Forest Learning based on the Chow-Liu Algorithm and its Application to Genome Differential Analysis: A Novel Mutual Information Estimation
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This document summarizes work on estimating mutual information for discrete and continuous data, and applying it to construct Chow-Liu forests. It then describes two experiments: one analyzing gene expression differences between breast cancer groups, finding one gene strongly connected to the class; another combining gene expression and SNPs, finding SNPs and genes interconnected in the causal network rather than separated.
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Forest Learning based on the Chow-Liu Algorithm and its Application to Genome Differential Analysis: A Novel Mutual Information Estimation
- 1. Forest Learning based on the Chow-Liu Algorithm and its Application to Genome Differential Analysis: A Novel Mutual Information Estimation Nov. 16-18, 2015 Joe Suzuki (Osaka Univ.) @joe_suzuki Prof-joe
- 2. Road Map • MI Estimation for Discrete (warming-up) • MI Estimation for Discrete/Coninuous (propose) • Experiment 1 (gene differential analysis) • Experiment 2 (combination of SNP and gene) • Concluding Remarks
- 3. How do you estimate MI given data ? For discrete data, a naïve way is
- 4. MI Estimation based on MDL (Suzuki, UAI93) P. Liang and N. Srebro 2004、K. Panayidou 2010、Edwards, et. al 2010 revisited the same
- 6. Overestimation occurs for 𝐼 𝑛
- 7. Dist. Chow-Liu (apply Kruskal) known approximation to trees with K-L minimum unknown ML spanning trees (Chow-Liu), MDL forests (Suzuki 93)
- 8. R package bnlearn data set “Asia” Forest Spanning Tree
- 10. X: Gauss, Y: Discrete (Edwards et. al. 2010) close to Naïve Bayes (ANOVA) Causal Direction
- 11. Gaussaian should not be between discrete variables Discrete Gaussian (Edwards, et. al 2010) SNP Gene Expression
- 12. Proposed MI estimation For each mesh (percentile), estimate the MI based on the quntized data Choose the maximum MI estimation
- 13. n=1000, 8x8 occurrences of X,Y occurrence of (X, Y)
- 14. Does not distinguish discrete and continuous For each u,v=1,2,…,s, Continue to divide the interval half (avoid to divide the mass intervals)
- 16. What can be proved?
- 17. Convex
- 18. Experimet 1: Genome expression profiling in breast cancer patients • 58 sample with p53 mutation and 192 without it • 1000 genes Why only Bonferroni and FDR rather than causality and regression?
- 19. Normality test: p-values are extreamely low
- 20. MI distributions for all (1000) and 50 least p-value genes
- 21. • 20 seconds for MI values and 30 seconds for a forest (1000 nodes) The class variable has only one connection with gene variables We conclude that regression may be more appropriate than a graphical model.
- 22. Experiment 2: 300 gene expression (continue) and 300 SNP (3 values) • Utah 90 residents SNP (HapMap) with northern and western European ancestry • R library (BioConductor) GGData ftp://ftp.sanger.ac.uk/pub/genevar/CEU_parents_norm_march2007.zip
- 23. 200 genes and 200 SNPs
- 24. Causality among genes and SNP can be explored!! Insights we obtain from the experiment: • In the real causality, SNP and genes are not separated as Edwards assumed !! • Both SNPs and gene expressions are hubs of the mixed network. variable cardinality SNP 3 values Gene expression continuous
- 25. Summary • MI estimtaion • Application to Chow-Liu • Gene Differential Analysis • Causality among SNPs and Gene Expressions Future Works Beyond Forests: • BNs with bounded TW • MNs not necessarily forests