Machine learning applications to genomics · 2017. 6. 26. · References...

Machine learning applicationsto genomicsChloé-Agathe Azencott

Center for Computational Biology (CBIO)Mines ParisTech – Institut Curie – INSERM U900

PSL Research University, Paris, France

BioComp Summer School 2017http://cazencott.info [email protected] @cazencott

http://[email protected]://twitter.com/cazencott

References

Precision MedicineI Adapt treatment to the (genetic) specificities of the patient.E.g. Trastuzumab for HER2+ breast cancer.

I Data-driven biology/medicineIdentify similarities between patients that exhibit similar phenotypes.

I Biomarker discovery = Feature SelectionI Prediction

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I Biomarker discovery = Feature Selection

I Prediction

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I Biomarker discovery = Feature SelectionI Prediction

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Sequencing costs

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Big data!

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Big data!

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Big data vs. fat data

p features

Big data

n sa

mpl

es

p features

n sa

mpl

e s

Fat data

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Challenges of high-dimensional data

I Computational challenges for some algorithmsLinear regression: invertingX>X takesO(p3) computations.

I The curse of dimensionality makes it hard to learnI Overfitting is more likelyI Ill-posed problems.

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The curse of dimensionality

I Methods and intuitions that work in low dimension might notapply to higher dimensions.

I Hyperspace is very big and everything is far apartFraction of the points within a cube that fall outside the inscribed circle:

– In two dimensions: 1− πr24r2

= 1− π4

– In three dimensions: 1− 4/3πr38r3

= 1− π6

– In higher dimension: tends towards 1.

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Large p, small n dataSimulation: n=100, p=1000, 10 causal features, y = Xw + e.

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Google Flu TrendsD. Lazer, R. Kennedy, G. King and A. Vespignani. The Parable of Google Flu: Traps in BigData Analysis. Science 2014 [Lazer et al. 2014]

I p = 50 million search termsI n = 1152 data points

I Predictive search terms include terms related to high-school basketball.10

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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

[Pennisi 2007]11

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Qualitative GWASBinary phenotype, i.e. case/controls encoded as 1/0.

I Contingency tableAA Aa aa

Cases

Ctrls

0 1

Cases a b

Ctrls c d

Statistical tests: χ2, Cochran-Armitage trend test, etc.I Logistic regression

logit(p(y|X)) = β0 + β1XI Odds-ratio

P(0|case)P(0|ctrl)︸︷︷︸

odds of 0 in cases

/P(1|case)P(1|ctrl)︸︷︷︸

odds of 1 in cases

=ad

bc

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Quantitative GWAS

I Linear regression

y = β0 + β1X

I p-value: Is β̂1 significantly different from 0?

Wald test: compare β̂21

Var(β̂1)to a χ2 distribution.

I Effect size: β1.

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Multiple Hypothesis Testing

I Probability of having at least one false positive:– For one test: α– For p tests: 1− (1− α)p

I Controlling Family-Wise Error Rate (FWER)FWER = P (|FP| ≥ 1)FP = number of false positives (Type I errors)

I Bonferroni correction: α→ αp 14

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GWAS discoveriesI The GWAS Catalog https://www.ebi.ac.uk/gwas/

I Clinical benefits: Ankylosing spondylitis– Role of interleukine 17 pathway– Consentyx (secukinumab), approved January 15, 2016.

I SNPs associated with drug resistancein e.g. Myobacterium tuberculosis, Staphylococcus aureus,Streptococcus pneumoniae or HIV.

Ref: [Visscher et al. 2012; Manolio 2013; Power, Parkhill, and Oliveira 2017]15

https://www.ebi.ac.uk/gwas/

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Missing heritability

GWAS fail to explain most of the inheritable variability ofcomplex 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.

Ref: [Manolio et al. 2009]16

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What solution doesmachine learning

provide? ???17

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Reducing p

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Dimensionality reduction

I Feature selection: Keep relevant features only– Filter approaches: Apply a statistical test to assign a score to eachfeature.

– Wrapper approaches: Use a greedy search to find the “best” set offeatures for a given predictive model.

– Embedded approaches: Fit a sparse model, i.e. that is encouraged tonot use all the features.

I Feature extraction: Project the data on a new space– Creates new features, which makes interpretability harder.– Matrice factorization techniques: PCA, factorial analysis, NMF, kPCA.– Manifold learning: Multidimensional scaling, t-SNE.– Autoencoders.

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Regularization

Control the number of parametersI limit model complexityI avoid overfitting

I Least-squares regression

arg minw∈Rp

||y −Xw||22︸︷︷︸loss

I Lasso [Tibshirani 1994]

arg minw∈Rp

||y −Xw||22︸︷︷︸loss

+λ ||w||1︸︷︷︸sparsity

Image credits: Harold M. Walker via Wikimedia Commons 20

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Large p, small n dataSimulation: n=100, p=1000, 10 causal features, y = Xw + e.

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Integrating prior knowledge

Use prior knowledge as a constraint on the selected features

Prior knowledge can be represented as structure:– Linear structure of DNA– Groups: e.g. pathways– Networks (molecular, 3D structure).

Elephant image by Danny Chapman @ Flickr.22

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Structured sparsityI Lasso: Selecting variables in high dimension.

arg minw∈Rp

||y −Xw||22︸︷︷︸loss

+λ ||w||1︸︷︷︸sparsity

I Lasso+: Structured regularizer.

arg minw∈Rp

||y −Xw||22︸︷︷︸loss

+λ Ω(w)︸︷︷︸structure

Image by Harold M. Walker via Wikimedia Commons23

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Structured regularizersI Group Lasso [Yuan and Lin 2006]

Ωgroup(w) =∑g∈G

||wg||

I Overlapping Group Lasso [Jacob, Obozinski, and Vert 2009]Ωoverlap(w) =

∑v∈VG ,

∑g∈G vg=w

||vg||

w =∑

g∈G vg and supp(vg) ⊂ g.Graph Lasso: groups = edges.

I ncLasso / Grace [Li and Li 2008; Li and Li 2010]ΩncLasso(w) = w

>Lw

L = D −W : Laplacian of the graph of adjacency matrixW anddegree matrixD.

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Gene selection with the Graph lasso

Lasso Graph Lasso

Ref: [Jacob, Obozinski, and Vert 2009]25

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Regularized relevanceSet V of p variables.

I Relevance scoreR : 2V → RQuantifies the importance of any subset of variables for the questionunder consideration.Ex : correlation, HSIC, statistical test of association.

I Structured regularizerΩ : 2V → RPromotes a sparsity pattern that is compatible with the constraint on thefeature space.Ex : cardinality Ω : S 7→ |S|.

I Regularized relevancearg maxS⊆V

R(S)− λΩ(S)

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Network-guided multi-locus GWAS

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

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Network-guided GWASI Additive test of association SKAT [Wu, Lee, et al. 2011]

R(S) =∑i∈S

ci ci = (X>(y − µ))2i

I Sparse Laplacian regularization

Ω : S 7→∑i∈S

∑j /∈S

Wij + α|S|

I Regularized maximization ofR

arg maxS⊆V

∑i∈S

ci︸︷︷︸association

− η |S|︸︷︷︸sparsity

−λ∑i∈S

∑j /∈S

Wij︸︷︷︸connectivity

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Minimum cut reformulationThe graph-regularized maximization of scoreQ(∗) is equivalent to a s/t-min-cut for agraph with adjacency matrixA and two additional nodes s and t, whereAij = λWijfor 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

0 otherwise and Ait ={η − ci if ci < η

0 otherwise .

SConES: Selecting Connected Explanatory SNPs.29

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Comparison partnersI Univariate linear regression yk = α0 + βGikI Lasso

arg minβ∈Rp

1

2||y −Gβ||22︸︷︷︸loss

+ η ||β||1︸︷︷︸sparsity

I Feature selection with sparsity and connectivity constraintsarg minβ∈Rp

L(y,Gβ)︸︷︷︸loss

+ η ||β||1︸︷︷︸sparsity

+ λΩ(β)︸︷︷︸connectivity

– ncLasso: network connected Lasso [Li and Li 2008]– Overlapping group Lasso [Jacob, Obozinski, and Vert 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)10−210−1

100

101

102

103

104

105

106

CP

Uru

ntim

e[s

ec](

log-

scal

e)

graphLassoncLassoncLasso (accelerated)SConESlinear regression

n = 200 exponential random network (2 % density)

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Data simulation

Arabidopsis thaliana genotypes[Atwell et al. 2010; Segura et al. 2012]

n = 500 samples, p = 1, 000 SNPs

TAIR Protein-Protein Interaction data→ ∼ 50× 106 edges20 causal SNPs: y = ω>x+ �I Causal SNPs adjacent in the genomic sequenceI Causal SNPs near the same geneI Causal SNPs near any of 2–5 interacting genes

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Performance on simulated data

0.0 0.2 0.4 0.6 0.8 1.0FDR

Adjacent

0.0

0.2

0.4

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0.8

1.0

Pow

er

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322818

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0.0 0.2 0.4 0.6 0.8 1.0FDR

Near the same gene

0.0

0.2

0.4

0.6

0.8

1.0

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3014 13

13

0.0 0.2 0.4 0.6 0.8 1.0FDR

Near one of 5 interacting genes

0.0

0.2

0.4

0.6

0.8

1.0

3628

223327

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Univariate Lasso ncLasso groupLasso graphLasso SConES

Power = precision = SNPs selected and causalcausal SNPs

False Discovery Rate (FDR) = 1 - recall = SNPs selected and non-causalselected SNPs

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Experiments: Performance on simulated dataI Arabidopsis thaliana genotypes

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

I Higher power and lower FDR than comparison partners

except for groupLasso when groups = causal structure

I Fairly robust to missing edgesI Fails if network is random.

Image source: Jean Weber / INRA via Flickr.34

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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.

Image credits: Dymek & Smith 10.1242/jcs.096941

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10.1242/jcs.096941

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Univa

riate

Lass

o

grou

pLas

so

ncLa

sso

SCon

ES0

150

300

450

600

#se

lect

edSN

Ps

Univa

riate

Lass

o

grou

pLas

so

ncLa

sso

SCon

ES0

5

10

#ca

ndid

ate

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shi

t

I SConES selects about as many SNPs as other network-guidedapproaches but detects more candidates.

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Predictivity of selected SNPs

0W LN220.0

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2

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ncLassoSConES

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SConES: Selecting Connected Explanatory SNPsI selects connected, explanatory SNPs;

I incorporates large networks into GWAS;

I is efficient, effective and robust.

C.-A. Azencott, D. Grimm, M. Sugiyama, Y. Kawahara and K. Borgwardt (2013) Efficientnetwork-guided multi-locus association mapping with graph cuts, Bioinformatics 29(13), i171–i179 doi:10.1093/bioinformatics/btt238 [Azencott et al. 2013]https://github.com/chagaz/scones

https://github.com/chagaz/sfan

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https://github.com/chagaz/sconeshttps://github.com/chagaz/sfan

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Increasing n

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Multi-phenotype GWAS

Increase sample size by jointly performing GWAS for multiplerelated phenotypes

Multi-task feature selectionTransfer learning

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Toxicogenetics / Pharmacogenomics

Tasks (phenotypes) = chemical compounds

F. Eduati, L. Mangravite, et al. (2015) Prediction of human population responses to toxiccompounds by a collaborative competition. Nature Biotechnology, 33 (9), 933–940 doi:10.1038/nbt.3299

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Multi-SConEST related phenotypes.

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

arg maxS1,...,ST⊆V

T∑t=1

∑i∈S

ci − η |S| − λ∑i∈S

∑j /∈S

Wij −∑u>t

µ |Su ∆ St|︸︷︷︸task sharing

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

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

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Multi-SConES: Multiple related tasksSimulations: retrieving causal features

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Model 4

M. Sugiyama, C.-A. Azencott, D. Grimm, Y. Kawahara and K. Borgwardt (2014) Multi-taskfeature selection on multiple networks via maximum flows, SIAM ICDM, 199–207doi:10.1137/1.9781611973440.23https://github.com/mahito-sugiyama/Multi-SConES

https://github.com/chagaz/sfan

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https://github.com/mahito-sugiyama/Multi-SConEShttps://github.com/chagaz/sfan

References

Using task similarity

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

arg maxS1,...,ST⊆V

T∑t=1

∑i∈S

ci − η |S| − λ∑i∈S

∑j /∈S

Wij − µT∑u=1

∑i∈St∩Su

Ω−1tu︸︷︷︸task sharing

Can also be mapped to a meta-network.

Code: http://github.com/chagaz/sfan

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http://github.com/chagaz/sfan

References

Multiplicative Multitask Lasso with Task DescriptorsI Multitask Lasso [Obozinski, Taskar, and Jordan 2006]

argminβ∈RT×p

L(ytm,

p∑i=1

βigtmi

)︸︷︷︸

loss

+ λ

p∑i=1

||βi||2︸︷︷︸task sharing

I Multilevel Multitask Lasso [Swirszcz and Lozano 2012]

argminθ∈Rp+,γ∈R

T×pL(ytm,

p∑i=1

θiγtigtmi

)︸︷︷︸

loss

+ λ1 ||θ||1︸︷︷︸sparsity

+ λ2

p∑i=1

T∑t=1

|γti |︸︷︷︸task sharing

I Multiplicative Multitask Lasso with Task Descriptors [Bellon, Stoven, andAzencott 2016]

argminθ∈Rp+,α∈R

p×LL(ytm,

p∑i=1

θi

(L∑l=1

αildtl

)gtmi

)︸︷︷︸

loss


+ λ2

p∑i=1

L∑l=1

|αil|︸︷︷︸task sharing

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Multiplicative Multitask Lasso with Task Descriptors

arg minθ∈Rp+,α∈Rp×L

L(ytm,

p∑i=1

θi

(L∑l=1

αildtl

)gtmi

)︸︷︷︸

loss


+ λ2

p∑i=1

L∑l=1

|αil|︸︷︷︸task sharing

I 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

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

V. Bellón, V. Stoven, and C.-A. Azencott (2016) Multitask feature selection with taskdescriptors, PSB.https://github.com/vmolina/MultitaskDescriptor

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https://github.com/vmolina/MultitaskDescriptor

References

Limitations of current approaches

I Robustness/stability– Doo we recover the same SNPs when the data changes slightly?– Mixed `1/`2 norms: Elastic Net [Zou and Hastie 2005].

I Complex interaction patterns– Limited to additive or quadrative effects (limited power)[Niel et al. 2015]

– A few papers on “higher-order epistasis”.

I Statistical significance– How do we compute p-values?– How do we correct for multiple hypotheses?

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References

Further challenges

PrivacyI More data→ Data sharing→ ethical concernsI How to learn from privacy-protected patient data?S. Simmons and B. Berger (2016) Realizing privacy preserving genome-wideassociation studies, Bioinformatics 32 (9), 1293–1300

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Further challenges

HeterogeneityI Multiple relevant data sources and types

I Multiple (unknown) populations of samples.

Tumor heterogeneity Heterogeneous data sources

L. Gay et al. (2016), F1000Research

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Further challenges

Risk predictionI State of the art: Polygenic Risk Scores

Linear combination of SNPs with high p-values (summary statistics)Weighted by log odd ratios / univariate linear regression coefficients.

I More complex models slow to be adopted – reliability?

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Further challenges

Bioimage informaticsHigh-throughput molecular and cellular images

BioImage Informatics http://bioimageinformatics.org/

Detecting cells undergoing apoptosis52

http://bioimageinformatics.org/

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Further challenges

Electronic health recordsI Clinical notes: incomplete, imbalanced, time series

I Combine text + images + genetics

I Assisting evidence-based medicine

R. Miotto et al. (2016) Deep Patient: An Unsupervised Representation to Predict theFuture of Patients from the Electronic Health Records Scientific Reports 6.

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References

https://github.com/chagaz/

source: http://www.flickr.com/photos/wwworks/

CBIO: Víctor Bellón, Yunlong Jiao, Véronique Stoven, Athénaïs Vaginay,Nelle Varoquaux, Jean-Philippe Vert, Thomas Walter.MLCB Tübingen: Karsten Borgwardt, Aasa Feragen, Dominik Grimm, TheofanisKaraletsos, 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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https://github.com/chagaz/http://www.flickr.com/photos/wwworks/

References

References I

Atwell, S. et al. (2010). “Genome-wide association study of 107 phenotypes in Arabidopsisthaliana inbred lines”. In: Nature 465.7298, pp. 627–631. ISSN: 0028-0836. DOI:10.1038/nature08800.Azencott, Chloé-Agathe et al. (2013). “Efficient network-guided multi-locus associationmapping with graph cuts”. In: Bioinformatics 29.13, pp. i171–i179.Bellon, Victor, VÃľronique Stoven, and ChloÃľ-Agathe Azencott (2016). “Multitask featureselection with task descriptors”. In: Pacific Symposium on Biocomputing. Vol. 21,pp. 261–272.Jacob, L., G. Obozinski, and J.-P. Vert (2009). “Group lasso with overlap and graph lasso”.In: ICML, pp. 433–440.Lazer, David et al. (2014). “The parable of Google Flu: traps in big data analysis”. In:Science 343.6176, pp. 1203–1205.Li, C. and H. Li (2008). “Network-constrained regularization and variable selection foranalysis of genomic data”. In: Bioinformatics 24.9, pp. 1175–1182.

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http://dx.doi.org/10.1038/nature08800

References

References IILi, Caiyan and Hongzhe Li (2010). “Variable selection and regression analysis forgraph-structured covariates with an application to genomics”. In: The annals of appliedstatistics 4.3, pp. 1498–1516.Manolio, Teri A (2013). “Bringing genome-wide association findings into clinical use”. In:Nature Reviews Genetics 14.8, pp. 549–558.Manolio, Teri A. et al. (2009). “Finding the missing heritability of complex diseases”. In:Nature 461.7265, pp. 747–753.Niel, Clément et al. (2015). “A survey about methods dedicated to epistasis detection”. In:Bioinformatics and Computational Biology, p. 285.Obozinski, Guillaume, Ben Taskar, and Michael I. Jordan (2006). Multi-task featureselection. Tech. rep. UC Berkeley.Pennisi, Elizabeth (2007). “Human Genetic Variation”. In: Science 318.5858,pp. 1842–1843.Power, Robert A., Julian Parkhill, and Tulio de Oliveira (2017). “Microbial genome-wideassociation studies: lessons from human GWAS”. In: Nature Reviews Genetics 18.1,pp. 41–50.

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References

References IIISegura, V. et al. (2012). “An efficient multi-locus mixed-model approach for genome-wideassociation studies in structured populations”. In: Nat Genet 44.7, pp. 825–830.Swirszcz, Grzegorz and Aurelie C. Lozano (2012). “Multi-level Lasso for Sparse Multi-taskRegression”. In: Proceedings of the 29th International Conference on Machine Learning(ICML-12), pp. 361–368.Tibshirani, Robert (1994). “Regression shrinkage and selection via the lasso”. In: J. R. Stat.Soc. 58, pp. 267–288.Visscher, Peter M. et al. (2012). “Five years of GWAS discovery”. In: Am. J. Hum. Genet.90.1, pp. 7–24.Wu, M. C., S. Lee, et al. (2011). “Rare-Variant Association Testing for Sequencing Data withthe Sequence Kernel Association Test”. In: AJHG 89.1, pp. 82–93.Yuan, Ming and Yi Lin (2006). “Model selection and estimation in regression with groupedvariables”. In: Journal of the Royal Statistical Society: Series B (Statistical Methodology)68.1, pp. 49–67.Zou, Hui and Trevor Hastie (2005). “Regularization and variable selection via the elasticnet”. In: Journal of the Royal Statistical Society: Series B (Statistical Methodology) 67.2,pp. 301–320.

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