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Robust Optimization and Applications in Machine Learning

This guide delves into Sparse PCA principles, outlining the importance of sparsity in unsupervised learning. The concept of Principal Component Analysis (PCA) is explored, emphasizing rank-one cases and SDP relaxations. Case studies include PITPROPS data analysis, financial examples, and gene expression data clustering. The text navigates through Sparse Gaussian networks, detailing correlation-based approaches, MLE estimations, and convex relaxations. Algorithms like Nesterov's method are discussed in the context of first-order vs. second-order techniques. Discover the application of sparsity in unsupervised learning and its role in robust machine learning models.

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Robust Optimization and Applications in Machine Learning

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  1. Robust Optimization andApplications in Machine Learning

  2. Part 4: Sparsity in Unsupervised Learning

  3. Unsupervised learning

  4. Sparse PCA: outline

  5. Principal Component Analysis

  6. PCA for visualization

  7. First principal component

  8. Sparse PCA: outline

  9. Why sparse factors?

  10. PCA: rank-one case

  11. sparse PCA: rank-one case

  12. Sparse PCA: outline

  13. SDP relaxation

  14. SDP relaxation

  15. Dual problem

  16. Sparsity and robustness

  17. Sparse PCA decomposition?

  18. Sparse PCA: outline

  19. First-order algorithm

  20. Sparse PCA: outline

  21. PITPROPS data

  22. PITPROPS data: numerical results

  23. Financial example

  24. Covariance matrix

  25. Second factor

  26. Gene expression data

  27. Clustering of gene expression data

  28. Conclusions on sparse PCA

  29. Part 4: Sparsity in Unsupervised Learning

  30. Sparse Gaussian networks: outline

  31. Gaussian network problem

  32. Correlation-based approach

  33. Approach based on the precision matrix

  34. Example

  35. Relevance network vs. graphical model

  36. Can we check this?

  37. Sparse inverse covariance and conditional independence

  38. Related work

  39. Maximum-likelihood estimation

  40. Problems with ordinary MLE

  41. MLE with cardinality penalty

  42. Convex relaxation

  43. Link with robustness

  44. Properties of estimate

  45. Algorithms: challenges

  46. First- vs. second-order algorithms

  47. Black- vs. grey-box first-order algorithms

  48. Algorithms: problem structure

  49. Nesterov’s smooth minimization algorithm

  50. Nesterov’s method

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