Machine Learning Summer School 2006 - Canberra

Exponential Families in Feature Space

author: S.V.N. Vishwanathan, National ICT Australia

Description

In this introductory course we will discuss how log linear models can be extended to feature space. These log linear models have been studied by statisticians for a long time under the name of exponential family of probability distributions. We provide a unified framework which can be used to view many existing kernel algorithms as special cases. Our framework also allows us to derive many natural generalizations of existing algorithms. In particular, we show how we can recover Gaussian Processes, Support Vector Machines, multi-class discrimination, and sequence annotation (via Conditional Random Fields). We also show to deal with missing data and perform MAP estimation on Conditional Random Fields in feature space. The requisite background for the course will be covered briskly in the first two lectures. Knowledge of linear algebra and familiarity with functional analysis will be helpful.

Categories

Top: Computer Science: Machine Learning: Linear Models

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*Slides*
0:01	Kernels and Dynamical Systems
2:28	Roadmap
6:00	Kernel Trick
10:13	The Basic Idea
13:42	Notation
16:23	Trajectories
18:19	Notation
18:24	Trajectories
19:39	Special Cases
21:51	Roadmap
22:06	Continuous Linear Systems
22:42	Notation
22:47	Trajectories
23:21	Notation
24:48	Trajectories
25:14	Special Cases
26:10	Continuous Linear Systems
29:13	Continuous Kernel
33:51	Special Cases
35:37	Diffusion Kernels
41:00	Graph Kernels
42:43	Continuous Linear Systems
43:39	Roadmap
44:22	Continuous Linear Systems
44:36	Diffusion Kernels
45:09	ARMA Models
49:28	Kernels on ARMA Models
52:41	Dynamic Textures

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