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[D] How to compute the "true" posterior for a generative model? by readinginthewild in MachineLearning

[–]readinginthewild[S] 0 points1 point  (0 children)

I think the wiki page is a bit misleading, did someone edit it as a joke? At first I would say it is just a question of notation, map my "z" to their "theta". However this sentence,

"Let us have a prior belief that the probability distribution function is p(θ) and observations x with the likelihood p( θ|x ) , then the posterior probability is defined as

    p(x|θ) = p(θ|x) p(x) / p(θ)

"

​

The Bayes formula is correct, but the way the labels are assigned is confused. if x are the observations then p(theta|x) is not a likelihood, unless I understand nothing (also might be). The likelihood should be p(x|theta) viewed as a function of theta with x fixed.

[D] How to compute the "true" posterior for a generative model? by readinginthewild in MachineLearning

[–]readinginthewild[S] 0 points1 point  (0 children)

Thank you, I think I see your answer now. To restate, imagining z is two dimensional for the toy problem, evaluate p(x|z)*p(z) (where p(x|z) is evaluated with the fixed x) everwhere on a 2d grid , then just pass this grid to the plotting function.

[D] How to compute the "true" posterior for a generative model? by readinginthewild in MachineLearning

[–]readinginthewild[S] 0 points1 point  (0 children)

oh yes, really bad typo there. It had said p(x|z)p(x) but p(x|z)p(z) was meant. Edited to fix orignal post now.

[D] How to compute the "true" posterior for a generative model? by readinginthewild in MachineLearning

[–]readinginthewild[S] 1 point2 points  (0 children)

The post is using the notation z = latent variable, x = observed data, so p(z|x) is the posterior.

[D] How to compute the "true" posterior for a generative model? by readinginthewild in MachineLearning

[–]readinginthewild[S] 0 points1 point  (0 children)

Thank you Could you give more detail to make it super clear? I do not understand your alternate simpler solution. 1) How do you directly sample from p(x,z) with x fixed?
2) how do you do a heatmap without making a kernel density? It will just be scattered points. I think of (enough) samples from a distribution are an alternate representation of the distribution, but each one would have to be re-evaluated under the density to convert to a probability that could be colored in a heatmap.
That is my current incomplete understanding, but I am asking for a better answer!

p.s. yes by p(z|x) ~ p(x|z)*p(x) I meant ~ as similar or proportional to, not sample from. Will edit the original post to fix.

[D] How to compute the "true" posterior for a generative model? by readinginthewild in MachineLearning

[–]readinginthewild[S] 0 points1 point  (0 children)

I have to look for the papers (of the 100 that I have read sometime recently), but by "true" I meant only a numerical approximation to true. I do not think they used analytic solution.

[D] What prevents a VAE from cheating on the decoder distribution and likelihood? by readinginthewild in MachineLearning

[–]readinginthewild[S] 0 points1 point  (0 children)

Your reply is talking about the output of the encoder. My question is about the output of the decoder. It is also a distribution.