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Machine LearningMachine Learninggg
Application I: Application I: Computational GenomicsComputational GenomicsComputational GenomicsComputational Genomics
Eric XingEric Xing
Lecture 18, August 16, 2010
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ectu e 8, ugust 6, 0 0
Biological Data AnalysisBiological Data Analysis Dynamic, noisy, heterogeneous, high-dimensional datay y g g
“High-resolution” inference Parsimonious
S l bilit Scalability Stability Sample complexity Sample complexity Confidence bound
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Genetic Basis of DiseasesGenetic Basis of Diseases
HealthyACTCGTACGTAGACCTAGCATTTACGCAATAATGCGA
ACTCGAACCTAGACCTAGCATTTACGCAATAATGCGAACTCGAACCTAGACCTAGCATTTACGCAATAATGCGA
TCTCGTACGTAGACGTAGCATTTACGCAATTATCCGA
ACTCGAACCTAGACCTAGCATTTACGCAATTATCCGA
ACTCGTACGTAGACGTAGCATAACGCAATAATGCGA
SickTCTCGTACCTAGACGTAGCATAACGCAATAATCCGA
ACTCGAACCTAGACCTAGCATAACGCAATTATCCGA
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Single nucleotide polymorphism (SNP)
Causal (or "associated") SNP
Genetic Association MappingData
Genetic Association Mapping
A . . . . T . . G . . . . . C . . . . . . T . . . . . A . . G .
Genotype Phenotype Standard Approach
A . . . . A . . C . . . . . C . . . . . . T . . . . . A . . G .
T . . . . T . . G . . . . . G . . . . . . T . . . . . T . . C .
causal SNPcausal SNP
A . . . . A . . C . . . . . C . . . . . . T . . . . . T . . C .
A . . . . T . . G . . . . . G . . . . . . A . . . . . A . . G .
T T C G A A C h th tT . . . . T . . C . . . . . G . . . . . . A . . . . . A . . C .
A . . . . A . . C . . . . . C . . . . . . A . . . . . T . . C .
• Cancer: Dunning et al. 2009.• Diabetes: Dupuis et al 2010
a univariate a univariate phenotypephenotype::e.g., disease/controle.g., disease/control
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Diabetes: Dupuis et al. 2010.• Atopic dermatitis: Esparza-Gordillo et al. 2009.• Arthritis: Suzuki et al. 2008
Genetic Basis of Complex DiseasesGenetic Basis of Complex Diseases
HealthyACTCGTACGTAGACCTAGCATTACGCAATAATGCGA
ACTCGAACCTAGACCTAGCATTACGCAATAATGCGAACTCGAACCTAGACCTAGCATTACGCAATAATGCGA
TCTCGTACGTAGACGTAGCATTACGCAATTATCCGA
ACTCGAACCTAGACCTAGCATTACGCAATTATCCGA
ACTCGTACGTAGACGTAGCATAACGCAATAATGCGA
CancerTCTCGTACCTAGACGTAGCATAACGCAATAATCCGA
ACTCGAACCTAGACCTAGCATAACGCAATTATCCGA
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Causal SNPs
Genetic Basis of Complex DiseasesGenetic Basis of Complex Diseases
HealthyHealthyACTCGTACGTAGACCTAGCATTACGCAATAATGCGA
ACTCGAACCTAGACCTAGCATTACGCAATAATGCGA
TCTCGTACGTAGACGTAGCATTACGCAATTATCCGA Biological TCTCGTACGTAGACGTAGCATTACGCAATTATCCGA
ACTCGAACCTAGACCTAGCATTACGCAATTATCCGA
ACTCGTACGTAGACGTAGCATAACGCAATAATGCGA
gmechanism
CancerTCTCGTACCTAGACGTAGCATAACGCAATAATCCGA
ACTCGAACCTAGACCTAGCATAACGCAATTATCCGA
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Causal SNPs
Genetic Basis of Complex DiseasesIntermediate Phenotype
Genetic Basis of Complex DiseasesAssociation to intermediate phenotypes
Healthy
Gene expressionphenotypes
HealthyACTCGTACGTAGACCTAGCATTACGCAATAATGCGA
ACTCGAACCTAGACCTAGCATTACGCAATAATGCGA
TCTCGTACGTAGACGTAGCATTACGCAATTATCCGATCTCGTACGTAGACGTAGCATTACGCAATTATCCGA
ACTCGAACCTAGACCTAGCATTACGCAATTATCCGA
ACTCGTACGTAGACGTAGCATAACGCAATAATGCGA
CancerTCTCGTACCTAGACGTAGCATAACGCAATAATCCGA
ACTCGAACCTAGACCTAGCATAACGCAATTATCCGA Clinical records
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Causal SNPs
Structured AssociationStructured Association
Association with Phenome
ACGTTTTACTGTACAATTACGTTTTACTGTACAATT
Traditional Approachcausal SNPcausal SNP
ACGTTTTACTGTACAATTACGTTTTACTGTACAATT
a univariate phenotype:a univariate phenotype:gene expression levelgene expression level
Multivariate complex syndrome (e.g., asthma)Multivariate complex syndrome (e.g., asthma)age at onset, history of eczemaage at onset, history of eczema
genomegenome‐‐wide expression profilewide expression profile
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Structured Association : a New Paradigma New Paradigm
Considerone phenotype at a
Considermultiple correlated vs.
Standard Approach New Approach
one phenotype at a time phenotypes (phenome)
jointly
vs.
Phenotypes Phenome
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Genetic Association for Asthma Clinical Traits
TCGACGTTTTACTGTACAATT
Asthma Clinical Traits
S b t k f
Statistical challengeHow to find
associations to a multivariate entity in a graph?Subnetworks for
lung physiology Subnetwork for quality of life
in a graph?
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Gene Expression TCGACGTTTTACTGTACAATT
Trait AnalysisGenes
Samples
St ti ti l h llStatistical challengeHow to find
associations to a multivariate entity in a tree?in a tree?
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Sparse AssociationsSparse Associations
Pleotropic effectsPleotropic effects
ffffEpistatic effectsEpistatic effects
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Sparse LearningSparse Learning
Linear Model: Linear Model:
Lasso (Sparse Linear Regression) [R.Tibshirani 96]
Wh l ti ? Why sparse solution? penalizing
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constraining
Multi Task ExtensionMulti-Task Extension Multi-Task Linear Model:
Input:Output:
Coefficients for k th task:
p
Coefficients for k-th task:Coefficient Matrix:
Coefficients for a variable (2nd)
Eric Xing © Eric Xing @ CMU, 2006-2010 14Coefficients for a task (2nd)
Outline
Background: Sparse multivariate regression for disease
Outline
g p gassociation studies
Structured association – a new paradigm Association to a graph-structured phenome
Graph-guided fused lasso (Kim & Xing PLoS Genetics 2009) Graph guided fused lasso (Kim & Xing, PLoS Genetics, 2009)
Association to a tree-structured phenome Tree-guided group lasso (Kim & Xing, ICML 2010) Tree guided group lasso (Kim & Xing, ICML 2010)
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Multivariate Regression for Single-Trait Association Analysis
GenotypeTrait
Trait Association AnalysisAssociation Strength
A G
T A
2.1 x= ?C
C A
T G
A ?
T G
A A
C
Xy x= β
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Multivariate Regression for Single-Trait Association Analysis
GenotypeTrait
Trait Association AnalysisAssociation Strength
A G
T A
2.1 x=
C C
A T
G A
T
G A
A C
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Many non-zero associations: Which SNPs are truly significant?
Lasso for Reducing False Positives (Tib hi i 1996)
GenotypeTrait
Positives (Tibshirani, 1996)
Association Strength
x=2.1 A G
T A
C
C A
T G
A
T G
A A
C Lasso Penalty for sparsity
+
J
j 1 |βj |
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Many zero associations (sparse results), but what if there are multiple related traits?
Multivariate Regression for Multiple-Trait Association Analysis
Genotype
Trait Association AnalysisAssociation Strength
(3.4, 1.5, 2.1, 0.9, 1.8) A G
T A
x=
Association strength between SNP j and Trait i: βj,i
LD
C C
A T
G A
Allergy Lung physiology
T G
A A
C Syntheticlethal
+ ji,
|βj,i|
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How to combine information across multiple traits to increase the power?
Multivariate Regression for Multiple-Trait Association Analysis
GenotypeTrait
Trait Association AnalysisAssociation Strength
(3.4, 1.5, 2.1, 0.9, 1.8) A G
T A
x=
Association strength between SNP j and Trait i: βj,i
C C
A T
G A
Allergy Lung physiology
T G
A A
C
+ ji,
|βj,i|
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+We introducegraph-guided fusion penalty
Multiple-trait Association:Graph-Constrained Fused LassoGraph-Constrained Fused Lasso
Step 1: Thresholded correlation graph of phenotypes
ACGTTTTACTGTACAATT
Step 2: Graph‐constrained fused lasso
ACGTTTTACTGTACAATT
F iFusion
Lasso Graph-constrained
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Penalty fusion penalty
Fusion PenaltyFusion PenaltySNP j
ACGTTTTACTGTACAATT
Association strength β
Association strength between SNP j and Trait m β
Trait m
between SNP j and Trait k: βjkSNP j and Trait m: βjm
Trait k
Fusion Penalty: | βjk - βjm |
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For two correlated traits (connected in the network), the association strengths may have similar values.
Graph-Constrained Fused Lasso
Overall effect
Graph-Constrained Fused Lasso
ACGTTTTACTGTACAATT
Fusion effect propagates to the entire network
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Association between SNPs and subnetworks of traits
Multiple-trait Association: Graph-Weighted Fused LassoGraph-Weighted Fused Lasso
Overall effect
ACGTTTTACTGTACAATT
Overall effect
Subnetwork structure is embedded as a densely connected nodes with large edge weights
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Edges with small weights are effectively ignored
Estimating ParametersEstimating Parameters
Quadratic programming formulationQ p g g Graph-constrained fused lasso
Graph-weighted fused lasso
Many publicly available software packages for solving convex optimization problems can be used
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convex optimization problems can be used
Improving ScalabilityImproving ScalabilityOriginal problem
Equivalentlyq y
Using a variational formulationUsing a variational formulation
Iterative optimization• Update βk• Update djk’s, djml’s
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Previous Works vs Our ApproachPrevious Works vs. Our Approach
Previous approach Our approachPrevious approach Our approachPCA-based approach (Weller et al., 1996, Mangin et al., 1998)
Implicit representation of trait correlations
Hard to interpret the derived traits
Explicit representation of trait correlations
A i i hi h iExtension of module network for eQTL study (Lee et al., 2009)
Average traits within each trait cluster
Loss of information
Original data for traits are used
Network-based approach Separate association Joint association analysis (Chen et al., 2008, Emilsson et al., 2008)
analysis for each trait (no information sharing)
Single-trait association are
of multiple traits
combined in light of trait network modules
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Simulation
• 50 SNPs t k f
Trait Correlation Matrix
Thresholded Trait Correlation Network
Results
taken from HapMap chromosome
PhenotypesS
NP
s
7, CEU population
• 10 traits• 10 traits
Highi ti
No
association
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True Regression Coefficients
Single SNP-Single Trait Test
Significant at α = 0.01
Lasso Graph-guided Fused Lasso
association
Simulation ResultsSimulation Results
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Asthma Association StudyAsthma Association Study
543 severe asthma patients from the Severe Asthma543 severe asthma patients from the Severe Asthma Research Program (SARP)
Genotypes : 34 SNPs in IL4R gene 40kb region of chromosome 16
I t i i t ith PHASE (Li d St h 2003) Impute missing genotypes with PHASE (Li and Stephens, 2003)
Traits : 53 asthma-related clinical traits Quality of Life: emotion, environment, activity, symptom Family history: number of siblings with allergy, does the father has asthma? Asthma symptoms: chest tightness, wheeziness
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y p g
Asthma and IL4R GeneAsthma and IL4R Gene
In normal individuals: allergen ignored by the immune system
Allergen (ragweed, grass, etc.)
T cell
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Asthma and IL4R GeneAsthma and IL4R Gene
In asthma patientsIn asthma patientsAllergen (ragweed, grass, etc.)
Th2 cell B cellT cell
ImmunoglobulinE (IgE) antibody
Inflammation!
Interleukin 4 Receptor
• Airway in lung narrows
Interleukin-4 Receptorregulates IgE antibody production
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• Difficult to breathe• Asthma symptoms
IL4R GeneIL4R Gene
Chr16: 27,325,251-27,376,098exonsintrons
IL4RSNPs in intronSNPs in intron
SNPs in exon
SNPs in promotor region
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Asthma Trait Network
Subnetwork for Asthma symptoms
Phenotype Correlation Network
Subnetwork for quality of life
Subnetwork for lung physiology
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Results from Single-SNP/Trait TestgPhenotypes
pes
Lung physiology‐related traits I• Baseline FEV1 predicted value: MPVLung • Pre FEF 25-75 predicted value • Average nitric oxide value: online
Phe
noty
p
• Body Mass Index • Postbronchodilation FEV1, liters: Spirometry • Baseline FEV1 % predicted: Spirometry • Baseline predrug FEV1, % predicted • Baseline predrug FEV1, % predicted
Q551R SNP• Codes for amino‐acid changes in the intracellular signaling portion of the receptor
NP
s Highassociation
Trait Network receptor• Exon 11
S
Noassociation
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Single‐Marker Single‐Trait Test
Permutation test α = 0.05
Permutation test α = 0.01
Comparison of Gflasso with OtherspPhenotypes
pes
Lung physiology‐related traits I• Baseline FEV1 predicted value: MPVLung • Pre FEF 25-75 predicted value • Average nitric oxide value: online
Phe
noty
p
• Body Mass Index • Postbronchodilation FEV1, liters: Spirometry • Baseline FEV1 % predicted: Spirometry • Baseline predrug FEV1, % predicted • Baseline predrug FEV1, % predicted
Q551R SNP• Codes for amino‐acid changes in the intracellular signaling portion of the receptorTrait Network
NP
s
?
receptor• Exon 11
Highassociation
S ?Noassociation
Eric Xing © Eric Xing @ CMU, 2006-2010 36
Lasso Graph‐guided Fused Lasso
Single‐Marker Single‐Trait Test
Linkage Disequilibrium Structure in IL-4R genein IL-4R gene
SNP rs3024660
SNP rs3024622
r2 =0.07
SNP Q551R
r2 =0.64
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IL4R GeneIL4R Gene
Chr16: 27,325,251-27,376,098exonsintrons
IL4RSNPs in intronSNPs in intron
SNPs in exon
SNPs in promotor regionQ551R
rs3024660rs3024622
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Association to a T t t d
TCGACGTTTTACTGTACAATT
Tree-structured Phenome
Eric Xing © Eric Xing @ CMU, 2006-2010 39
TCGACGTTTTACTGTACAATT
Tree-guided Group LassoTree-guided Group Lasso
Why tree?Why tree? Tree represents a clustering structure
Scalability to a very large number of phenotypes Graph : O(|V|2) edges Tree : O(|V|) edges(| |) g
Expression quantitative trait mapping (eQTL)Agglomerative hierarchical clustering is a popular tool Agglomerative hierarchical clustering is a popular tool
Eric Xing © Eric Xing @ CMU, 2006-2010 40
Tree-Guided Group LassoTree-Guided Group Lasso
In a simple case of two genesp g
h
h
• Low height • Large height• Tight correlation• Joint selection
g g• Weak correlation• Separate selection
type
s
ypes
Gen
ot
Gen
oty
Eric Xing © Eric Xing @ CMU, 2006-2010 41
Tree-Guided Group LassoTree-Guided Group Lasso
In a simple case of two genes
h Select the child nodes jointly or
p g
j yseparately?
Tree-guided group lassoTree guided group lasso
L1 penalty• Lasso penalty
S t l ti
L2 penalty • Group lasso
Joint selection
Eric Xing © Eric Xing @ CMU, 2006-2010 42
• Separate selection • Joint selection
Elastic net
Tree-Guided Group LassoTree-Guided Group Lasso
For a general tree
h2 Select the child nodes jointly or
g
h1
separately?
Tree-guided group lasso
Joint selection
Separate selection
Eric Xing © Eric Xing @ CMU, 2006-2010 43
Tree-Guided Group LassoTree-Guided Group Lasso
For a general tree
h2 Select the child nodes jointly or
g
h1
separately?
Tree-guided group lasso
Eric Xing © Eric Xing @ CMU, 2006-2010 44
Joint selection
Separate selection
Balanced ShrinkageBalanced Shrinkage
Previously, in Jenatton, Audibert & Bach, 2009
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Estimating ParametersEstimating Parameters
Second-order cone programp g
Many publicly available software packages for solving convex optimization problems can be used
Also, variational formulation
Eric Xing © Eric Xing @ CMU, 2006-2010 46
Illustration with Simulated DataIllustration with Simulated Datas
Phenotypes
SN
Ps
Highi ti
No
association
Eric Xing © Eric Xing @ CMU, 2006-2010 47
True association strengths
Lasso Tree‐guided group lasso
association
Yeast eQTL AnalysisYeast eQTL Analysis
HierarchicalHierarchical clustering tree
Ps
Phenotypes
SN
P
Highassociation
Tree‐guided group lasso
Single‐Marker Single Trait Test
Noassociation
Eric Xing © Eric Xing @ CMU, 2006-2010 48
group lasso Single‐Trait Test
Ph SG St t Phenome StructureGraph
Genome StructureLinkage Disequilibrium
Structured A i ti
Graph-guided fused lasso (Kim & Xing, PLoS Genetics, 2009)
Stochastic block regression (Kim & Xing, UAI, 2008)
Association TreePopulation Structure
Tree-guided fused lasso (Kim & Xing, Submitted)
Multi-population group lasso (Puniyani, Kim, Xing, Submitted)
Epistasis Dynamic TraitEpistasisACGTTTTACTGTACAATT
Eric Xing © Eric Xing @ CMU, 2006-2010 49
Temporally smoothed lasso (Kim, Howrylak, Xing, Submitted)
Group lasso with networks(Lee, Kim, Xing, Submitted)
Ph SG St t Phenome StructureGraph
Genome StructureLinkage Disequilibrium
Structured A i ti
Graph-guided fused lasso (Kim & Xing, PLoS Genetics, 2009)
Stochastic block regression (Kim & Xing, UAI, 2008)
Association TreePopulation Structure
Tree-guided fused lasso (Kim & Xing, Submitted)
Multi-population group lasso (Puniyani, Kim, Xing, Submitted)
Epistasis Dynamic TraitEpistasisACGTTTTACTGTACAATT
Eric Xing © Eric Xing @ CMU, 2006-2010 50
Temporally smoothed lasso (Kim, Howrylak, Xing, Submitted)
Group lasso with networks(Lee, Kim, Xing, Submitted)
Computation TimeComputation Time
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Proximal Gradient DescentProximal Gradient DescentOriginal gProblem:
Approximation Problem:
Gradient of theApproximation:
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Geometric InterpretationGeometric Interpretation Smooth approximation
Uppermost LineNonsmooth
U tUppermost LineSmooth
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Convergence RateConvergence RateTheorem: If we require and set , the number of iterations is upper bounded by:
Remarks: state of the art IPM method for for SOCP converges at a rate
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Multi Task Time ComplexityMulti-Task Time Complexity Pre-compute:
Per-iteration Complexity (computing gradient)
Tree: IPM for SOCP
Proximal-Gradient
Graph:
Proximal Gradient
IPM for SOCP
P i l G di tProximal-Gradient
P i l G di t I d d t f S l Si
Eric Xing © Eric Xing @ CMU, 2006-2010 55
Proximal-Gradient: Independent of Sample Size Linear in #.of Tasks
ExperimentsExperiments
Multi-task Graph Structured Sparse Learning G p S Sp g(GFlasso)
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ExperimentsExperiments
Multi-task Tree-Structured Sparse Learning (TreeLasso)
Eric Xing © Eric Xing @ CMU, 2006-2010 57
ConclusionsConclusions
Novel statistical methods for joint association analysis to j ycorrelated phenotypes Graph-structured phenome : graph-guided fused lasso Tree-structured phenome : tree-guided group lasso Tree structured phenome : tree guided group lasso
Advantages Greater power to detect weak association signals Fewer false positives Joint association to multiple correlated phenotypes
Other structures In phenotypes: dynamic trait
Eric Xing © Eric Xing @ CMU, 2006-2010 58
p yp y In genotypes: linkage disequilibrium, population structure, epistasis
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Reference• Tibshirani R (1996) Regression shrinkage and selection via the lasso. Journal of Royal Statistical Society, Series B
58:267–288.• Weller J, Wiggans G, Vanraden P, Ron M (1996) Application of a canonical transformation to detection of quantitative trait
loci with the aid of genetic markers in a multi-trait experiment. Theoretical and Applied Genetics 92:998–1002.• Mangin B, Thoquet B, Grimsley N (1998) Pleiotropic QTL analysis. Biometrics 54:89–99.g y ( ) y• Chen Y, Zhu J, Lum P, Yang X, Pinto S, et al. (2008) Variations in DNA elucidate molecular networks that cause disease.
Nature 452:429–35.• Lee SI, Dudley A, Drubin D, Silver P, Krogan N, et al. (2009) Learning a prior on regulatory potential from eQTL data.
PLoS Genetics 5:e1000358.• Emilsson V, Thorleifsson G, Zhang B, Leonardson A, Zink F, et al. (2008) Genetics of gene expression and its effect onEmilsson V, Thorleifsson G, Zhang B, Leonardson A, Zink F, et al. (2008) Genetics of gene expression and its effect on
disease. Nature 452:423–28.• Kim S, Xing EP (2009) Statistical estimation of correlated genome associations to a quantitative trait network. PLoS
Genetics 5(8): e1000587.• Kim S, Xing EP (2008) Sparse feature learning in high-dimensional space via block regularized regression. In Proceedings
of the 24th International Conference on Uncertainty in Artificial Intelligence (UAI) pages 325-332 AUAI Pressof the 24th International Conference on Uncertainty in Artificial Intelligence (UAI), pages 325 332. AUAI Press.• Kim S, Xing EP (2010) Exploiting a hierarchical clustering tree of gene-expression traits in eQTL analysis. Submitted.• Kim S, Howrylak J, Xing EP (2010) Dynamic-trait association analysis via temporally-smoothed lasso. Submitted.• Puniyani K, Kim S, Xing EP (2010) Multi-population GWA mapping via multi-task regularized regression. Submitted.• Lee S, Kim S, Xing EP (2010) Leveraging genetic interaction networks and regulatory pathways for joint mapping of
i t ti d i l QTL S b itt depistatic and marginal eQTLs. Submitted.• Dunning AM et al. (2009) Association of ESR1 gene tagging SNPs with breast cancer risk. Hum Mol Genet. 18(6):1131-9. • Esparza-Gordillo J et al. (2009) A common variant on chromosome 11q13 is associated with atopic dermatitis. Nature
Genetics 41:596-601.• Suzuki A et al. (2008) Functional SNPs in CD244 increase the risk of rheumatoid arthritis in a Japanese population. Nature
Eric Xing © Eric Xing @ CMU, 2006-2010 59
Genetics 40:1224-1229.• Dupuis J et al. (2010) New genetic loci implicated in fasting glucose homeostasis and their impact on type 2 diabetes risk.
Nature Genetics 42:105-116.
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