Factorisation and denoising of 0–1 data: A variational approach

Presence–absence (0–1) observations are special in that often the absence of evidence is not evidence of absence. Here we develop an independent factor model, which has the unique capability to isolate the former as an independent discrete binary noise factor. This representation then forms the basis of inferring missed presences by means of denoising. This is achieved in a probabilistic formalism, employing independent beta latent source densities and a Bernoulli data likelihood model. Variational approximations are employed to make the inferences tractable. We relate our model to existing models of 0–1 data, demonstrating its advantages for the problem considered, and we present applications in several problem domains, including social network analysis and DNA fingerprint analysis.