Exponential family extensions of principal component analysis (EPCA) have
received a considerable amount of attention in recent years, demonstrating the
growing need for basic modeling tools that do not assume the squared loss or
Gaussian distribution. We extend the EPCA model toolbox by presenting the first
exponential family multi-view learning methods of the partial least squares and
canonical correlation analysis, based on a unified representation of EPCA as
matrix factorization of the natural parameters of exponential family. The
models are based on a new family of priors that are generally usable for all
such factorizations. We also introduce new inference strategies, and
demonstrate how the methods outperform earlier ones when the Gaussianity
assumption does not hold.