The definition of the usual Boltzmann machine is extended to allow for
neurons with polytomous (multicategory) rather than simply binary res
ponses. Updating rules are defined along with the associated stationar
y distributions, and an alternating minimization method is described f
or the purposes of training. Emphasis Is placed on the relevance of st
atistical ideas, including polytomous logistic regression, the iterati
ve proportional fitting procedure and the EM algorithm. The paper buil
ds on previous work in [1] and [2].