## Univariate Polynomial Inference by Monte Carlo Message Length Approximation

#### Leigh J. Fitzgibbon, David L. Dowe, & Lloyd Allison,
Nineteenth International Conference on Machine Learning (ICML-2002),
Sydney, Australia,
8-12 July **2002**

**2002**

**Abstract**:
We apply the Message from Monte Carlo (MMC) algorithm to
inference of univariate polynomials. MMC is an algorithm for
point estimation from a Bayesian posterior sample. It partitions the
posterior sample into sets of regions that contain similar models.
Each region has an associated message length (given by
Dowe's MMLD approximation) and a point estimate that is
representative of models in the region. The regions and point
estimates are chosen so that the Kullback-Leibler distance between
models in the region and the associated point estimate is small
(using Wallace's FSMML Boundary Rule). We compare the MMC
algorithm's point estimation performance with Minimum Message Length [12]
and Structural Risk Minimisation on a set of ten polynomial and
non-polynomial functions with Gaussian noise. The orthonormal
polynomial parameters are sampled using reversible jump Markov
chain Monte Carlo methods.

[preprint.html][6/'02].