Best linear prediction, inverse models in statistical sense: example (I)

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 15:46

Summary:

A first numerical example on the ideas of video [vicinv1EN] is presented. Given a covariance matrix between a pair of random variables $(a,b)$, a linear model with additive noise $b=𝜃a+𝜖$ is built, as well as another one $a=\eta b+{𝜀}^{\prime }$.

Note that we might think that one model would be the algebraic inverse of the other, but it is not true, i.e., $\eta \ne {𝜃}^{-1}$. A graphical representation of the idea is discussed.

Some information is lost when contaminating something with noise so we cannot revert back to where we started with... Unless you train a ”difussion neural network” trying to do exactly that: recover a picture from a random seed... but we are NOT discussing that in the video!

A second example delving on the same idea appears in video [vcinv2EN].

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