  We propose a parsimonious topic model for text corpora. In related models
such as Latent Dirichlet Allocation (LDA), all words are modeled
topic-specifically, even though many words occur with similar frequencies
across different topics. Our modeling determines salient words for each topic,
which have topic-specific probabilities, with the rest explained by a universal
shared model. Further, in LDA all topics are in principle present in every
document. By contrast our model gives sparse topic representation, determining
the (small) subset of relevant topics for each document. We derive a Bayesian
Information Criterion (BIC), balancing model complexity and goodness of fit.
Here, interestingly, we identify an effective sample size and corresponding
penalty specific to each parameter type in our model. We minimize BIC to
jointly determine our entire model -- the topic-specific words,
document-specific topics, all model parameter values, {\it and} the total
number of topics -- in a wholly unsupervised fashion. Results on three text
corpora and an image dataset show that our model achieves higher test set
likelihood and better agreement with ground-truth class labels, compared to LDA
and to a model designed to incorporate sparsity.
