# Part III - Modern Statistical Methods

## Lectured by R. D. Shah, Michaelmas 2017

These notes are not endorsed by the lecturers, and I have modified them (often significantly) after lectures. They are nowhere near accurate representations of what was actually lectured, and in particular, all errors are almost surely mine.

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# Contents

- V Full version
- 0 Introduction
- 1 Classical statistics
- 2 Kernel machines
- 2.1 Ridge regression
- 2.2 v-fold cross-validation
- 2.3 The kernel trick
- 2.4 Making predictions
- 2.5 Other kernel machines
- 2.6 Large-scale kernel machines
- 3 The Lasso and beyond
- 3.1 The Lasso estimator
- 3.2 Basic concentration inequalities
- 3.3 Convex analysis and optimization theory
- 3.4 Properties of Lasso solutions
- 3.5 Variable selection
- 3.6 Computation of Lasso solutions
- 3.7 Extensions of the Lasso
- 4 Graphical modelling
- 5 High-dimensional inference