Bayesian Exponential Family PCA
Shakir Mohamed, Katherine Heller and Zoubin Ghahramani
In: NIPS 2008, Vancouver, Canada(2008).
Principal Components Analysis (PCA) has become established as one of the key tools for dimensionality reduction when dealing with real valued data. Ap- proaches such as exponential family PCA and non-negative matrix factorisation have successfully extended PCA to non-Gaussian data types, but these techniques fail to take advantage of Bayesian inference and can suffer from problems of over- fitting and poor generalisation. This paper presents a fully probabilistic approach to PCA, which is generalised to the exponential family, based on Hybrid Monte Carlo sampling. We describe the model which is based on a factorisation of the observed data matrix, and show performance of the model on both synthetic and real data.