful in producing the required solution. However, it can only be used to solve a limited set of problems. In this paper, a Teachable GP (TGP) system is proposed. An external GP system evolves a complete computer program, which acceptable solution is then added automatically to the existing grammar definition as a function and made available to the TGP system. This dynamic grammar definition allows for a more complex program to be generated, solving more complex problems. Experiments are performed to compare performances between GP without the added function, GP with a user-defined function and GP with the evolved function and results shows that GP with an evolved function is comparable to the GP with user-defined function and outperformed GP without function

Phenotype Search Trajectory Networks for Linear Genetic Programming

Genotype-to-phenotype mappings translate genotypic variations such as mutations into phenotypic changes. Neutrality is the observation that some mutations do not lead to phenotypic changes. Studying the search trajectories in genotypic and phenotypic spaces, especially through neutral mutations, helps us to better understand the progression of evolution and its algorithmic behaviour. In this study, we visualise the search trajectories of a genetic programming system as graph-based models, where nodes are genotypes/phenotypes and edges represent their mutational transitions. We also quantitatively measure the characteristics of phenotypes including their genotypic abundance (the requirement for neutrality) and Kolmogorov complexity. We connect these quantified metrics with search trajectory visualisations, and find that more complex phenotypes are under-represented by fewer genotypes and are harder for evolution to discover. Less complex phenotypes, on the other hand, are over-represented by genotypes, are easier to find, and frequently serve as stepping-stones for evolution

Computational pan-genomics: status, promises and challenges

International audienceMany disciplines, from human genetics and oncology to plant breeding, microbiology and virology, commonly face the challenge of analyzing rapidly increasing numbers of genomes. In case of Homo sapiens, the number of sequenced genomes will approach hundreds of thousands in the next few years. Simply scaling up established bioinformatics pipelines will not be sufficient for leveraging the full potential of such rich genomic data sets. Instead, novel, qualitatively different computational methods and paradigms are needed. We will witness the rapid extension of computational pan-genomics, a new sub-area of research in computational biology. In this article, we generalize existing definitions and understand a pan-genome as any collection of genomic sequences to be analyzed jointly or to be used as a reference. We examine already available approaches to construct and use pan-genomes, discuss the potential benefits of future technologies and methodologies and review open challenges from the vantage point of the above-mentioned biological disciplines. As a prominent example for a computational paradigm shift, we particularly highlight the transition from the representation of reference genomes as strings to representations as graphs. We outline how this and other challenges from different application domains translate into common computational problems, point out relevant bioinformatics techniques and identify open problems in computer science. With this review, we aim to increase awareness that a joint approach to computational pan-genomics can help address many of the problems currently faced in various domains

Artificial evolution with Binary Decision Diagrams: a study in evolvability in neutral spaces

This thesis develops a new approach to evolving Binary Decision Diagrams, and uses it to study evolvability issues. For reasons that are not yet fully understood, current approaches to artificial evolution fail to exhibit the evolvability so readily exhibited in nature. To be able to apply evolvability to artificial evolution the field must first understand and characterise it; this will then lead to systems which are much more capable than they are currently. An experimental approach is taken. Carefully crafted, controlled experiments elucidate the mechanisms and properties that facilitate evolvability, focusing on the roles and interplay between neutrality, modularity, gradualism, robustness and diversity. Evolvability is found to emerge under gradual evolution as a biased distribution of functionality within the genotype-phenotype map, which serves to direct phenotypic variation. Neutrality facilitates fitness-conserving exploration, completely alleviating local optima. Population diversity, in conjunction with neutrality, is shown to facilitate the evolution of evolvability. The search is robust, scalable, and insensitive to the absence of initial diversity. The thesis concludes that gradual evolution in a search space that is free of local optima by way of neutrality can be a viable alternative to problematic evolution on multi-modal landscapes