Rich Probabilistic Methods for Gene Expression

1
Rich Probabilistic Methodsfor Gene Expression
Eran Segal Ben Taskar Audrey Gasch Nir Friedman
Daphne Koller
2
Outline

• Motivation for richer models
• PRMs for gene expression Modeling Learning Inf
  erence
• Results Synthetic Stress Compendium

3
One Sided Clustering

• Non-Parametric Clustering
• Hierarchical Agglomerative
• SVD
• K-means
• Parametric Clustering
• Probabilistic Clustering

Autoclass using expression levels
Gene-cluster
Level-1
Level-n
Level-2
experiments
4
One Sided Clustering
Experiments
Undetected Separability
Cluster 1
Cluster 2
Undetected Similarity
Cluster 3
Genes
Cluster 4
Cluster 5
Cluster 6
5
Basic Bi-Clustering
Experiments
Detected Separability
C1
C2
C3
C4
C5
C6
Undetected Similarity
C7
C8
C9
Genes
C11
C10
C12
C14
C13
C15
C17
C16
C18
6
Desired Clustering

• Allow for non-grid clusters
• Rows no longer correspond to genes (similarly
  for columns)

Experiments
Detected Separability
C1
C2
C3
C4
C5
Detected Similarity
C6
C7
Genes
C8
C9
C11
C10
C12
C14
C13
C15
7
Basic Bi-Clustering
Clust(gene2)
Clust(exp2)
Clust(gene1)
Clust(exp1)
G1-E2
G1-E1
G2-E2
G2-E1
Two-sided clustering (PLSA, Hoffman)
8
Outline

• Motivation for richer models
• PRMs for gene expression Modeling Learning Inf
  erence
• Results Synthetic Stress Compendium

9
PRMs Basic Bi-Clustering
Classes of objects
Gene
Experiment
Gene-cluster
Exp. cluster
Expression
Level
Compact representation of two-sided clustering
10
PRMs Relational Schema

• Describes the types of objects and relations in
  the database

Gene
Experiment
Mutation
Cluster
Cluster
Binding Sites
Exp. Attributes
Functional Classes
Expression
Exp. Level
11
PRM for Compendium Data

• Parameters for nodes
• Structure over gene features

Gene
Array/Mutated Gene
GCluster
GCluster (of mutated gene)
GCN4
HSF
Lipid (of mutated gene)
ACluster
Lipid
Endoplasmatic
Expression
Level
12
Resulting Bayesian Network

• 3 Genes, 2 Mutation Experiment

Lipid
Lipid
ACluster1
ACluster1
GCluster1
Endoplasmatic
E1,2
E1,1
GCluster2
Endoplasmatic
E2,1
E2,2
GCluster2
Endoplasmatic
E3,1
E3,2
13
PRM Learning
Data
Gene
Experiment
Gene-cluster
Exp. cluster
Learner
Expression
Level
Expert knowledge

• PRM models can be learned from empirical data
• parameter estimation
• structure learning learning the dependency
  structure
• Can learn with missing data hidden variables

14
PRM Learning

• Goal Find PRM structure that explains the data
  well
• Define scoring function to evaluate models
• Bayesian Score works bestScore (SD) log
  P(D S) P(S)
• Automatically trades off fit to data (likelihood
  of data) with model complexity
• Do heuristic search to find high-scoring
  structure
• Structure found is not necessarily best one

Marginal likelihood
Prior
15
Learning PRMs

• Parameter Estimation EM Approximate Inference
  for E-Step
• Structure Learning Complete Data Learning Tree
  splits Avoiding Local Maxima
• Structure Learning Incomplete Data Iterate
  until convergence (Hard SEM) EM Hard
  assignment Structure Learning

16
Context Specific Dependencies
GCluster 0 (of gene)
true
false
GCluster 3(of mutant)
. . .
false
true
HSF gt 2
ACluster 4
false
true
false
true
Endoplasmatic
Level
Level
. . .
true
false
Level
Level
17
Learning Process
Gene
Array/Mutated Gene
GCluster
HSF
GCN4
Lipid (of mutated gene)
GCluster (of mutated gene)
Lipid
Endoplasmatic
ACluster
Expression
Level
Experiments
Genes
18
Learning Process
Gene
Array/Mutated Gene
GCluster
HSF
GCN4
Lipid (of mutated gene)
GCluster (of mutated gene)
Lipid
Endoplasmatic
ACluster
Expression
Level
Experiments
Genes
19
Learning Process
Gene
Array/Mutated Gene
GCluster
HSF
GCN4
Lipid (of mutated gene)
GCluster (of mutated gene)
Lipid
Endoplasmatic
ACluster
Expression
Level
Gene Similarity
Experiments
Genes
20
Learning Process
Gene
Array/Mutated Gene
GCluster
HSF
GCN4
Lipid (of mutated gene)
GCluster (of mutated gene)
Lipid
Endoplasmatic
ACluster
Expression
Level
Experiment Similarity
Experiments
Genes
21
Learning Process
Gene
Array/Mutated Gene
GCluster
HSF
GCN4
Lipid (of mutated gene)
GCluster (of mutated gene)
Lipid
Endoplasmatic
ACluster
Expression
Level
Separability by TF
Experiments
Genes
22
Learning Process
Gene
Array/Mutated Gene
GCluster
HSF
GCN4
Lipid (of mutated gene)
GCluster (of mutated gene)
Lipid
Endoplasmatic
ACluster
Expression
Level
Attribute Dependencies
Experiments
InduceCluster Change
Genes
23
Learning Process
Gene
Array/Mutated Gene
GCluster
HSF
GCN4
Lipid (of mutated gene)
GCluster (of mutated gene)
Lipid
Endoplasmatic
ACluster
Expression
Level
Achieved Desired Clustering
Experiments
Genes
24
Outline

• Motivation for richer models
• PRMs for gene expression Modeling Learning Inf
  erence
• Results Synthetic Stress Compendium

25
Synthetic Data Recovering Structure

• Synthetic data 1000 genes, 90 arrays (12 types)
• Parents recovered Simulated data 84.5 /-
  2.5 Permuted data 56 /- 2.5
• Cluster recovery Simulated data PRMs
  98.4 /- 1.07 Naïve Bayes 90.8
  /- 0.42 Permuted data PRMs 88.1
  /- 1.52 Naïve Bayes 76.7 /-
  1.42

26
Stress Data

• 954 genes, 88 arrays (12 types)
• Structure learning 15 significant TFs 7
  significant function categories
• Cluster coherence Average variance reduction
  0.69 -gt 0.61 in 3 iterations
• Allowing annotation changes Average variance
  reduction 0.69 -gt 0.56 in 3 iterations

27
Fragment of PRM for Yeast Stress Data (Gasch al)
Gene
GCluster
Array
Carbon
AAM
Condition
Mig1
Expression
Level
28
Result Context-Specific Groupings

• A grouping is a set of genes that behave the same
  within a certain context a condition or a set
  of conditions
• Breakdown of genes into clusters is different in
  different contexts

Yeast Stress Data (Gasch al)
29
Example Biological Result

• Discovered grouping of 17 genes
• all induced in diauxic shift
• all have ? 2 binding sites for Mig1 transcription
  factor
• many not known to have been regulated by Mig1
• Context-sensitive groupings were key to
  identifying cluster

30
Compendium Data Results

• Figure out array cluster of particular gene
  mutation before performing the experiment
• Can hope to do this because
• array cluster depends on gene cluster
• gene cluster predicted based on behavior in other
  arrays

1
44 arrays predictedat 95 accuracy
0.8
0.6
Correct predictions
Accuracy / Predicted
Total predicted
0.4
0.2
0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Prediction confidence
31
Future Directions

• Handling time
• Handling sequence data (TFs)
• Incorporate structure information
• Discovering pathways