(5/5) Multi-output Gaussian Processes: latent factor estimation

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 22:55

Summary:

This video discusses the prediction of the value of ‘internal’ hidden components or ’latent factors’ of a 2-output Gaussian process where the statistical model is $y=Cu$, with $y$ of size 2x1 being the observable outputs and $u$ of 3x1 being the latent components, not directly ‘measurable’. Obviously, when the components are the ‘states’ of differential equations what we are doing would be analogous to Kalman filters or RTS/Wiener smoothing, but those techniques are not within the scope of this video.

Basically the covariance between the components and the outputs is $E[u(x_1)y{(x_2)}^T]=K(x_1,x_2)C^T$ so that using this covariance, the usual prediction formulas can be applied, illustrated in the video by a numerical example based on the case study of the previous videos, in particular [mimogp4predAEN].

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