The paper introduces a stochastic variational inference and learning algorithm that scales to large datasets. The contribution is two folds.
(1) A reparameterization of the variational lower bound yields a lower bound estimator that can be straightforwardly optimized using standard stochastic gradient methods.
(2) Datasets with continuous latent variables per data point, posterior inference can be made especially efficient by fitting an approximate inference model to the intractable posterior using the proposed lower bound estimator.
1. Lower bound estimator, a stochastic objective function, can be derived for a variety of directed graphical models with continuous latent variables using VAE.
2. Important equations to reach the VAE:
The marginal likelihood has been written as the sum of two terms: (1) KL divergence (regularization term) and (2) variational lower bound on the marginal likelihood ( expected negative reconstruction error).
3. Reparameterization trick: Let z be a continuous random variable with some distribution conditioned on x. It can be expressed as the output of a function g() with some parameter.
4. The steps in the VAE is (1) encode, (2) reparametrize and (3) decode. Then the reconstruction loss is used to optimize.
Fundamental paper for VAE. Need to derive the equation by hand to understand better.