  We introduce a novel, probabilistic binary latent variable model to detect
noisy or approximate repeats of patterns in sparse binary data. The model is
based on the "Noisy-OR model" (Heckerman, 1990), used previously for disease
and topic modelling. The model's capability is demonstrated by extracting
structure in recordings from retinal neurons, but it can be widely applied to
discover and model latent structure in noisy binary data. In the context of
spiking neural data, the task is to "explain" spikes of individual neurons in
terms of groups of neurons, "Cell Assemblies" (CAs), that often fire together,
due to mutual interactions or other causes. The model infers sparse activity in
a set of binary latent variables, each describing the activity of a cell
assembly. When the latent variable of a cell assembly is active, it reduces the
probabilities of neurons belonging to this assembly to be inactive. The
conditional probability kernels of the latent components are learned from the
data in an expectation maximization scheme, involving inference of latent
states and parameter adjustments to the model. We thoroughly validate the model
on synthesized spike trains constructed to statistically resemble recorded
retinal responses to white noise stimulus and natural movie stimulus in data.
We also apply our model to spiking responses recorded in retinal ganglion cells
(RGCs) during stimulation with a movie and discuss the found structure.
