(5/5) Multi-output Gaussian Processes: latent factor estimation, hidden components
Автор: Modeling, Identification, Control (A. Sala)
Загружено: 2025-05-09
Просмотров: 61
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 100% analogous to Kalman filters or RTS/Wiener smoothing. Still, 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 • (4/5) Multi-output Gaussian Processes: joi... .
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PDF/code/notes at: https://personales.upv.es/asala/YT/V/...
#gaussianprocesses #signalprocessing #statisticsfordatascience #statistics
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Antonio Sala
Full collection of videos at: https://personales.upv.es/asala/YT/in...
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