Dynamical Systems, Stochastic Processes and Bayesian Inference

Inferring Latent Functions with Gaussian Processes in Differential Equations

author: Neil Lawrence, University of Manchester

Categories

Top: Computer Science: Machine Learning: Gaussian Processes

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*Slides*
0:00	Inferring Latent Functions with Gaussian Processes in Differential Equations
0:45	Advert!
1:31	Gaussian Processes
1:47	Application Overview
2:35	Methodology
3:42	Linear Response Model
5:06	Linear Response Solution
7:22	Covariance Functions - Visualisation of RBF Covariance
7:53	Covariance Samples
8:39	Induced Covariance
9:22	Covariance Result
10:13	Cross Covariance
10:40	Posterior for f
11:10	Covariance for Transcription Model
12:00	Joint Sampling of x (t) and f (t)
12:29	Joint Sampling of x (t) and f (t)01
13:52	Joint Sampling of x (t) and f (t)02
13:55	Covariance for Transcription Model
14:06	Noise Corruption
14:39	Artificial Data Results
16:22	Results
16:59	Linear response analysis
17:03	Linear Response Results
18:01	Results Transcription Rates
18:14	Results Transcription Rates01
18:28	Results Transcription Rates02
18:35	Linear Response Discussion
20:08	Non-linear Response Model
20:17	Formalism
21:31	Example: linear response
22:20	Oscillatory Behaviour - Fix with MLP Covariance
23:11	Covariance Samples
23:17	Covariance Samples01
24:13	Response Results
24:30	Non-linear response analysis
25:35	exp (·) Response Results
25:47	log (1 + exp (f )) Response Results
26:15	3 /1+exp(-f ) Response Results
27:05	Discussion
30:22	Other Relevant Work
34:57	Open Question

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