approximations to those density functions currently one of the most popular members of this family is the variational auto-encoder the basic idea is to write down a density function log P of X where the density is intractable because we need to marginalize out a random variable Z Z is a vector of latent variables that provide a hidden code describing the input image and because of the process of marginalizing these variables out to recover simply the distribution over X is intractable we're forced to use instead a variational approximation this