# MDL Histogram Density Estimation

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Petri Kontkanen,
Petri Myllymäki
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Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, PMLR 2:219-226, 2007.

#### Abstract

We regard histogram density estimation as a model selection problem. Our approach is based on the information-theoretic minimum description length (MDL) principle, which can be applied for tasks such as data clustering, density estimation, image denoising and model selection in general. MDL-based model selection is formalized via the normalized maximum likelihood (NML) distribution, which has several desirable optimality properties. We show how this framework can be applied for learning generic, irregular (variable-width bin) histograms, and how to compute the NML model selection criterion efficiently. We also derive a dynamic programming algorithm for finding both the MDL-optimal bin count and the cut point locations in polynomial time. Finally, we demonstrate our approach via simulation tests.

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