Exponential Families and Kernels
Abstract
In this course I will discuss how exponential families, a standard tool
in statistics, can be used with great success in machine learning to
unify many existing algorithms and to invent novel ones quite
effortlessly. In particular, I will show how they can be used in feature
space to recover Gaussian Process classification for multiclass
discrimination, sequence annotation (via Conditional Random Fields), and
how they can lead to Gaussian Process Regression with heteroscedastic
noise assumptions.
Prerequisites
Elementary Linear Algebra
Calculus
Experience with Bayesian Methods is beneficial, however not required.
Experience with Kernel Methods is likewise beneficial, but not
required.
A background in statistics would be useful, however it is not required.
Contents
Unit 1:
Exponential Families
Unit 2:
Conditioning and Feature Spaces
Unit 3:
Applications 1 (Classification, Regression, Novelty Detection)
Unit 4:
Applications 2 (Graphical Models and Conditional Random Fields)