Kernels for Multiple Outputs and Multi-task Learning

Geostatistics for Gaussian Processes

author: Hans Wackernagel, MINES ParisTech
published: Jan. 19, 2010, recorded: December 2009, views: 939

Slides

Slides
0:00	Geostatistics for Gaussian processes
0:23	Introduction
0:26	Geostatistics and Gaussian processes
0:43	Geostatistics -1
1:55	Geostatistics -2
3:08	Geostatistics: definition
4:22	Stationarity
5:54	Second-order stationary model
6:09	Non-stationary model
6:49	The variogram
7:29	What is a variogram?
8:16	Ordinary kriging
9:17	Mobile phone exposure of children
9:31	Phone position and child head
9:59	SAR exposure
10:13	Max SAR for different positions of phone
11:00	Variogram
12:29	Max SAR kriged map
12:36	Prediction error -1
13:12	Prediction error -2
13:57	Geostatistical Model
14:04	Linear model of coregialization
14:40	Two linear models
15:31	Linear Model of Coregionalization
17:21	Coregionalization matrices
18:35	LMC: intrinsic correlation
19:55	Regionalized Multivariate Data Analysis
20:24	Regionalized PCA?
20:53	Multivariate Geostatistical filtering
20:59	Modeling of spatial variability
21:05	Multivariate Geostatistical filtering
21:10	Modeling of spatial variability
22:33	Geostatical filtering
23:25	Zoom into corner
25:23	Cokriging in NE corner
26:24	Consequence
26:31	Covariance structure
26:36	Separable multivariate and spatial correlation
27:24	Codispersion Coefficients
28:09	Intrinsic Correlation
28:44	Testing for Intrinsic Correlation
29:18	Cross variogram
29:58	Testing for Intrinsic Cerrelation
30:38	Cokriging
30:44	Ordinary cokriging
32:02	Data configuration and neighborhood
33:17	Data configurations
34:35	Configuration -1
35:16	Configuration -2
36:24	Neighborhood -1
37:24	Neighborhood -2
38:17	Neighborhood -3
39:19	Cokriging neighborhoods
40:14	Conclusion -1
40:19	Conclusion -2
46:40	Neighborhood -2

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Description

Gaussian process methodology has inspired a number of stimulating new ideas in the area of machine learning. Kriging has been introduced as a statistical interpolation method for the design of computer experiments twenty years ago. However, some aspects of the geostatistical methodology originally developed for natural resource estimation have been ignored when switching to this new context. This talk reviews concepts of geostatistics and in particular the estimation of components of spatial variation in the context of multiple correlated outputs.