Matérn kernel regression (1): basic setup, 1st order filter example, linear interpolation

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 16:40

Summary:

This video presents an example of GP regression using a Gaussian process with autocovariance given by a Matérn kernel. The definition of it was discussed in the video [[maternEN], of which this is a continuation. To illustrate other concepts making the example richer, a ’parametric’ component is incorporated saying that the stochastic process could not have zero mean and wishing to estimate that mean from a prior with a normal distribution, more details in other materials.

First, the example setup is presented and, then, a demonstration of interpolation with a spectral factor of order 1 is made. If the correlation distance $\rho$ is small, with distant samples interpolation (mean) falls exponentially to the estimated “constant mean”. If the correlation distance is large, then interpolation between nearby samples tends toward a piecewise linear interpolation.

Cases of higher order (and its relationship with splines), fractional order and infinite order (exponential-quadratic kernel) are discussed in the video [maternr2EN], continuation of this one.

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.