### 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
pulp quality is predicted from a set of process values. The values
being predicted are results from time consuming laboratory experiments.
In most *regression* models, like the error backpropagation
network, the 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 a certain 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.
Explanatory and response variable spaces are represented by Gaussian
RBF:s * (Radial Basis Functions)* using the stochastic EM
*(Expectation Maximization)* algorithm for calculation
of positions and variances. These RBF:s or
*(density functions)* model the *a priori* density for each
variable space. Bayesian associative connections
are used to generate
the response variable *a posteriori* density when it is
conditioned by an explanatory variable value.
We found that this method for function approximation performs
comparably well with the best backpropagation network we could find
on the same pulp and paper data.
It is also straight forward to use with just two design parameters, the
number of units which code the explanatory
and response variables respectively.

**Pulp quality modelling using Bayesian mixture density neural networks.**

In A. Bulsari and S. Kallio, editors, *Engineering Applications of Artificial Neural Networks*,
pages 351-358, Otaniemi, Finland, August 21-23 1995. Finnish Artificial Intelligence Society.
Proc. EANN-95

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

Roland Orre
Last modified: Mon May 31 13:27:53 CEST 2010