Everyday Multithreading
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1 Everyday Multithreading Parallel computing for genomic evaluations in R C. Heuer, D. Hinrichs, G. Thaller Institute of Animal Breeding and Husbandry, Kiel University August 27, 2014 C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
2 Introduction Introduction C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
3 Introduction Introduction High Dimensional livestock data sets New computational challenges Paradigm shift in breeding programs and computing From sparse to dense MME (or mixtures) High storage, memory and computing demands C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
4 Introduction Introduction High Dimensional livestock data sets New computational challenges Paradigm shift in breeding programs and computing From sparse to dense MME (or mixtures) High storage, memory and computing demands Solution: Making use of available hardware resources by parallel computing C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
5 What parallel computing is: Parallel Computing C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
6 What parallel computing is: Parallel Computing Splitting up a big problem into chunks that are simultaneously being solved by several processing units C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
7 What parallel computing is: Parallel Computing Splitting up a big problem into chunks that are simultaneously being solved by several processing units = C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
8 What parallel computing is: Parallel Computing Splitting up a big problem into chunks that are simultaneously being solved by several processing units = C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
9 Parallel Computing Paradigms Parallel Computing C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
10 Parallel Computing Paradigms Parallel Computing 1 Most importantly: Single Core parallelism Vectorization 2 Shared Memory multi-threading OpenMP 3 Distributed Memory multi-processing MPI 4 GPU-programming CUDA, OpenCL, Intel Xeon-Phi C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
11 Parallel Computing Paradigms Parallel Computing 1 Most importantly: Single Core parallelism Vectorization 2 Shared Memory multi-threading OpenMP 3 Distributed Memory multi-processing MPI 4 GPU-programming CUDA, OpenCL, Intel Xeon-Phi Efficiency/Scaling: Depends on size of the problem: Overhead The less efficient a single-threaded application, the better the scaling C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
12 Parallel Computing Paradigms Parallel Computing 1 Most importantly: Single Core parallelism Vectorization 2 Shared Memory multi-threading OpenMP 3 Distributed Memory multi-processing MPI 4 GPU-programming CUDA, OpenCL, Intel Xeon-Phi Efficiency/Scaling: Depends on size of the problem: Overhead The less efficient a single-threaded application, the better the scaling In general: First single-threaded optimization then parallelization C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
13 R-Package R-package cpgen C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
14 R-Package R-package cpgen Advantages of R: 1 Very flexible open source interpreter language 2 Easy to use, available on all platforms and widely spread Drawbacks of R: C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
15 R-Package R-package cpgen Advantages of R: 1 Very flexible open source interpreter language 2 Easy to use, available on all platforms and widely spread Drawbacks of R: 1 Not designed for big data problems 2 Needs a lot of effort to extend R 3 Strictly single-threaded C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
16 R-Package R-package cpgen Advantages of R: 1 Very flexible open source interpreter language 2 Easy to use, available on all platforms and widely spread Drawbacks of R: 1 Not designed for big data problems 2 Needs a lot of effort to extend R 3 Strictly single-threaded But: Can be extended and multi-threaded through C/C++/Fortran shared libraries C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
17 R-Package General Implementation C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
18 R-Package General Implementation 1 R as the basic environment for data preparation and supply 2 Linking C++ to R: Rcpp (Eddelbuettel and Francois, 2011) 3 Linear Algebra: Eigen Vectorization! (Guennebaud et al., 2010) 4 Eigen + Rcpp + Sparse-Matrix support: RcppEigen (Bates and Eddelbuettel, 2013) 5 Parallelization: OpenMP C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
19 R-Package Parallel Computing in cpgen C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
20 R-Package Parallel Computing in cpgen C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
21 R-Package Functionality C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
22 R-Package Functionality 1 Single-Site Gibbs Sampler for Mixed Models with arbitrary number of random effects (sparse or dense design matrices) 2 Genomic Prediction Module: Different Methods, Cross Validation 3 GWAS Module: EMMAX - highly efficient and very flexible single marker GWAS 4 Tools: Genomic additive and dominance relationships, Crossproducts, Covariance Matrices,... C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
23 R-Package Gibbs Sampler Runs models of the following form: y = Xb + Z 1 u 1 + Z 2 u 2 + Z 3 u Z n u n + e For all u k : MVN(0, Iσ 2 u k ) If u k is assumed to follow some MVN(0, G k σk 2): Design matrix must be constructed as: Z k = Z k G 1/2, yielding independent effect in u k (Waldmann et al., 2008). C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
24 R-Package Genomic BLUP GBLUP can be accomplished very efficiently (Kang et al., 2008): y = Xb + a + e with: a MVN(0, Gσ 2 a) By finding the decomposition: G = UDU and premultiplying the model equation by U we get: U y = U Xb + U a + U e with: Var(U y)=u GUσ 2 a + U Uσ 2 e = U UDU Uσ 2 a + Iσ 2 e = Dσ 2 a + Iσ 2 e C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
25 R-Package GWAS Single marker regression Controlling for polygenic background effect through [assumed] covariance structure V of y - EMMAX (Kang et al., 2010) Obtaining General Least Squares estimates for marker effects: ˆβ =(X V 1 X) 1 X V 1 y This is equivalent to: ˆβ =(X X ) 1 X y, with X = V 1/2 X, y = V 1/2 y C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
26 R-Package Parallel Computing in cpgen What is parallelized: 1 All crossproduct-like computations 2 Sampling of random effects in Gibbs Sampler (dot product, vector-vector subtraction) Fernando et al., Cross Validation for genomic prediction 4 GWAS C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
27 R-Package Parallel Computing in cpgen What is parallelized: 1 All crossproduct-like computations 2 Sampling of random effects in Gibbs Sampler (dot product, vector-vector subtraction) Fernando et al., Cross Validation for genomic prediction 4 GWAS Number of threads being used can be controlled during runtime C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
28 Parallel Scaling 2,000 Observations, 50,000 Markers C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
29 Parallel Scaling 2,000 Observations, 50,000 Markers C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
30 Parallel Scaling Gibbs Sampler (BRR) - 10,000 Markers C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
31 Parallel Scaling Gibbs Sampler (BRR) - 10,000 Markers C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
32 Conclusions Conclusions C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
33 Conclusions Conclusions Shared Memory multithreading can decrease computation time significantly Bridges the gap between single threaded applications and heavily parallelized standalone programs for HPC Clusters We can make use of the computational power present in workstation PCs Everyday Multithreading C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
34 Conclusions Conclusions Shared Memory multithreading can decrease computation time significantly Bridges the gap between single threaded applications and heavily parallelized standalone programs for HPC Clusters We can make use of the computational power present in workstation PCs Everyday Multithreading But: Size of solvable problem is limited by available memory With 1 TB of memory, the package could fit a BRR model with 3 million observations and 40k markers C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
35 Thank you for the attention Github R-Forge C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
36 Absolute Timings 10 Cores, 30,000 markers BRR: 1 million observations, 30k iterations 100 hours GWAS: 10k observations 7 minutes G-Matrix: 10k observations 2 minutes C. Heuer, D. Hinrichs, G. Thaller Parallel Computing in R August 27, / 17
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