Week 46: Gradient Boosting Summary and Support Vector Machines
Contents
Overview of week 46
Thursday
Friday
Support Vector Machines, overarching aims
Hyperplanes and all that
What is a hyperplane?
A \( p \)-dimensional space of features
The two-dimensional case
Getting into the details
First attempt at a minimization approach
Solving the equations
Code Example
Problems with the Simpler Approach
A better approach
A quick Reminder on Lagrangian Multipliers
Adding the Multiplier
Setting up the Problem
The problem to solve
The last steps
A soft classifier
Soft optmization problem
Kernels and non-linearity
The equations
The problem to solve
Different kernels and Mercer's theorem
The moons example
Mathematical optimization of convex functions
How do we solve these problems?
A simple example
Back to the more realistic cases
Overview of week 46
Thursday
: Summary of Gradient Boosting and further examples of applications, from the physical sciences to the social sciences.
Guest lecture by John M. Aiken on Gradient Boosting and XGboost
.
Friday
: Support Vector Machines, classification and regression.
Geron's chapter 5. Chapter 12 (sections 12.1-12.3 are the most relevant ones) of Hastie et al contains also a good discussion.
Overview of Support Vector Machines
. see also
this video
.
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