### Roland Orre and Anders Lansner.

### Abstract

We model a part of a process in pulp to paper production using
Bayesian mixture density networks.
A set of parameters measuring paper quality is predicted from
a set of process values.
In most *regression* models,
the response output is a real value but in this mixture density model
the output is an approximation of the density function for a response
variable conditioned by an explanatory variable value, i.e.,
**f_Y(y|X=x)**. This density function gives information about the confidence
interval for the predicted value as well as modality of the density.
The representation is Gaussian RBFs *(Radial Basis Functions)*,
which model the *a priori* density for each variable space,
using the stochastic EM *(Expectation Maximization)* algorithm for
calculation of positions and variances.
Bayesian associative connections are used to generate
the response variable *a posteriori* density.
We found that this method, with only two design parameters,
performs comparably well with backpropagation on the same data.

**keywords:** mixture density neural network function approximation

**Pulp quality modelling using Bayesian mixture density neural networks.**
*Journal of Systems Engineering*, 6:128-136, 1996.

(PDF)
Pulp Quality Modelling Using
Bayesian Mixture Density Neural Networks

Roland Orre
Last modified: Mon May 31 13:32:41 CEST 2010