1. Central dogma of biology DNA  RNA  pre-mRNA  mRNA  Protein Central dogma

2. CGAACAAACCTCGAACCTGCT DNA: mRNA: GCU UGU UUA CGA Polypeptide: Ala Cys Leu Arg Translation Transcription Basic molecular biology

3. Transcription End modification Splicing Transport Translation Less basic molecular biology

4. Cy3 Cy5 ReferenceTest Sample cDNA Clone (LIBRARY) PCR Product PE Test Sample Oligonucleotide Synthesis Biological Sample RNA ARRAY Ramaswamy and Golub, JCO Microarray technology

5. Lockhart and Winzler 2000 Oligonucleotide cDNA Microarray technology

6. Yeast experiment Microarray experiment

7. When the science is not well understood, resort to statistics: Ultimate goal: discover the genetic pathways of cancers Infer cancer genetics by analyzing microarray data from tumors Curse of dimensionality: Far too few examples for so many dimensions to predict accurately Immediate goal: models that discriminate tumor types or treatment outcomes and determine genes used in model Basic difficulty: few examples 20-100, high-dimensionality 7,000-16,000 genes measured for each sample, ill-posed problem Analytic challenge

8. Cancer Diagnosis Acute Myeloblastic Leukemia v Acute Lymphoblastic Leukemia

9. 38 examples of Myeloid and Lymphoblastic leukemias Affymetrix human 6800, (7128 genes including control genes) 34 examples to test classifier Results: 33/34 correct d perpendicular distance from hyperplane Test data d Cancer Classification

10. Coregulation: the expression of two genes must be correlated for a protein to be made, so we need to look at pairwise correlations as well as individual expression Size of feature space: if there are 7,000 genes, feature space is about 24 million features, so the fact that feature space is never computed is important Two gene example: two genes measuring Sonic Hedgehog and TrkC Coregulation and kernels

11. Nonlinear SVM helps when the most informative genes are removed, Informative as ranked using Signal to Noise (Golub et al). Genes removederrors 1 st order2 nd order3 rd order polynomials 01110111 10211 20321 30332 40332 50322 100332 200333 1500778 Gene coregulation

12. Golub et al classified 29 test points correctly, rejected 5 of which 2 were errors using 50 genes Need to introduce concept of rejects to SVM g1 g2 Normal Cancer Reject Rejecting samples

14. Estimating a CDF

15. The regularized solution

16. 1/d P(c=1 | d).95 95% confidence or p =.05d =.107 Rejections for SVMs

17. Results: 31 correct, 3 rejected of which 1 is an error Test data d Results with rejections

18. SVMs as stated use all genes/features Molecular biologists/oncologists seem to be convinced that only a small subset of genes are responsible for particular biological properties, so they want the genes most important in discriminating Practical reasons, a clinical device with thousands of genes is not financially practical Possible performance improvement Wrapper method for gene/feature selection Gene selection

19. AML vs ALL: 40 genes 34/34 correct, 0 rejects. 5 genes 31/31 correct, 3 rejects of which 1 is an error. B vs T cells for AML: 10 genes 33/33 correct, 0 rejects. d Test data d Results with gene selection

20. Hierarchy of difficulty: 1.Histological differences: normal vs. malignant, skin vs. brain 2.Morphologies: different leukemia types, ALL vs. AML 3.Lineage B-Cell vs. T-Cell, folicular vs. large B-cell lymphoma 4.Outcome: treatment outcome, elapse, or drug sensitivity. Molecular classification of cancer

21. Morphology classification

22. Outcome classification

23. Error rates ignore temporal information such as when a patient dies. Survival analysis takes temporal information into account. The Kaplan-Meier survival plots and statistics for the above predictions show significance. p-val = 0.0015 p-val = 0.00039 Lymphoma Medulloblastoma Outcome classification

24. BreastProstate Lung Colorec tal Lympho ma Bladd er Meleno ma Uterus Leuke mia Renal Pancr eas Ovary Mesothe lioma Brain AbrevBPLCRLyBlMULeRPAOvMSC Total11101113221110 3011 20 Train88881688824888816 Test32356323633334 Note that most of these tumors came from secondary sources and were not at the tissue of origin. Multi tumor classification

25. CNS, Lymphoma, Leukemia tumors separate Adenocarcinomas do not separate Clustering is not accurate

26. Combination approaches: All pairs One versus all (OVA) Multi tumor classification

27. Supervised methodology

28. Well differentiated tumors

29. Feature selection hurts performance

30. 0 0.2 0.4 0.6 0.8 1 01234 AccuracyFraction of Calls 0 1 2 3 4 5 Low High Confidence Low High Confidence Correct Errors 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 FirstTop 2Top 3 Prediction Calls DatasetSample TypeValidation Method Sample Number Total Accuracy Confidence High Low Fraction Accuracy TestPoorly DifferentiatedTrain/test2030%50% 50% 50% 10% Poorly differentiated tumors

31. Morphing

33. Talking faces

36. Recursive feature elimination (RFE): based upon perturbation analysis, eliminate genes that perturb the margin the least Optimize leave-one out (LOO): based upon optimization of leave-one out error of a SVM, leave-one out error is unbiased Two feature selection algorithms

37. Recursive feature elimination

38. Use leave-one-out (LOO) bounds for SVMs as a criterion to select features by searching over all possible subsets of n features for the ones that minimizes the bound. When such a search is impossible because of combinatorial explosion, scale each feature by a real value variable and compute this scaling via gradient descent on the leave-one-out bound. One can then keep the features corresponding to the largest scaling variables. The rescaling can be done in the input space or in a “Principal Components” space. Optimizing the LOO

39. Rescale features to minimize the LOO bound R 2 /M 2 x2x2 x1x1 R 2 /M 2 >1 M R x2x2 R 2 /M 2 =1 M = R Pictorial demonstration

40. Radius margin bound: simple to compute, continuous very loose but often tracks LOO well Jaakkola Haussler bound: somewhat tighter, simple to compute, discontinuous so need to smooth, valid only for SVMs with no b term Span bound: tight complicated to compute, discontinuous so need to smooth Three LOO bounds

41. We add a scaling parameter  to the SVM, which scales genes, genes corresponding to small  j are removed. The SVM function has the form: Classification function with scaling

42. SVM and other functionals

43. Algorithm

44. Computing gradients

45. Linear problem with 6 relevant dimensions of 202 Nonlinear problem with 2 relevant dimensions of 52 number of samples error rate Toy data