infinite Latent Process Decomposition

Tomonari MASADA (正田備也 )tomonari.masada@gmail.com

Nagasaki University (長崎大學 )

From array dataextract gene clusterssample-by-sample

[Intuition]Different samples may

show different groupings of

gene expressionsProblem

Neither gene clusteringnor sample clustering

Clustering ofgene-sample pairs

WhatWeDo

LPD [Rogers et al. 05]

LatentProcessDecomposition

• Bayesian modeling

• Assignment of eachgene-sample pair

to a processprocess = cluster

PreviousWork

[Ying et al. 08]

• K (# processes) shouldbe given as an input.

• LPD is inefficientwhen K is large.

In many cases,we don’t knowoptimal K. Weakness

iLPDinfiniteLatentProcessDecomposition

• Bayesian nonparametrics(K ∞)

OurNewMethod

• K can be truncated.(K∞ only theoretically.)• Memory size is fixed.• Parallelization is easy.

• K can be setwith little thought. Merits

ModelDetails

γtruncatedGEM~ ,11

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

Collapsed Variational Bayesian Inference

○ Fixed memory size

○ Easy parallelization

× Special function evaluation– digamma, trigamma, tetragamma functions

Inference(CVB)

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 and12 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

• Compare iLPD withLPD [Ying et al. 08]

• Train iLPD on90% randomly selected data

• Evaluate posterior density at 10% test data and

calculate geometric mean

• Average over 25 runs Evaluation

• 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 ProcessesResults

• Practical evaluation

• Result interpretation

• GPGPU acceleration

• Visualization

FutureWork

10 processes 20 processes 40 processes0.270

0.280

0.290

0.300 iLPD LPD

Brain_Tumor1

10 processes 20 processes 40 processes0.225

0.235

0.245

0.255 iLPD LPD

Brain_Tumor2

10 processes 20 processes 40 processes0.250

0.260

0.270

0.280 iLPD LPD

DLBCL

10 processes 20 processes 40 processes0.230

0.240

0.250

0.260 iLPD LPD

Leukemia1

10 processes 20 processes 40 processes0.300

0.310

0.320

0.330 iLPD LPD

Leukemia2

10 processes 20 processes 40 processes0.340

0.345

0.350

0.355

0.360 iLPD LPD

Lung_Cancer

10 processes 20 processes 40 processes0.425

0.445

0.465

0.485 iLPD LPD

Prostate_Tumor

10 processes 20 processes 40 processes0.230

0.240

0.250

0.260

0.270

0.280 iLPD LPD

SRBCT

10 processes 20 processes 40 processes0.305

0.310

0.315

iLPD LPD

11_Tumors

10 processes 20 processes 40 processes0.470

0.480

0.490

0.500 iLPD LPD

14_Tumors

10 processes 20 processes 40 processes0.140

0.150

0.160

0.170

0.180

0.190 iLPD LPD

9_Tumors