The information bottleneck (IB) method is an information-theoretic formulation for clustering problems. Given a joint distribution (x, y), this method constructs a new variable that defines partitions over the values of X that are informative about Y. Maximum likelihood (ML) of mixture models is a standard statistical approach to clustering problems. In this paper, we ask: how are the two methods related ? We define a simple mapping between the IB problem and the ML problem for the multinomial mixture model. We show that under this mapping the problems are strongly related. In fact, for uniform input distribution over X or for large sample size, the problems are mathematically equivalent. Specifically, in these cases, every fixed point of the IB-functional defines a fixed point of the (log) likelihood and vice versa. Moreover, the values of the functionals at the fixed points are equal under simple transformations. As a result, in these cases, every algorithm that solves one of the problems, induces a solution for the other.
|Title of host publication
|Subtitle of host publication
|Proceedings of the 15th International Conference on Neural Information Processing Systems
|Suzanna Becker, Sebastian Thrun, Klaus Obermayer
|MIT Press Journals
|Number of pages
|Published - 2002
|15th International Conference on Neural Information Processing Systems, NIPS 2002 - Vancouver, Canada
Duration: 9 Dec 2002 → 14 Dec 2002
|NIPS 2002: Proceedings of the 15th International Conference on Neural Information Processing Systems
|15th International Conference on Neural Information Processing Systems, NIPS 2002
|9/12/02 → 14/12/02
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