A topic model for analyzing microarray data

1. infinite Latent Process
Decomposition
Tomonari MASADA (正田備也)
tomonari.masada@gmail.com
Nagasaki University (長崎大學)

2. From array data
extract gene clusters
sample-by-sample
[Intuition]
Different samples may
show different
groupings of
gene expressionsProblem

3. Neither gene clustering
nor sample clustering
Clustering of
gene-sample pairs
What
We
Do

4. LPD [Rogers et al. 05]
Latent
Process
Decomposition
• Bayesian modeling
• Assignment of each
gene-sample pair
to a process
process = cluster
Previous
Work

5. [Ying et al. 08]
• K (# processes) should
be given as an input.
• LPD is inefficient
when K is large.
In many cases,
we don’t know
optimal K. Weakness

6. iLPD
infinite
Latent
Process
Decomposition
• Bayesian nonparametrics
(K  ∞)
Our
New
Method

7. • K can be truncated.
(K∞ only theoretically.)
• Memory size is fixed.
• Parallelization is easy.
• K can be set
with little thought. Merits

8. Model
Details
γtruncatedGEM~
,1
1
1
k
l lkk πππ
απd Dirichlet~
γγ,baGamma~
αα,baGamma~
,1Beta~ ,γk
ρρ,baGamma~
,ρμgk 0Gauss~
00Gamma~ ,bagk
dgdg gzgzdg ,λμx Gauss~
ddg θz Multi~
Kk ,,1 

9. Collapsed Variational
Bayesian Inference
○ Fixed memory size
○ Easy parallelization
× Special function evaluation
– digamma, trigamma, tetragamma functions
Inference
(CVB)

10. Experiment
http://www.gems-system.org/
Dataset name Sample Gene Diagnostic Task
11_Tumors 174 12,534 11 various human tumor types
14_Tumors 308 15,010
14 various human tumor types and
12 normal tissue types
9_Tumors 60 5,727 9 various human tumor types
Brain_Tumor1 90 5,921 5 human brain tumor types
Brain_Tumor2 50 10,368 4 malignant glioma types
Leukemia1 72 5,328 AML, ALL B-cell, and ALL T-cell
Leukemia2 72 11,226 AML, ALL, and mixed-lineage leukemia (MLL)
Lung_Cancer 203 12,601 4 lung cancer types and normal tissues
SRBCT 83 2,309 Small, round blue cell tumors (SRBCT) of childhood
Prostate_Tumor 102 10,510 Prostate tumor and normal tissues
DLBCL 77 5,470 DLBCL and follicular lymphomas

11. • Compare iLPD with
LPD [Ying et al. 08]
• Train iLPD on
90% randomly selected data
• Evaluate posterior density
at 10% test data and
calculate geometric mean
• Average over 25 runs Evaluation

12. • iLPD is more efficient
for a large K than LPD.
• There is a dataset that
is not well analyzed.
–LPD-type methods may
not be a panacea.
Cf. BMC Bioinformatics 2010, 11:552
– Nonparametric Bayesian method based on
Indian Buffet Processes
Results

13. • Practical evaluation
• Result interpretation
• GPGPU acceleration
• Visualization
Future
Work

14. 0.270
0.280
0.290
0.300
10 processes 20 processes 40 processes
iLPD LPD
Brain_Tumor1

15. 0.225
0.235
0.245
0.255
10 processes 20 processes 40 processes
iLPD LPD
Brain_Tumor2

16. 0.250
0.260
0.270
0.280
10 processes 20 processes 40 processes
iLPD LPD
DLBCL

17. 0.230
0.240
0.250
0.260
10 processes 20 processes 40 processes
iLPD LPD
Leukemia1

18. 0.300
0.310
0.320
0.330
10 processes 20 processes 40 processes
iLPD LPD
Leukemia2

19. 0.340
0.345
0.350
0.355
0.360
10 processes 20 processes 40 processes
iLPD LPD
Lung_Cancer

20. 0.425
0.445
0.465
0.485
10 processes 20 processes 40 processes
iLPD LPD
Prostate_Tumor

21. 0.230
0.240
0.250
0.260
0.270
0.280
10 processes 20 processes 40 processes
iLPD LPD
SRBCT

22. 0.305
0.310
0.315
10 processes 20 processes 40 processes
iLPD LPD
11_Tumors

23. 0.470
0.480
0.490
0.500
10 processes 20 processes 40 processes
iLPD LPD
14_Tumors

24. 0.140
0.150
0.160
0.170
0.180
0.190
10 processes 20 processes 40 processes
iLPD LPD
9_Tumors