Multi-Task Learning with Gaussian Processes with Applications to Robot Inverse Dynamics

author: Chris Williams, University of Edinburgh
published: Jan. 19, 2010, recorded: December 2009, views: 286

Slides

Slides
0:00	Multi-task Learning with Gaussian Processes, with Applications to Robot Inverse Dynamics
1:34	Motivation
3:20	Outline
4:45	1. What is a Gaussian process?
5:38	The Marginalization Property
7:05	Drawing Random Functions from a Gaussian Process
8:20	output, f(x) , input x
8:33	3 D graph 1
8:36	From Prior to Posterior
10:12	Marginal Likelihood
11:20	From Prior to Posterior
12:09	2. Co-kriging
13:37	3 D graph 2
14:04	From Prior to Posterior
14:12	3 D graph 2
14:25	Some questions
14:41	3. Intrinsic Correlation Model (ICM)
16:50	ICM as a linear combination of indepenent GPs
18:14	Some problems conform
18:51	4 A. Multi-task Learning as Hierarchical Modelling
19:45	Regularization framework
20:58	ICM as a linear combination of indepenent GPs
21:33	Regularization framework
22:36	GP view
23:08	4 B. MTL as Input-space Transformation (1)
24:16	4 B. MTL as Input-space Transformation (2)
26:05	4 C. Shared Feature Extraction (1)
27:48	4 C. Shared Feature Extraction (2)
28:01	4 C. Shared Feature Extraction (1)
29:15	4 C. Shared Feature Extraction (2)
30:43	5. Some Theory for the ICM
34:04	Theory: Result on lower bound
36:01	Discussion
36:10	Multi-task Learning in Robot Inverse Dynamics
37:02	Inverse Dynamics Characteristics of T (1)
38:21	Inverse Dynamics Characteristics of T (2)
38:49	Inverse Dynamics Characteristics of T (3)
40:03	GP prior for Inverse Dynamics for multiple loads
41:00	GP prior for k(x, x0)
41:49	Data (1)
42:43	Data (2)
44:34	GP prior for k(x, x0)
44:47	Data (2)
44:49	Methods
45:33	Results
46:52	Interpolation ( j=5), Extrapolation ( j=5)
46:58	Results
47:33	Interpolation ( j=5), Extrapolation ( j=5)
48:20	Conclusions and Discussion
49:28	- Questions

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Description

I will discuss multi-task learning, and a number of ways in which transfer between tasks can take place, mainly in a co-kriging (or Gaussian process) framework. I will then go into more detail on multi-task Gaussian process learning of robot inverse dynamics (joint work with Kian Ming Chai, Stefan Klanke, Sethu Vijayakumar).