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Abstract:
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Latent feature models seek to uncover hidden categorical variables that explain observed data. These models often use the Indian buffet process (IBP), a distribution over a binary feature matrix with an infinite number of columns and one row per observation. The IBP assumes that the observations are exchangeable, which is not reasonable in the presence of pairwise similarity information. We propose the attraction Indian buffet distribution (aIBD), a distribution for a binary feature matrix indexed by pairwise similarity. Our formulation preserves many of the properties of the original IBP, including having the same distribution of the total number of features. Thus, much of the interpretation and intuition that one has for the IBP carries over directly to our aIBD. A temperature parameter controls the degree to which the similarity information affects feature sharing. The probability function can be written explicitly and has a tractable normalizing constant, making posterior inference on hyperparameters straight-forward using standard MCMC methods. We demonstrate the feasibility and performance of our method in examples.
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