  We consider the problem of identifying stable sets of mutually associated
features in moderate or high-dimensional binary data. In this context we
develop and investigate a method called Latent Association Mining for Binary
Data (LAMB). The LAMB method is based on a simple threshold model in which the
observed binary values represent a random thresholding of a latent continuous
vector that may have a complex association structure. We consider a measure of
latent association that quantifies association in the latent continuous vector
without bias due to the random thresholding. The LAMB method uses an iterative
testing based search procedure to identify stable sets of mutually associated
features. We compare the LAMB method with several competing methods on
artificial binary-valued datasets and two real count-valued datasets. The LAMB
method detects meaningful associations in these datasets. In the case of the
count-valued datasets, associations detected by the LAMB method are based only
on information about whether the counts are zero or non-zero, and is
competitive with methods that have access to the full count data.
