  We consider analysis of relational data (a matrix), in which the rows
correspond to subjects (e.g., people) and the columns correspond to attributes.
The elements of the matrix may be a mix of real and categorical. Each subject
and attribute is characterized by a latent binary feature vector, and an
inferred matrix maps each row-column pair of binary feature vectors to an
observed matrix element. The latent binary features of the rows are modeled via
a multivariate Gaussian distribution with low-rank covariance matrix, and the
Gaussian random variables are mapped to latent binary features via a probit
link. The same type construction is applied jointly to the columns. The model
infers latent, low-dimensional binary features associated with each row and
each column, as well correlation structure between all rows and between all
columns.
