Least Square Variational Bayesian Autoencoder with Regularization

In recent years Variation Autoencoders have become one of the most popular unsupervised learning of complicated distributions.Variational Autoencoder (VAE) provides more efficient reconstructive performance over a traditional autoencoder. Variational auto enocders make better approximaiton than MCMC. The VAE defines a generative process in terms of ancestral sampling through a cascade of hidden stochastic layers. They are a directed graphic models. Variational autoencoder is trained to maximise the variational lower bound. Here we are trying maximise the likelihood and also at the same time we are trying to make a good approximation of the data. Its basically trading of the data log-likelihood and the KL divergence from the true posterior. This paper describes the scenario in which we wish to find a point-estimate to the parameters $\theta$ of some parametric model in which we generate each observations by first sampling a local latent variable and then sampling the associated observation. Here we use least square loss function with regularization in the the reconstruction of the image, the least square loss function was found to give better reconstructed images and had a faster training time.