Density Estimation via Discrepancy

Kun Yang; Hao Su; Wing Hung Wang

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arXiv · 1509.06831

Density Estimation via Discrepancy

Kun Yang·Hao Su·Wing Hung Wang

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Abstract

Given i.i.d samples from some unknown continuous density on hyper-rectangle $[0, 1]^d$, we attempt to learn a piecewise constant function that approximates this underlying density non-parametrically. Our density estimate is defined on a binary split of $[0, 1]^d$ and built up sequentially according to discrepancy criteria; the key ingredient is to control the discrepancy adaptively in each sub-rectangle to achieve overall bound. We prove that the estimate, even though simple as it appears, preserves most of the estimation power. By exploiting its structure, it can be directly applied to some important pattern recognition tasks such as mode seeking and density landscape exploration. We demonstrate its applicability through simulations and examples.

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BibTeX RIS

Kun Yang, Hao Su, Wing Hung Wang. 2015-09-23. Density Estimation via Discrepancy. https://arxiv.org/abs/1509.06831

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