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Density Estimation via Discrepancy Based Adaptive Sequential Partition
Dangna Li · Kun Yang · Wing Hung Wong

Tue Dec 06 09:00 AM -- 12:30 PM (PST) @ Area 5+6+7+8 #57
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.

Author Information

Dangna Li (Stanford university)
Kun Yang (Google Inc)
Wing Hung Wong (Stanford university)

Wing Hung Wong is currently Professor of Statistics and Professor of Biomedical Data Science at Stanford University. He had held teaching positions at the University of Chicago (1980-1994), The Chinese University of Hong Kong (1994-1997), UCLA (1997-2000) and Harvard University (2000-2004), before joining Stanford University in 2004. His research contributions include 1) mathematical statistics, where he clarified the large sample properties of sieve maximum likelihood estimates in general spaces; 2) Bayesian statistics, where he introduced sampling-based algorithms into Bayesian computational inference; and 3) computational biology, where he developed basic models and methods for the analysis of microarrays gene expression data and RNA sequencing data. He is a member of the US National Academy of Sciences, the Academia Sinica, and the Academy of Sciences of Hong Kong.

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