Gamma-VAE: Speech representation based on VAE assuming gamma distribution for both latent variables and observation

In recent years, deep generative models that can represent complex relationships in data generation have attracted significant attention. One example is the variational autoencoder (VAE), which usually assumes a Gaussian distribution for both the encoder and decoder and often utilizes amplitude spectra because they are suitable as input features. However, the amplitude spectrum is always positive because it is a Fourier transform of the aperiodic waveform and is taken in the absolute value. Thus, a Gaussian distribution is not appropriate to assume a Gaussian distribution when using VAE with amplitude spectra as the input features. As an alternative, we propose the Gamma-VAE, which is a VAE that assumes a gamma distribution; a probability distribution that considers only positive values; and a method of back-propagation by the reparameterization trick, which also assumes a gamma distribution for latent variables. Experiments using various evaluation methods showed the effectiveness of Gamma-VAE.