Homeomorphic smoothing splines: monotonizing an unconstrained estimator in nonparametric regression

author: Jérémie Bigot, Université Paul Sabatier Toulouse III

You might be experiencing some problems with Your Video player.

*Slides*
0:00	Homeomorphic smoothing splines: monotonizing an unconstrained estimator in nonparametric regression
0:20	Overview
1:24	Formulation of the problem
2:11	Spline smoothing - 1
3:04	Spline smoothing - 2
4:35	Example of Spline smoothing - 1
4:47	Example of Spline smoothing - 2
5:10	Example of Spline smoothing - 3
5:31	Example of Spline smoothing - 4
5:49	Regression under shape constraints: some existing approaches
8:27	Some problems with monotone regression
9:24	Image warping and construction of bijective functions
11:12	Construction of a class of monotone functions - 1
11:48	Construction of a class of monotone functions - 2
12:55	Construction of a class of monotone functions - 3
13:34	Construction of a class of monotone functions - 4
15:03	Numerical example - 1
15:22	Numerical example - 2
15:36	Numerical example - 3
15:42	Numerical example - 4
15:44	Numerical example - 5
15:46	Numerical example - 6
15:47	Numerical example - 7
16:29	Construction of a class of monotone functions - 5
17:00	Construction of a class of monotone functions - 6
17:10	Construction of a class of monotone functions - 7
17:37	Construction of a class of monotone functions - 8
19:20	Estimation of the vector field
19:32	Construction of a class of monotone functions - 8
20:05	Estimation of the vector field
22:29	- Questions
22:44	- Questions
24:17	Minimisation of a global energy
26:24	Example of monotone Spline smoothing - 1
26:27	Example of monotone Spline smoothing - 2
26:36	Example of monotone Spline smoothing - 3
26:58	Example of monotone Spline smoothing - 4
27:09	Example of monotone Spline smoothing - 5
27:37	Convergence of the monotone estimator - 1
28:16	Convergence of the monotone estimator - 2
28:55	Convergence of the monotone estimator - 3
29:33	Convergence of the monotone estimator - 4
29:49	Convergence of the monotone estimator - 5
30:39	Rate of convergence for Sobolev spaces
34:25	Choice of λn - 1
34:59	Choice of λn - 2
35:36	Choice of λn - 3
36:36	Choice of λn - 4
37:32	A simple algorithm
38:50	Comparison with two other methods
42:03	Simulations - 1
42:16	Simulations - 2
43:05	Simulations - 3
43:12	Simulations - 4
43:27	Simulations - 5
44:03	A real example - 1
44:43	A real example - 2
44:55	Conclusion

Lecture rating

People found this lecture:
Worth seeing
because it is:
Valuable and informative
Well presented
Easily understandable
Acceptably recorded
You need to login to cast your vote.

Report a problem or upload files

If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.