Antti Honkela, Harri Valpola
In this paper we present a framework for using multi-layer per- ceptron (MLP) networks in nonlinear generative models trained by variational Bayesian learning. The nonlinearity is handled by linearizing it using a Gauss–Hermite quadrature at the hidden neu- rons. This yields an accurate approximation for cases of large pos- terior variance. The method can be used to derive nonlinear coun- terparts for linear algorithms such as factor analysis, independent component/factor analysis and state-space models. This is demon- strated with a nonlinear factor analysis experiment in which even 20 sources can be estimated from a real world speech data set.