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Robust Optimization andApplications in Machine Learning
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Time-series prediction via linear least-squares
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Predicted output
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Properties of solution
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Non-linear prediction and kernels
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Properties of solution
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What is a kernel, anyway?
SVM, LR, LS, MPM, PCA, CCA, FDA…
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Example: 2nd-order polynomial kernel
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Example: 2nd-order polynomial kernel
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A classical way to use kernels
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Transduction framework
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Important property of kernel matrices
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Kernel optimization in least-squares
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Kernel optimization for least-squares
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Kernel optimization via SDP or SOCP
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A non-classical way to use kernels
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Kernel optimization in other problems
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Kernel optimization in SVM classifiers
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Kernel optimization in SVM classifiers (cont’d)
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Link with robust optimization
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Kernel optimization and data fusionmRNA
expression data
upstream region data
(TF binding sites)
protein-protein interaction data
hydrophobicity data
sequence data
(gene, protein)
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Challenge
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Example of a Kernel for Genomic Data: Pairwise Comparison
Kernel
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1 0 0 1 0 1 0 11 0 1 0 1 1 0 10 0 0 0 1 1 0 00 0 1 0 1 1 0 10 0 1 0 1 0 0 11 0 0 0 0 0 0 10 0 1 0 1 0 0 0
protein
protein
2
Example of a Kernel for Genomic Data: Linear Interaction Kernel
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Exampe of a Kernel for Genomic Data: Diffusion Kernel
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Learning the Optimal Kernel
K
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Learning the Optimal KernelIntegrate constructed Integrate constructed kernelskernels
Learn a linear mix
Large margin classifier Large margin classifier (SVM)(SVM)
Maximize the margin
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Yeast Protein Function Prediction
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Yeast Protein Function Prediction
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MRF
SDP/SVM(binary)
SDP/SVM(enriched)
Yeast Protein Function Prediction
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MRF
SDP/SVM(binary)
SDP/SVM(enriched)
Yeast Protein Function Prediction
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Part 3: summary