[PPT] - Feature selection in high dimension for precision medicine PowerPoint Presentation

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Feature selection in high dimension for precision medicine

Chloé-Agathe Azencott

Center for Computational Biology (CBIO) Mines ParisTech – Institut Curie – INSERM U900 PSL Research University, Paris, France

March 21, 2017 – MACARON Workshop

http://cazencott.info chloe-agathe.azencott@mines-paristech.fr @cazencott

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Precision Medicine

◮ Treatment adapted to the (genetic) specificities of the

patient. E.g. Trastuzumab for HER2+ breast cancer.

◮ Data-driven biology/medicine

Identify similarities between patients that exhibit similar susceptibilities / prognoses / responses to treatment.

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Sequencing costs

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Big data!

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Big data!

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GWAS: Genome-Wide Association Studies

Which genomic features explain the phenotype? p = 105 − 107 Single Nucleotide Polymorphisms (SNPs) n = 102 − 104 samples

◮ High-dimensional (large p) ◮ Low sample size (small n)

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Google Flu Trends

D. Lazer, R. Kennedy, G. King and A. Vespignani. The Parable of Google Flu: Traps in Big

Data Analysis. Science 2014

◮ p = 50 million search terms ◮ n = 1152 data points ◮ Predictive search terms include keywords related to high

school basketball.

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Is extracting information from this data doomed from the start? ?

? ?

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GWAS successes

Multiple sclerosis HaemGen consortium Ankylosing spondylitis

P. Visscher, M. Brown, M. McCarthy, J. Yang. Five years of GWAS discovery. AJHG 2012.

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Missing heritability

GWAS fail to explain most of the inheritable variability of complex traits. Many possible reasons: – non-genetic / non-SNP factors – heterogeneity of the phenotype – rare SNPs – weak effect sizes – few samples in high dimension (p ≫ n) – joint effets of multiple SNPs.

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Integrating prior knowledge

Use additional data and prior knowledge to constrain the feature selection procedure.

– Consistant with previously established knowledge – More easily interpretable – Statistical power.

Prior knowledge can be represented as structure:

– Linear structure of DNA – Groups: e.g. pathways – Networks (molecular, 3D structure).

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Regularized relevance

Set V of p variables.

◮ Relevance score R : 2V → R

Quantifies the importance of any subset of variables for the question under consideration. Ex : correlation, HSIC, statistical test of association.

◮ Structured regularizer Ω : 2V → R

Promotes a sparsity pattern that is compatible with the constraint on the feature space. Ex : cardinality Ω : S → |S|.

◮ Regularized relevance

arg max

S⊆V

R(S) − λΩ(S)

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Network-guided multi-locus GWAS

Goal: Find a set of explanatory SNPs compatible with a given network structure.

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Network-guided GWAS

◮ Additive test of association SKAT [Wu et al. 2011]

R(S) =

i∈S

ci ci = (G⊤(y − µ))2

i

◮ Sparse Laplacian regularization

Ω : S →

i∈S
j /

∈S

Wij + α|S|

◮ Regularized maximization of R

arg max

S⊆V

i∈S

ci association − η |S|

sparsity

− λ

i∈S
j /

∈S

Wij

connectivity

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Minimum cut reformulation

The graph-regularized maximization of score Q(∗) is equivalent to a s/t-min-cut for a graph with adjacency matrix A and two additional nodes s and t, where Aij = λWij for 1 ≤ i, j ≤ p and the weights of the edges adjacent to nodes s and t are defined as Asi = ci − η if ci > η

therwise

and Ait = η − ci if ci < η

therwise .

SConES: Selecting Connected Explanatory SNPs.

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Comparison partners

◮ Univariate linear regression

yk = α0 + βGi

k

◮ Lasso

arg min

β∈Rp

1 2 ||y − Gβ||2

2

loss

+ η ||β||1 sparsity

◮ Feature selection with sparsity and connectivity constraints

arg min

β∈Rp

L(y, Gβ)

loss

+ η ||β||1 sparsity + λ Ω(β) connectivity

– ncLasso: network connected Lasso [Li and Li, Bioinformatics 2008] – Overlapping group Lasso [Jacob et al., ICML 2009]

– groupLasso: E.g. SNPs near the same gene grouped together – graphLasso: 1 edge = 1 group.

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Runtime

102 103 104 105 106

#SNPs (log-scale)

10−2 10−1 100 101 102 103 104 105 106

CPU runtime [sec] (log-scale)

graphLasso ncLasso ncLasso (accelerated) SConES linear regression

n = 200 exponential random network (2 % density)

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Experiments: Performance on simulated data

◮ Arabidopsis thaliana genotypes

n=500 samples, p=1 000 SNPs TAIR Protein-Protein Interaction data ∼ 50.106 edges

◮ Higher power and lower FDR than comparison partners

except for groupLasso when groups = causal structure

◮ Fairly robust to missing edges ◮ Fails if network is random. 18

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Arabidopsis thaliana flowering time

17 flowering time phenotypes

[Atwell et al., Nature, 2010]

p ∼ 170 000 SNPs (after MAF filtering) n ∼ 150 samples 165 candidate genes

[Segura et al., Nat Genet 2012]

Correction for population structure: regress out PCs.

✶✵✳✶✷✹✷✴❥❝s✳✵✾✻✾✹✶ 19

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Arabidopsis thaliana flowering time

U n i v a r i a t e L a s s

g

r

u

p L a s s

n

c L a s s

S

C

n

E S 150 300 450 600 # selected SNPs U n i v a r i a t e L a s s

g

r

u

p L a s s

n

c L a s s

S

C

n

E S 5 10 # candidate genes hit

◮ SConES selects about as many SNPs as other network-guided

approaches but detects more candidates.

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Arabidopsis thaliana flowering time

Predictivity of selected SNPs

0W LN22 0.0 0.2 0.4 0.6 0.8 1.0 R2 Lasso groupLasso ncLasso SConES

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SConES: Selecting Connected Explanatory SNPs

◮ selects connected, explanatory SNPs; ◮ incorporates large networks into GWAS; ◮ is efficient, effective and robust.

C.-A. Azencott, D. Grimm, M. Sugiyama, Y. Kawahara and K. Borgwardt (2013) Efficient network-guided multi-locus association mapping with graph cuts, Bioinformatics 29 (13), i171–i179 doi:10.1093/bioinformatics/btt238 ❤tt♣s✿✴✴❣✐t❤✉❜✳❝♦♠✴❝❤❛❣❛③✴s❝♦♥❡s ❤tt♣s✿✴✴❣✐t❤✉❜✳❝♦♠✴❝❤❛❣❛③✴s❢❛♥ ❤tt♣s✿✴✴❣✐t❤✉❜✳❝♦♠✴❞♦♠✐♥✐❦❣r✐♠♠✴❡❛s②●❲❆❙❈♦r❡

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Multi-trait GWAS

Increase sample size by jointly performing GWAS for multiple related phenotypes

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Toxicogenetics / Pharmacogenomics

Tasks (phenotypes) = chemical compounds

F. Eduati, L. Mangravite, et al. (2015) Prediction of human population responses to toxic

compounds by a collaborative competition. Nature Biotechnology, 33 (9), 933–940 doi: 10.1038/nbt.3299

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Multi-SConES

T related phenotypes.

◮ Goal: obtain similar sets of features on related tasks.

arg max

S1,...,ST ⊆V T

t=1

   

i∈S

ci − η |S| − λ

i∈S
j /

∈S

Wij − µ |St−1 ∆ St|

task sharing

   

S ∆ S′ = (S ∪ S′) \ (S ∩ S′) (symmetric difference)

◮ Can be reduced to single-task by building a meta-network. 25

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Multi-SConES: Multiple related tasks

Simulations: retrieving causal features

0.2 0.4 0.6 0.8 1.0 Model 1 Model 2 1.0 Model 3 0.2 0.4 0.6 0.8 1.0 LA CR EN GL GR AG SC Single task CR LA GR SC Two tasks CR LA GR SC Three tasks CR LA GR SC Four tasks LA CR EN GL GR AG SC Single task CR LA GR SC Two tasks CR LA GR SC Three tasks CR LA GR SC Four tasks MCC MCC 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 LA CR EN GL GR AG SC Single task CR LA GR SC Two tasks CR LA GR SC Three tasks CR LA GR SC Four tasks LA CR EN GL GR AG SC Single task CR LA GR SC Two tasks CR LA GR SC Three tasks CR LA GR SC Four tasks Single task Two tasks Three tasks Four tasks MCC MCC Model 4

M. Sugiyama, C.-A. Azencott, D. Grimm, Y. Kawahara and K. Borgwardt (2014) Multi-task

feature selection on multiple networks via maximum flows, SIAM ICDM, 199–207 doi:10.1137/1.9781611973440.23 ❤tt♣s✿✴✴❣✐t❤✉❜✳❝♦♠✴♠❛❤✐t♦✲s✉❣✐②❛♠❛✴▼✉❧t✐✲❙❈♦♥❊❙ ❤tt♣s✿✴✴❣✐t❤✉❜✳❝♦♠✴❝❤❛❣❛③✴s❢❛♥

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Leveraging similarity between tasks

Use prior knowledge about the relationship between the tasks: Ω ∈ RT×T

arg max

S1,...,ST ⊆V T

t=1

       

i∈S

ci − η |S| − λ

i∈S
j /

∈S

Wij − µ

T

u=1
i∈St∩Su

Ω−1

tu

task sharing

       

Can also be mapped to a meta-network. Code: ❤tt♣✿✴✴❣✐t❤✉❜✳❝♦♠✴❝❤❛❣❛③✴s❢❛♥

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Multiplicative Multitask Lasso with Task Descriptors

◮ Multitask Lasso [Obozinski et al. 2006] arg min

β∈RT ×p

L

yt

m, p

i=1

βigt

mi

loss

+ λ

p

i=1

||βi||2

task sharing

◮ Multilevel Multitask Lasso [Lozano and Swirszczw, 2012] arg min

θ∈Rp

+,γ∈RT ×p

L

yt

m, p

i=1

θiγt

igt mi

loss

+ λ1 ||θ||1

sparsity

+ λ2

p

i=1

T

t=1

|γt

i|

task sharing

◮ Multiplicative Multitask Lasso with Task Descriptors arg min

θ∈Rp

+,α∈Rp×L

L

yt

m, p

i=1

θi L

l=1

αildt

l

gt

mi

loss

+ λ1 ||θ||1

sparsity

+ λ2

p

i=1

L

l=1

|αil|

task sharing

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Multiplicative Multitask Lasso with Task Descriptors

arg min

θ∈Rp

+,α∈Rp×L

L

yt

m, p

i=1

θi L

l=1

αildt

l

gt

mi

loss

+ λ1 ||θ||1

sparsity

+ λ2

p

i=1

L

l=1

|αil|

task sharing

◮ On simulations:

◮ Sparser solution ◮ Better recovery of true features (higher PPV) ◮ Improved stability ◮ Better predictivity (RMSE).

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Multiplicative Multitask Lasso with Task Descriptors

◮ Making predictions for tasks for which you have no data.

V. Bellón, V. Stoven, and C.-A. Azencott (2016) Multitask feature selection with task

descriptors, PSB. ❤tt♣s✿✴✴❣✐t❤✉❜✳❝♦♠✴✈♠♦❧✐♥❛✴▼✉❧t✐t❛s❦❉❡s❝r✐♣t♦r

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Limitations of current approaches

◮ Robustness/stability

Recovering the same SNPs when the data changes slightly.

◮ Complex epistasis patterns

– Limited to additive or quadrative effects – Some work on e.g. random forests + importance score.

◮ Statistical significance

– Computing p-values – Correcting for multiple hypotheses.

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❤tt♣s✿✴✴❣✐t❤✉❜✳❝♦♠✴❝❤❛❣❛③✴

source: ❤tt♣✿✴✴✇✇✇✳❢❧✐❝❦r✳❝♦♠✴♣❤♦t♦s✴✇✇✇♦r❦s✴

CBIO: Víctor Bellón, Yunlong Jiao, Véronique Stoven, Athénaïs Vaginay, Nelle Varoquaux, Jean-Philippe Vert, Thomas Walter. MLCB Tübingen: Karsten Borgwardt, Aasa Feragen, Dominik Grimm, Theofanis Karaletsos, Niklas Kasenburg, Christoph Lippert, Barbara Rakitsch, Damian Roqueiro, Nino Shervashidze, Oliver Stegle, Mahito Sugiyama. MPI for Intelligent Systems: Lawrence Cayton, Bernhard Schölkopf. MPI for Developmental Biology: Detlef Weigel. MPI for Psychiatry: André Altmann, Tony Kam-Thong, Bertram Müller-Myhsok, Benno Pütz. Osaka University: Yoshinobu Kawahara.

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