A heterogeneous compute solution for optimized genomic selection analysis

This paper presents a heterogeneous computing solution for an optimized genetic selection analysis tool, GenSel. GenSel can be used to efficiently infer the effects of genetic markers on a desired trait or to determine the genomic estimated breeding values (GEBV) of genotyped individuals. To predict which genetic markers are informational, GenSel performs Bayesian inference using Gibbs sampling, a Markov Chain Monte Carlo (MCMC) algorithm. Parallelizing this algorithm proves to be a technically challenging problem because there exists a loop carried dependence between each iteration of the Markov chain. The approach presented in this paper exploits both task-level parallelism (TLP) and data-level parallelism (DLP) that exists within each iteration of the Markov chain. More specifically, a combination of CPU threads using OpenMP and GPU threads using NVIDIA\u27s CUDA paradigm is implemented to speed up the sampling of each genetic marker used in creating the model. Performance speedup will allow this algorithm to accommodate the expected increase in observations on animals and genetic markers per observation. The current implementation executes 1.84 times faster than the optimized CPU implementation

A Multi-GPU Compute Solution for Optimized Genomic Selection Analysis

Many modern-day Bioinformatics algorithms rely heavily on statistical models to analyze their biological data. Some of these statistical models lend themselves nicely to standard high performance computing optimizations such as parallelism, while others do not. One such algorithm is Markov Chain Monte Carlo (MCMC). In this thesis, we present a heterogeneous compute solution for optimizing GenSel, a genetic selection analysis tool. GenSel utilizes a MCMC algorithm to perform Bayesian inference using Gibbs sampling. Optimizing an MCMC algorithm is a difficult problem because it is inherently sequential, containing a loop carried dependence between each Markov Chain iteration. The optimization presented in this thesis utilizes GPU computing to exploit the data-level parallelism within each of these iterations. In addition, it allows for the efficient management of memory, the pipelining of CUDA kernels, and the use of multiple GPUs. The optimizations presented show performance improvements of up to 1.84 times that of the original algorithm

Convergent Stochastic Expectation Maximization algorithm with efficient sampling in high dimension. Application to deformable template model estimation

Estimation in the deformable template model is a big challenge in image analysis. The issue is to estimate an atlas of a population. This atlas contains a template and the corresponding geometrical variability of the observed shapes. The goal is to propose an accurate algorithm with low computational cost and with theoretical guaranties of relevance. This becomes very demanding when dealing with high dimensional data which is particularly the case of medical images. We propose to use an optimized Monte Carlo Markov Chain method into a stochastic Expectation Maximization algorithm in order to estimate the model parameters by maximizing the likelihood. In this paper, we present a new Anisotropic Metropolis Adjusted Langevin Algorithm which we use as transition in the MCMC method. We first prove that this new sampler leads to a geometrically uniformly ergodic Markov chain. We prove also that under mild conditions, the estimated parameters converge almost surely and are asymptotically Gaussian distributed. The methodology developed is then tested on handwritten digits and some 2D and 3D medical images for the deformable model estimation. More widely, the proposed algorithm can be used for a large range of models in many fields of applications such as pharmacology or genetic

An Overview of Schema Theory

The purpose of this paper is to give an introduction to the field of Schema Theory written by a mathematician and for mathematicians. In particular, we endeavor to to highlight areas of the field which might be of interest to a mathematician, to point out some related open problems, and to suggest some large-scale projects. Schema theory seeks to give a theoretical justification for the efficacy of the field of genetic algorithms, so readers who have studied genetic algorithms stand to gain the most from this paper. However, nothing beyond basic probability theory is assumed of the reader, and for this reason we write in a fairly informal style. Because the mathematics behind the theorems in schema theory is relatively elementary, we focus more on the motivation and philosophy. Many of these results have been proven elsewhere, so this paper is designed to serve a primarily expository role. We attempt to cast known results in a new light, which makes the suggested future directions natural. This involves devoting a substantial amount of time to the history of the field. We hope that this exposition will entice some mathematicians to do research in this area, that it will serve as a road map for researchers new to the field, and that it will help explain how schema theory developed. Furthermore, we hope that the results collected in this document will serve as a useful reference. Finally, as far as the author knows, the questions raised in the final section are new.Comment: 27 pages. Originally written in 2009 and hosted on my website, I've decided to put it on the arXiv as a more permanent home. The paper is primarily expository, so I don't really know where to submit it, but perhaps one day I will find an appropriate journa