Distance Dependent Infinite Latent Feature Models

TL;DR

This paper introduces the distance dependent Indian buffet process (dd-IBP), a Bayesian nonparametric model that captures non-exchangeable data dependencies through distance measures, enabling flexible feature sharing.

Contribution

It generalizes the IBP by incorporating data point distances, providing a new framework for modeling non-exchangeable data with theoretical analysis and a practical MCMC inference method.

Findings

dd-IBP captures temporal and spatial dependencies effectively

The MCMC sampler performs well on non-exchangeable datasets

The model generalizes the original IBP as a special case

Abstract

Latent feature models are widely used to decompose data into a small number of components. Bayesian nonparametric variants of these models, which use the Indian buffet process (IBP) as a prior over latent features, allow the number of features to be determined from the data. We present a generalization of the IBP, the distance dependent Indian buffet process (dd-IBP), for modeling non-exchangeable data. It relies on distances defined between data points, biasing nearby data to share more features. The choice of distance measure allows for many kinds of dependencies, including temporal and spatial. Further, the original IBP is a special case of the dd-IBP. In this paper, we develop the dd-IBP and theoretically characterize its feature-sharing properties. We derive a Markov chain Monte Carlo sampler for a linear Gaussian model with a dd-IBP prior and study its performance on several non-exchangeable data sets.