Infinite Latent Process Decomposition
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infinite Latent Process Decomposition
Tomonari MASADA (正田備也 )[email protected]
Nagasaki University (長崎大學 )
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From array dataextract gene clusterssample-by-sample
[Intuition]Different samples may
show different groupings of
gene expressionsProblem
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Neither gene clusteringnor sample clustering
Clustering ofgene-sample pairs
WhatWeDo
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LPD [Rogers et al. 05]
LatentProcessDecomposition
• Bayesian modeling
• Assignment of eachgene-sample pair
to a processprocess = cluster
PreviousWork
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[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
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iLPDinfiniteLatentProcessDecomposition
• Bayesian nonparametrics(K ∞)
OurNewMethod
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• K can be truncated.(K∞ only theoretically.)• Memory size is fixed.• Parallelization is easy.
• K can be setwith little thought. Merits
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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
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Collapsed Variational Bayesian Inference
○ Fixed memory size
○ Easy parallelization
× Special function evaluation– digamma, trigamma, tetragamma functions
Inference(CVB)
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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
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• 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
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• 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
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• Practical evaluation
• Result interpretation
• GPGPU acceleration
• Visualization
FutureWork
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10 processes 20 processes 40 processes0.270
0.280
0.290
0.300 iLPD LPD
Brain_Tumor1
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10 processes 20 processes 40 processes0.225
0.235
0.245
0.255 iLPD LPD
Brain_Tumor2
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10 processes 20 processes 40 processes0.250
0.260
0.270
0.280 iLPD LPD
DLBCL
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10 processes 20 processes 40 processes0.230
0.240
0.250
0.260 iLPD LPD
Leukemia1
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10 processes 20 processes 40 processes0.300
0.310
0.320
0.330 iLPD LPD
Leukemia2
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10 processes 20 processes 40 processes0.340
0.345
0.350
0.355
0.360 iLPD LPD
Lung_Cancer
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10 processes 20 processes 40 processes0.425
0.445
0.465
0.485 iLPD LPD
Prostate_Tumor
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10 processes 20 processes 40 processes0.230
0.240
0.250
0.260
0.270
0.280 iLPD LPD
SRBCT
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10 processes 20 processes 40 processes0.305
0.310
0.315
iLPD LPD
11_Tumors
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10 processes 20 processes 40 processes0.470
0.480
0.490
0.500 iLPD LPD
14_Tumors
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10 processes 20 processes 40 processes0.140
0.150
0.160
0.170
0.180
0.190 iLPD LPD
9_Tumors
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