I am hopping to use Gaussian Processes (GPs) to model scientific values that can only be positive (think weight, length...). However, GPs map the latent variable as Gaussian distributions spanning across positive and negative numbers.

Are there any ways to create a map from the real numbers to the positive real numbers allowing for Gaussian processes to create a series of probability distributions over the real positive numbers?

Related Work: I have seen people use Linear Logistic Regression or take the integral to the mean to squeeze the output of a GP to between 0 and 1.

An Idea: Assume the positive Scientific Value of interest (height) h = e^x where x~N. Then P(h) = N(ln(h)). I understand this to essentially be a mapping from Normal distributions to Log-Normal distributions.



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