  The logistic normal distribution has recently been adapted via the
transformation of multivariate Gaus- sian variables to model the topical
distribution of documents in the presence of correlations among topics. In this
paper, we propose a probit normal alternative approach to modelling correlated
topical structures. Our use of the probit model in the context of topic
discovery is novel, as many authors have so far con- centrated solely of the
logistic model partly due to the formidable inefficiency of the multinomial
probit model even in the case of very small topical spaces. We herein
circumvent the inefficiency of multinomial probit estimation by using an
adaptation of the diagonal orthant multinomial probit in the topic models
context, resulting in the ability of our topic modelling scheme to handle
corpuses with a large number of latent topics. An additional and very important
benefit of our method lies in the fact that unlike with the logistic normal
model whose non-conjugacy leads to the need for sophisticated sampling schemes,
our ap- proach exploits the natural conjugacy inherent in the auxiliary
formulation of the probit model to achieve greater simplicity. The application
of our proposed scheme to a well known Associated Press corpus not only helps
discover a large number of meaningful topics but also reveals the capturing of
compellingly intuitive correlations among certain topics. Besides, our proposed
approach lends itself to even further scalability thanks to various existing
high performance algorithms and architectures capable of handling millions of
documents.
