04 Non-parametrics and Missing Data

In Block 4 we cover:

• Non-parametric statistics:
  • Transforms and their uses:
    • Fourier Transform
    • Hadamard Transform
  • Kernel Density Estimation
  • k-Nearest Neighbour Density Estimation
  • The Kernel Trick
  • Kernel PCA as an example of the Kernel Trick
• Handling Outliers and Missing Data:
  • Outlier detection and/or removal
  • Robust algorithms
  • Classes of Missing data
  • Approaches for filtering data based on missingness
  • Approaches for imputing missing data
  • How to undersstand the consequences of these choices

Lectures:

• 04.1 Non-parametric Statistics
  • Reference R code
• Missing Data:
  • 04.2 Outliers and Missing data
  • Reference R code

Worksheets:

• Worksheet 4.1 Non-parametrics
• Worksheet 4.2 Outliers and Missing Data
• Portfolio 04

Workshop:

• 04.3 Workshop on Missing Data (.Rmd)
• 04.3 Workshop on Missing Data (.html)

Reference material:

Non-parametric Statistics:

• Transforms:
  • Nonparametric Statistics by Eduardo García Portugués
  • Basis Expansions: Chapter 5 of The Elements of Statistical Learning: Data Mining, Inference, and Prediction (Friedman, Hastie and Tibshirani).
• Density Estimation:
  • Kernel Smoothing: Chapter 6 of The Elements of Statistical Learning: Data Mining, Inference, and Prediction (Friedman, Hastie and Tibshirani).
  • For kNN Yen-Chi Chen’s notes on kNN and the Basis
• The Kernel Trick and its applications:
  • For the Kernel Trick Dave Krebs’ Intro to Kernels
  • For the Kernel PCA: Rita Osadchi’s Kernel PCA notes
  • Hofmann, Schoelkopf, & Smola (2008) “Kernel Methods in Machine Learning” (Ann. Stat.)
  • Schoelkopf B., A. Smola, K.-R. Mueller (1998) “Nonlinear component analysis as a kernel eigenvalue problem”.
• Outlier detection:
  • “A Survey of Outlier Detection Methodologies” by Victoria Hodge & Jim Austin, Artificial Intelligence Review 22:85–126 (2004).
  • Outlier Analysis by Charu C. Aggarwal. NB: Not freely available.
  • Chapter 10 of The Elements of Statistical Learning: Data Mining, Inference, and Prediction (Friedman, Hastie and Tibshirani) discusses the robustness to outliers for various methods.

Missing data:

• Chapter 9.6 of The Elements of Statistical Learning: Data Mining, Inference, and Prediction (Friedman, Hastie and Tibshirani).
• I would recommend Andrew Gelman’s Missing Data Notes.

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