|
About
NeuroCOLT
Papers
Archive
Books
info@neurocolt.org
|
NeuroCOLT
Technical Report NC-TR-97-004
Comparing
Predictive Inference Methods for Discrete Domains
Petri
Kontkanen, Petri Myllymäki, Tom Silander, Henry Tirri
University of Helsinki
Finland
Peter
Grunwald
CWI, Amsterdam
The Netherlands
Abstract
Predictive inference is seen here as the process of determining
the predictive distribution of a discrete variable, given a data set
of training examples and the values for the other problem domain variables.
We consider three approaches for computing this predictive distribution,
and assume that the joint probability distribution for the variables
belongs to a set of distributions determined by a set of parametric
models. In the simplest case, the predictive distribution is computed
by using the model with the maximum a posteriori (MAP) posterior
probability. In the evidence approach, the predictive distribution
is obtained by averaging over all the individual models in the model
family. In the third case, we define the predictive distribution by
using Rissanen's new definition of stochastic complexity.
Our experiments performed with the family of Naive Bayes models suggest
that when using all the data available, the stochastic complexity
approach produces the most accurate predictions in the log-score sense.
However, when the amount of available training data is decreased,
the evidence approach clearly outperforms the two other approaches.
The MAP predictive distribution is clearly inferior in the log-score
sense to the two more sophisticated approaches, but for the 0/1-score
the MAP approach may still in some cases produce the best results.
Download Compressed
Postscript
Title
Page
|