I have been puzzled trying to convert MSE to Log Likelihood in VAEs. Relevant Questions:
Relevant Discussion: Reddit: [Discussion] Calculation of bits/dims
In the paper: Masked Autoregressive Flow for Density Estimation
They provide a formula from going from "Pixel space" to logit space, but I don't understand the logic behind it.
They normalize the pixel values and then multiply by some hyper parameter that is chosen arbitrarily.
They then derive this formula:
For which it is not clear if $x_i$ is an image in the dataset/batch or a pixel of image $x_i$ (most likely the later one but still unsure)
For which $x_i$ is a pixel value of image x.
But it is not clear what is p(x) for my VAE trained on MSE.