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Robust Optimization and Applications in Machine Learning

Robust Optimization and Applications in Machine Learning. Time-series prediction via linear least-squares. Predicted output. Properties of solution. Non-linear prediction and kernels. Properties of solution. What is a kernel, anyway?. SVM, LR, LS, MPM, PCA, CCA, FDA….

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Robust Optimization and Applications in Machine Learning

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  1. Robust Optimization andApplications in Machine Learning

  2. Time-series prediction via linear least-squares

  3. Predicted output

  4. Properties of solution

  5. Non-linear prediction and kernels

  6. Properties of solution

  7. What is a kernel, anyway? SVM, LR, LS, MPM, PCA, CCA, FDA…

  8. Example: 2nd-order polynomial kernel

  9. Example: 2nd-order polynomial kernel

  10. A classical way to use kernels

  11. Transduction framework

  12. Important property of kernel matrices

  13. Kernel optimization in least-squares

  14. Kernel optimization for least-squares

  15. Kernel optimization via SDP or SOCP

  16. A non-classical way to use kernels

  17. Kernel optimization in other problems

  18. Kernel optimization in SVM classifiers

  19. Kernel optimization in SVM classifiers (cont’d)

  20. Link with robust optimization

  21. Kernel optimization and data fusion mRNA expression data hydrophobicity data protein-protein interaction data sequence data (gene, protein) upstream region data (TF binding sites)

  22. Challenge

  23. Example of a Kernel for Genomic Data: Pairwise Comparison Kernel

  24. protein 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 protein 2 Example of a Kernel for Genomic Data: Linear Interaction Kernel

  25. Exampe of a Kernel for Genomic Data: Diffusion Kernel

  26. Learning the Optimal Kernel K

  27. Learning the Optimal Kernel Integrate constructed kernels Learn a linear mix Large margin classifier (SVM) Maximize the margin

  28. Yeast Protein Function Prediction

  29. Yeast Protein Function Prediction

  30. Yeast Protein Function Prediction MRF SDP/SVM (binary) SDP/SVM (enriched)

  31. Yeast Protein Function Prediction MRF SDP/SVM (binary) SDP/SVM (enriched)

  32. Part 3: summary

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