EPSRC Winter School in Mathematics for Data Modelling

Introduction to data modelling

author: Tony Dodd, University of Sheffield

Description

This first presentation introduces the basic principles of data modelling together with linear in the parameters models.

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*Slides*
0:00	Linear Models
0:58	Overview
2:12	Linear models
6:30	- Questions
15:49	Least squares cost function
16:15	Least squares parameters
18:30	A bit of maths
18:36	Parameter estimation
18:41	A bit of maths
22:12	Example - 1
22:39	Example - 2
22:45	- Questions
28:43	- Questions
30:58	Linear in the parameters
31:19	Nonlinear mapping (regression) - 1
32:04	Nonlinear mapping (regression) - 2
32:43	Nonlinear mapping (regression) - 3
33:10	Nonlinear mapping (regression) - 4
33:25	Parameter estimation
33:39	- Questions
34:08	- Questions
36:37	Example (a) - 1
36:45	Example (a) - 2
36:55	Example (a) - 3
37:13	Example – how does it work? - 1
37:36	Example – how does it work? - 2
37:55	- Questions
38:58	Example – when it all goes wrong
39:24	- Questions
44:15	- Questions
48:40	Can we generalise it?
49:40	Nonlinear mapping (classification) - 1
50:05	Nonlinear mapping (classification) - 2
50:26	- Questions
52:50	Nonlinear mapping (classification) - 4
52:53	Parameter estimation
54:01	Example (b) - 1
54:23	Example (b) - 2
54:41	Example (b) - 3
55:12	Example (b) - 4
55:41	Example – class probabilities
56:17	Example (b) - 4
56:21	Example – class probabilities
56:28	But...
57:37	Basis function optimisation
58:28	- Questions
62:14	Number of basis functions
63:24	Positions of basis functions
63:42	Types of basis functions
64:03	Positions of basis functions
64:46	Types of basis functions
65:33	- Questions
66:07	- Questions
67:19	- Questions
69:45	Concluding remarks

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