I have a classification task and was
reading up on various approaches. In the specific case where all inputs are
categorical, one can use “Bayesian Naïve Bayes” using the Dirichlet distribution.

Poking through the freely available text by Barber, I found a rather detailed discussion in chapters 9 and 10, as well as example
matlab code for the book, so took it upon myself to port it to R as a learning
exercise.

I was not immediately familiar with the
Dirichlet distribution, but in this case it appeals to the intuitive counting
approach to discrete event probabilities.

In a nutshell we use the training data to
learn the posterior distribution, which turns out to be counts of how often a
given event occurs, grouped by class, feature and feature state.

Prediction is a case of counting events in the test vector. The more this count differs from the per-class
trained counts, the lower the probability the current candidate class is a
match.

Anyway, there are three files. The first is
a straightforward port of Barber’s code, but this wasn’t very R-like, and in
particular only seemed to handle input features with the same number of states.

I developed my own version that expects
everything to be represented as factors. It is all a bit rough and ready but
appears to work and there is a test/example script up here. As a bigger test I
ran it on a sample car evaluation data set from here, the confusion matrix is as follows:

testY
acc good unacc vgood

acc 83 3
29 0

good 16 5
0 0

unacc 17 0
346 0

vgood 13 0
0 6

That’s it for now. Comments/feedback appreciated. You can find me on twitter here

Links to files:

Everything in one directory (with data) here