ContextSpecific Bayesian Clustering for Gene Expression Data

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Context-Specific Bayesian Clustering for Gene
Expression Data

• Yoseph Barash and Nir Friedman
• RECOMB01
• Talk by Kyu-Baek Hwang

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Abstract

• Clustering of genes by their expression levels
  and their putative TF binding sites
• Extended naïve Bayes classifier
• Context-specific independencies
• Structural EM algorithm
• Experiments on the yeast dataset

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Introduction

• A central goal of molecular biology
• To understand the regulation of protein synthesis
• New technologies
• DNA sequencing (promoter regions that contain the
  binding sites of transcription factors)
• DNA microarrays
• The hypothesis
• Genes with a common functional role have similar
  expression patterns across different experiments
  and similar binding sites
• Clustering of genes

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Naïve Bayesian Clustering

• Random variables X1, , XN
• The expression levels of a particular gene
  through all experiments
• The number of occurrences of each binding sites
  in the promoter region
• A joint probability distribution
• P(X1, , XN)
• A dataset D sampled from P(X1, , XN)
• A probabilistic model that represents P(X1, ,
  XN) efficiently

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Naïve Bayesian Clustering (Contd)

• Naïve Bayes assumption

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Naïve Bayesian Clustering (Contd)

• For conditionals
• The probability of an example belonging to a
  cluster

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Selective Naïve Bayesian Models

• All the variables X1, , XN are not dependent on
  the cluster.
• The simple naïve model is vulnerable to noisy
  samples.

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Context-Specific Independence

• If a certain binding site Xi is regulating genes
  in only two clusters,
• P(Xi C) is represented by

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Learning of Bayesian Clustering Models

• The Bayesian clustering model in this paper is a
  subclass of Bayesian networks.
• The cluster label is missing.
• Structural EM algorithm with specified size of
  clusters

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The Bayesian Score

• A model M ltK, Ligt
• Model parameters
• The Bayesian approach
• Model prior

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The Bayesian Score (Contd)

• The likelihood
• Decomposable conjugate priors

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For Complete Data

• If we know the number of clusters and to which
  cluster an example belongs,
• The marginal likelihood

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For Incomplete Data

• Approximation to the marginal likelihood
• The Bayesian information criterion (BIC)
• The Cheeseman-Stutz (CS) score

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Learning CSI Clustering

• The search space is huge.
• Bayesian structural EM algorithm

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Structural EM Procedure

• Initialization
• The full model
• The random model
• To escape local maxima
• A random first-ascent hill-climb search
• Restart the structural EM algorithm and find the
  local maxma again
• If the score of this model is better than the
  former, restart the structural EM algorithm

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Simulation Studies

• The synthetic dataset
• Five clusters
• 50 continuous variables and 100 discrete
  variables
• Training sets of size 200, 500, and 800
• A test set of size 2000
• Additional noises (10 and 30 of genes)
• The number of clusters ranging from 3 to 7 (K
  values)

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Result on the Simulation Studies

• Cluster number
• Models with fewer clusters were sharply
  penalized.
• Structure accuracy
• Small false negative
• Mutual information ratio I(Ct, Ce)
• With the more training data, there was the more
  information gain.

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Biological Data

• Budding yeast gene expression data
• Spellmans cell-cycle data (800 genes and 77
  experiments)
• Garshs stress data (1271 genes and 92
  experiments)
• The number of putative binding sites in the
  1000bp upstream of the ORF (from SCPD and
  TRANSFAC) for each gene
• With MatInspector program
• The whole upstream region and four sub-regions
• Initialization point
• k-means clustering with only gene expression data

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Clusterings for Two Datasets
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Clusters for the Stress Data
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Clusters for the Cell-Cycle Data
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Discussion

• Bayesian clustering
• Two heterogeneous data
• Bayesian networks