1. Infinite Mixture Model-Based Clustering of DNA Microarray Data Using openMP

2. DNA microarrays

3. Clustering MA data (not computers)
Conditions
Clustering
Genes

4. Why do I need sooo much computing power?
Goal: Determine all posterior pairwise probabilities of two genes/samples belonging to same cluster
IMMs cannot be solved analytically
Use sampling method to approximate posterior probabilities
Typically
10,000 iterations
Sevaral 1,000 genes
10 … 200 samples
Compute O(genes2 x samples2) probabilities per iteration
Some overhead for cluster-reassignment, other model parameters

5. Open Multi-Processing (OpenMP)
Facilitates parallelization of C++ and Fortran code for shared memory environments
e.g. multi-processor machines
Set of compiler directives, system variables, and library functions
Platform-independent
Website:
Parallelize sequential code by using compiler directives
Relatively small programming effort
Reduced risk for programming errors
Use of shared memory
Reduces the communication overhead required to synchronize multiple threads
But cannot run threads on multiple nodes

6. “Hello World” in openMP
#include <stdio.h>
#include <omp.h>
int main(int argc, char *argv[]) {
int id, nthreads;
#pragma omp parallel private(id) {
id = omp_get_thread_num();
printf("Hello World from thread %d\n", id);
#pragma omp barrier
if ( id == 0 ) {
nthreads = omp_get_num_threads();
printf("There are %d threads\n",nthreads); }
return 0;

7. OpenMP examples Header Library Functions Compiler directives
#include <omp.h>
Library Functions
omp_set_num_threads(4);
printf("number of threads %d\n", omp_get_num_threads());
Compiler directives
#pragma omp for schedule(dynamic, 1)
for(j=0;j<=Q;j++){
clusterProbabilities[j]= getProbCsMissing2(i,j,Contexts); }

8. OpenMP examples More Compiler directives #pragma omp for
for(j=0;j<=Q;j++){ …
#pragma omp critical
sigmas[i][j]=1.0/gengam(beta[i]* v[i]/2.0,beta[i]/2.0); }

9. OpenMP examples More Compiler directives … same as … int i;
#pragma omp parallel for private(i, pos)
for(j=0;i<T;i++){ … }
… same as …
#pragma omp parallel for private(pos)

10. Some more compiler directives
Reduction
#pragma omp do reduction (+:sum)
 summarize the share variable “sum”
Parallel region
#pragma omp parallel { … }
Sections
#pragma omp sections
#pragma omp section
Code block 1
Code block 2

11. The making-of Start an interactive session Intel compiler g++ compiler
qsub -I -l nodes=1:opteron
Intel compiler
module load openmpi-intel
icpc -w –openmp
g++ compiler
module load gcc-4.2.3
g++ -fopenmp

12. The batch file #PBS -S /bin/csh #PBS -l nodes=1:opteron:ppn=2
#PBS -l walltime=18:00:00
#PBS –e /users/jfreuden/runGimm/stderr.txt
#PBS -o /users/jfreuden/runGimm/stdout.txt
setenv OMP_NUM_THREADS `cat $PBS_NODEFILE | grep $HOST | wc -l`
module load intel
cd /users/jfreuden/runGimm/
R CMD BATCH runGimm.R

13. Simulation study: Non-informative samples
4 gene clusters of sizes 20, 20, 80, and 80
3 sample clusters of size 5
Additional samples
m+ = 5, 10, 20, 50, 100
No change in expression
Same noise level
100 repeats for each level

14. Simulation study: Non-informative samples

15. Simulation study: Non-informative samples

16. Simulation study: Non-informative samples

17. Questions? Comments?

18. Additional Slides

19. Clustering
D’haeseleer (2005)

20. Example for Gibbs Sampling: BUGS

21. Simulation study: Simple Case

22. Simulation study: Simple Case

23. Simulation study: ‘Time course 1’

24. Simulation study: ‘Time course 2’

25. Simulation study: Non-informative samples

26. Simulation study: Non-informative samples