"This is also called the (single datapoint) marginal likelihood or the model evidence, when taken as a function of θ." Kingma. (2019). An Introduction to Variational Autoencoders. Foundations and Trends in Machine Learning.
"This is due to the integral ... for computing the marginal likelihood ..., not having an analytic solution or efficient estimator." Kingma. (2019). An Introduction to Variational Autoencoders. Foundations and Trends in Machine Learning.
"The intractability of pθ(x), is related to the intractability of the posterior distribution pθ(z|x). ... Since pθ(x, z) is tractable to compute, a tractable marginal likelihood pθ(x) leads to a tractable posterior pθ(z|x), and vice versa. Both are intractable in DLVMs." Kingma. (2019). An Introduction to Variational Autoencoders. Foundations and Trends in Machine Learning.
"We use the term deep latent variable model (DLVM) to denote a latent variable model pθ(x, z) whose distributions are parameterized by neural networks." Kingma. (2019). An Introduction to Variational Autoencoders. Foundations and Trends in Machine Learning.
