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Density Estimation via Discrepancy Based Adaptive Sequential Partition

Dangna Li · Kun Yang · Wing Hung Wong

Area 5+6+7+8 #57

Keywords: [ (Other) Machine Learning Topics ] [ (Other) Statistics ] [ Clustering ]

Abstract: Given $iid$ observations from an unknown continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function. Our density estimate is a piecewise constant function defined on a binary partition of $\Omega$. The key ingredient of the algorithm is to use discrepancy, a concept originates from Quasi Monte Carlo analysis, to control the partition process. The resulting algorithm is simple, efficient, and has provable convergence rate. We demonstrate empirically its efficiency as a density estimation method. We also show how it can be utilized to find good initializations for k-means.

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