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Density Estimation via Discrepancy Based...
Li, Dangna...

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Density Estimation via Discrepancy Based Adaptive Sequential Partition by Li, Dangna ( Author )
Lemonjar Open Access
Australian National University
01-09-2023
Given $iid$ observations from an unknown absolute 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 a provable convergence rate. We empirically demonstrate its efficiency as a density estimation method. We present its applications on a wide range of tasks, including finding good initializations for k-means.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1404.1425
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