2021 Volume 36 Issue 3 Pages A-KA4_1-9
We propose the Student-t variational autoencoder (VAE), which is a robust multivariate density estimatorbased on the VAE. The VAE is a powerful deep generative model, and used for multivariate density estimation. Withthe original VAE, the distribution of observed continuous variables is assumed to be a Gaussian, where its mean andvariance are modeled by deep neural networks taking latent variables as their inputs. This distribution is called thedecoder. However, the training of VAE often becomes unstable. One reason is that the decoder of VAE is sensitiveto the error between the data point and its estimated mean when its estimated variance is almost zero. To solve thisinstability problem, our Student-t VAE uses a Student-t distribution as the decoder. This distribution is a heavytaileddistribution, of which the probability in the tail region is higher than that of a light-tailed distribution such as aGaussian. Therefore, the Student-t decoder is robust to the error between the data point and its estimated mean, whichmakes the training of the Student-t VAE stable. Numerical experiments with various datasets show that training ofthe Student-t VAE is robust, and the Student-t VAE achieves high density estimation performance.
