1 A combining approach to statistical methods for p >> n problems Shinto Eguchi Workshop on Statistical Genetics, Nov 9, 2004 at ISM

2 Microarray data cDNA microarry

3 Prediction from gene expressions Feature vector dimension = number of genes p components = quantities of gene expression Class label disease, adverse effect Classification machine based on training dataset

4 Leukemic diseases, Golub et al

5 Web microarray data p n y = +1 y = － 1 ALLAML Colon Estrogen p >> n micro/work/

6 Genomic data SNPsProteomeMicroarray Data dimension p 1,000 ～ 100,000 function5,000~20,000 data size n 100 ～ ～ 2020 ～ 100 mRNA ProteinGenome

7 Problem: p >> n Fundamental issue on Bioinformatics p is the dimension of biomarker (SNPs, proteome, microarray, …) n is the number of individuals (informed consent, institutional protocol, … bioethics)

8 Current paradigm Biomarker space SNPsHaplotype block (Fujisawa) Microarray Model-based clustering Proteome Peak data reduction (Miyata) GroupBoost (Takenouchi) Network gene model Haplotype & adverse effects (Matsuura)

9 An approach by combining Let B be a biomarker space Rapid expansion of genomic data Let be K experimental facilities

10 Bridge Study? CAMDA (Critical Assessment of Microarray Data Analysis ) DDBJ (DNA Data Bank Japan, NIG) …. result

11 CAMDA datasets for Lung Cancer HarvardPNAS, 2001Affymetrix MichiganNature Med, 2002 Affymetrix StanfordPNAS, 2001cDNA OntarioCancer Res 2001 cDNA

12 Some problems 1. Heterogeneity in feature space cDNA, Affymetrix Differences in covariates ， medical diagnosis Uncertainty for microarray experiments 2. Heterogeneous class-labeling 3. Heterogeneous generalization powers A vast of unpublished studies 4. Publication bias

13 Machine learning Leanability: boosting weak learners? AdaBoost :Freund & Schapire (1997) weak classifiersA strong classifier stagewise

14 AdaBoost

15 One-gene classifier Error number one-gene classifier Let be expressions of the j-th gene

16 The second training Errror number Update the weight: 4.5 Weight up to 2 Weight down to 0.5

17 Learning algorithm Final machine

18 Exponential loss Update :

19 Different datasets Normalization: ∋ expression vector of the same genes label of the same clinical item

20 Weighted Errors The k-th weighted error The combined weighted error

21 BridgeBoost

22 Learning Stage t :Stage t+1 :

23 Mean exponential loss Exponential loss Mean exponential loss Note: convexity of Expo-Loss

24 Meta-leaning Separate learning Meta-learning

25 Simulation Collapsed dataset Traning errorTest error 3 datasets Test error 0 （ ideal ） Test error 0.5 （ ideal ） data 1, data2 data3

26 Comparison Separate AdaBoost BridgeBoost Training error Test error

27 Min =15%Min =4% Min =43% Min = 3% Min = 4% Collapsed AdaBoost Separate AdaBoost BridgeBoost Test errors

28 Conclusion …. result Separate Leaning Meta-leaning

29 Unsolved problems 3. On the information on the unmatched genes in combining datasets 2. Prediction for class-label for a given new x ? 4. Heterogeneity is OK, but publication bias? 1. Which dataset should be joined or deleted in BridgeBoost ?

30 Mean and s.d. of 37 studies Passive smokers vs lung cancer Funnel plot heterogeneity publication bias Publication bias? (Copas & Shi, 2001)

31 References [1] A class of logistic-type discriminant functions. S. Eguchi and J. Copas, Biometrika 89, 1-22 (2002). [2] Information geometry of U-Boost and Bregman divergence. N. Murata, T. Takenouchi, T. Kanamori and S. Eguchi Neural Computation 16, (2004). [3] Robustifying AdaBoost by adding the naive error rate. T. Takenouchi and S. Eguchi. Neural Computation 16, (2004). [4] GroupAdaBoost for selecting important genes. In preparation. T. Takenouchi, M. Ushijima and S. Eguchi [5] Local model uncertainty and incomplete data bias. J. Copas and S. Eguchi. ISM Research Memo. 884 July. (2003). [6] Local sensitivity approximation for selectivity bias. J. Copas and S. Eguchi. J. Royal Statistical Society B 63 (2001) [7] Reanalysis of epidemiological evidence on lung cancer and passive smoking. J. Copas and J.Q. Shi, British Medical Journal 7232 (2000)