a multitask multiple kernel learning algorithm for survival ...12-11-00)-12...2000/12/11 · a...
TRANSCRIPT
-
A Multitask Multiple Kernel Learning Algorithm forSurvival Analysis
with Application to Cancer Biology
Onur Dereli, Ceyda Oğuz, Mehmet Gönen
Koç University, İstanbul, [email protected] [email protected] [email protected]
June 12, 2019 / Long Beach
Dereli, O., Oğuz, C., Gönen, M. (KU) ICML 2019 June 12, 2019 / Long Beach 1 / 9
-
Proposed Approach
Gene set1G1
G3
G6
G17
G19
G28
G42
···
Gene setP
G8
G12
G19
G25
G42
G47
···
···
X1
XT
Genes
Patie
nts
Genes
Patie
nts
Genes
Patients
Genes
Patients
X1,1
X1,P
···
Genes
Patients
Genes
Patients
XT,1
XT,P
···
···
Patients
Patients
···
Patients
Patients
K1,1
K1,P
···
Patients
Patients
···
Patients
Patients
KT,1
KT,P
η1
ηP
···
η1
ηP
···
Patients
Patients
···
Patients
Patients
K1,η
KT,η
Multitaskmultiple kernel learning
f1
Survivalanalysis Vital Days to Days to last
status death follow-upAlive NA 678Dead 364 NA...
......
Alive NA 2555Dead 520 NA
Y1
···
···
fT
Survivalanalysis Vital Days to Days to last
status death follow-upDead 456 NADead 3200 NA...
......
Alive NA 2208Dead 1891 NA
YT
Dereli, O., Oğuz, C., Gönen, M. (KU) ICML 2019 June 12, 2019 / Long Beach 2 / 9
-
Proposed Approach
Gene set1G1
G3
G6
G17
G19
G28
G42
···
Gene setP
G8
G12
G19
G25
G42
G47
···
···
X1
XT
Genes
Patie
nts
Genes
Patie
nts
Genes
Patients
Genes
Patients
X1,1
X1,P
···
Genes
Patients
Genes
Patients
XT,1
XT,P
···
···
Patients
Patients
···
Patients
Patients
K1,1
K1,P
···
Patients
Patients
···
Patients
Patients
KT,1
KT,P
η1
ηP
···
η1
ηP
···
Patients
Patients
···
Patients
Patients
K1,η
KT,η
Multitaskmultiple kernel learning
f1
Survivalanalysis Vital Days to Days to last
status death follow-upAlive NA 678Dead 364 NA...
......
Alive NA 2555Dead 520 NA
Y1
···
···
fT
Survivalanalysis Vital Days to Days to last
status death follow-upDead 456 NADead 3200 NA...
......
Alive NA 2208Dead 1891 NA
YT
Dereli, O., Oğuz, C., Gönen, M. (KU) ICML 2019 June 12, 2019 / Long Beach 2 / 9
-
Proposed Approach
Gene set1G1
G3
G6
G17
G19
G28
G42
···
Gene setP
G8
G12
G19
G25
G42
G47
···
···
X1
XT
Genes
Patie
nts
Genes
Patie
nts
Genes
Patients
Genes
Patients
X1,1
X1,P
···
Genes
Patients
Genes
Patients
XT,1
XT,P
···
···
Patients
Patients
···
Patients
Patients
K1,1
K1,P
···
Patients
Patients
···
Patients
Patients
KT,1
KT,P
η1
ηP
···
η1
ηP
···
Patients
Patients
···
Patients
Patients
K1,η
KT,η
Multitaskmultiple kernel learning
f1
Survivalanalysis Vital Days to Days to last
status death follow-upAlive NA 678Dead 364 NA...
......
Alive NA 2555Dead 520 NA
Y1
···
···
fT
Survivalanalysis Vital Days to Days to last
status death follow-upDead 456 NADead 3200 NA...
......
Alive NA 2208Dead 1891 NA
YT
Dereli, O., Oğuz, C., Gönen, M. (KU) ICML 2019 June 12, 2019 / Long Beach 2 / 9
-
Proposed Approach
Gene set1G1
G3
G6
G17
G19
G28
G42
···
Gene setP
G8
G12
G19
G25
G42
G47
···
···
X1
XT
Genes
Patie
nts
Genes
Patie
nts
Genes
Patients
Genes
Patients
X1,1
X1,P
···
Genes
Patients
Genes
Patients
XT,1
XT,P
···
···
Patients
Patients
···
Patients
Patients
K1,1
K1,P
···
Patients
Patients
···
Patients
Patients
KT,1
KT,P
η1
ηP
···
η1
ηP
···
Patients
Patients
···
Patients
Patients
K1,η
KT,η
Multitaskmultiple kernel learning
f1
Survivalanalysis Vital Days to Days to last
status death follow-upAlive NA 678Dead 364 NA...
......
Alive NA 2555Dead 520 NA
Y1
···
···
fT
Survivalanalysis Vital Days to Days to last
status death follow-upDead 456 NADead 3200 NA...
......
Alive NA 2208Dead 1891 NA
YT
Dereli, O., Oğuz, C., Gönen, M. (KU) ICML 2019 June 12, 2019 / Long Beach 2 / 9
-
Multitask Survival MKL Formulation
minimizeT∑
t=1
[12
w>t w t + CNt∑
i=1
(ξ+ti + (1− δti)ξ−ti )
]with respect to w t ∈ RDt , ξ+t ∈ R
Nt , ξ−t ∈ RNt , bt ∈ R
subject to �+ ξ+ti ≥ yti −w>t x ti − bt ∀(t , i)
�+ ξ−ti ≥ w>t x ti + bt − yti ∀(t , i)
ξ+ti ≥ 0 ∀(t , i)ξ−ti ≥ 0 ∀(t , i)
Dereli, O., Oğuz, C., Gönen, M. (KU) ICML 2019 June 12, 2019 / Long Beach 3 / 9
-
Multitask Survival MKL Formulation
minimize −T∑
t=1
Nt∑i=1
yti(α+ti − α−ti ) + �
T∑t=1
Nt∑i=1
(α+ti + α−ti )
+12
T∑t=1
Nt∑i=1
Nt∑j=1
(α+ti − α−ti )(α
+tj − α
−tj )
P∑m=1
ηmkm(x ti ,x tj)
with respect to α+t ∈ RNt , α−t ∈ R
Nt , η ∈ RP
subject toNt∑
i=1
(α+ti − α−ti ) = 0 ∀t
C ≥ α+ti ≥ 0 ∀(t , i)C(1− δti) ≥ α−ti ≥ 0 ∀(t , i)
P∑m=1
ηm = 1
ηm ≥ 0 ∀m
Dereli, O., Oğuz, C., Gönen, M. (KU) ICML 2019 June 12, 2019 / Long Beach 3 / 9
-
Multitask Survival MKL Formulation
η(s+1)m =
T∑t=1
η(s)m
√Nt∑
i=1
Nt∑j=1
α(s)ti α
(s)tj km(x ti ,x tj)
T∑t=1
P∑o=1
η(s)o
√Nt∑
i=1
Nt∑j=1
α(s)ti α
(s)tj ko(x ti ,x tj)
∀m
Dereli, O., Oğuz, C., Gönen, M. (KU) ICML 2019 June 12, 2019 / Long Beach 3 / 9
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Data Sets
●BLCA(402)
BRCA(1067)
CESC(291)
COAD(433)
ESCA(160)
GBM(152)
HNSC(498)
KIRC(526)
KIRP(285)
LAML(130)
LGG(506)
LIHC(365)
LUAD(500)
LUSC(493)
OV(372)
PAAD(176)
READ(156)
SARC(256)
STAD(348)
UCEC(539)
• 20 cancer data sets from TCGA databaseGene expression profiles and survival characteristics
• Hallmark Gene Set [1] & PID Pathway [2] Collections
Dereli, O., Oğuz, C., Gönen, M. (KU) ICML 2019 June 12, 2019 / Long Beach 4 / 9
-
BLCA
p < 1e−3p = 0.640
p < 1e−3p = 0.016
p < 1e−3
p < 1e−3 p < 1e−3
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inde
x
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0.4
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0.6
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BRCA
p < 1e−3p < 1e−3
p < 1e−3p < 1e−3
p < 1e−3
p < 1e−3 p = 0.023
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0.4
0.5
0.6
0.7
0.8
CESC
p < 1e−3p < 1e−3
p < 1e−3p < 1e−3
p < 1e−3
p < 1e−3 p < 1e−3
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0.4
0.5
0.6
0.7
0.8
0.9
COAD
p < 1e−3p < 1e−3
p < 1e−3p < 1e−3
p = 0.086
p = 0.012 p < 1e−3
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0.8
ESCA
p = 0.009p = 0.360
p = 0.074p = 0.834
p = 0.656
p = 0.313 p = 0.740
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0.3
0.4
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0.8
0.9
GBM
p < 1e−3p < 1e−3
p < 1e−3p < 1e−3
p < 1e−3
p < 1e−3 p = 0.681
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inde
x
0.3
0.4
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0.8
HNSC
p < 1e−3p < 1e−3
p < 1e−3p < 1e−3
p < 1e−3
p < 1e−3 p < 1e−3
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0.3
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0.5
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0.8
KIRC
p = 0.030p < 1e−3
p = 0.778p = 0.083
p = 0.331
p < 1e−3 p < 1e−3
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0.6
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KIRP
p = 0.230p = 0.833
p = 0.888p = 0.096
p = 0.592
p = 0.866 p = 0.006●
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0.5
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0.8
0.9
1.0
LAML
p < 1e−3p = 0.001
p = 0.325p < 1e−3
p = 0.931
p < 1e−3 p < 1e−3
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0.4
0.5
0.6
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0.8
0.9
LGG
p < 1e−3p = 0.026
p = 0.803p = 0.541
p = 0.483
p < 1e−3 p = 0.922
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C−
inde
x
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0.6
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0.9
LIHC
p = 0.349p = 0.505
p = 0.003p = 0.620
p = 0.008
p = 0.004 p < 1e−3
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0.4
0.5
0.6
0.7
0.8
LUAD
p < 1e−3p < 1e−3
p < 1e−3p < 1e−3
p < 1e−3
p < 1e−3 p < 1e−3
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0.4
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0.6
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0.8
LUSC
p < 1e−3p < 1e−3
p < 1e−3p < 1e−3
p < 1e−3
p < 1e−3 p < 1e−3
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0.3
0.4
0.5
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0.7
0.8
OV
p < 1e−3p < 1e−3
p < 1e−3p = 0.001
p < 1e−3
p < 1e−3 p < 1e−3
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0.3
0.4
0.5
0.6
0.7
PAAD
p < 1e−3p < 1e−3
p < 1e−3p < 1e−3
p < 1e−3
p < 1e−3 p = 0.001
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