Triply stochastic variational inference for non-linear beta process factor analysis

We propose a non-linear extension to factor analysis with beta process priors for improved data representation ability. This non-linear Beta Process Factor Analysis (nBPFA) allows data to be represented as a non-linear transformation of a standard sparse factor decomposition. We develop a scalable variational inference framework, which builds upon the ideas of the variational auto-encoder, by allowing latent variables of the model to be sparse. Our framework can be readily used for real-valued, binary and count data. We show theoretically and with experiments that our training scheme, with additive or multiplicative noise on observations, improves performance and prevents overfitting. We benchmark our algorithms on image, text and collaborative filtering datasets. We demonstrate faster convergence rates and competitive performance compared to standard gradient-based approaches.