# Inferring Latent Functions with Gaussian Processes in Differential Equations

Lecture slides:

- Inferring Latent Functions with Gaussian Processes in Differential Equations
- Advert!
- Gaussian Processes
- Application Overview
- Methodology
- Linear Response Model
- Linear Response Solution
- Covariance Functions - Visualisation of RBF Covariance
- Covariance Samples
- Induced Covariance
- Covariance Result
- Cross Covariance
- Posterior for f
- Covariance for Transcription Model
- Joint Sampling of x (t) and f (t)
- Joint Sampling of x (t) and f (t)01
- Joint Sampling of x (t) and f (t)02
- Covariance for Transcription Model
- Noise Corruption
- Artificial Data Results
- Results
- Linear response analysis
- Linear Response Results
- Results Transcription Rates
- Results Transcription Rates01
- Results Transcription Rates02
- Linear Response Discussion
- Non-linear Response Model
- Formalism
- Example: linear response
- Oscillatory Behaviour - Fix with MLP Covariance
- Covariance Samples
- Covariance Samples01
- Response Results
- Non-linear response analysis
- exp (·) Response Results
- log (1 + exp (f )) Response Results
- 3/1+exp(-f ) Response Results
- Discussion
- Other Relevant Work
- Open Question

*Author: Neil Lawrence, University Of Manchester*