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

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    • Matérn and squared-exponential kernels: in...   , of which this is a continuation. To illustrate other concepts and make 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    • Matérn kernel regression (2): 2nd, 3rd, an...   , continuation of this one.
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PDF/code/notes at: https://personales.upv.es/asala/YT/V/...
#gaussianprocess #regression #kernelmethods #statistics
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Antonio Sala, UPV
University lectures
Full collection of videos at: https://personales.upv.es/asala/YT/in...