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Paper · 1504.01227 · 2015

Chebyshev polynomials, moment matching, and optimal estimation of the unseen

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 3 functions out of this paper's own repositories and ran 3 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
Albuso0/support reimplementation 3 of 3
FunctionStatusWhere it lives
get_sample_size Ran Albuso0/support/support.py
pointer only (licence: NONE) · get_code("3c21a2aea30fbfce")
hist_to_fin Ran Albuso0/support/support.py
pointer only (licence: NONE) · get_code("316f4171d5206404")
sample_to_fin Ran Albuso0/support/support.py
pointer only (licence: NONE) · get_code("63fc527bb9e69717")

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Abstract

We consider the problem of estimating the support size of a discrete distribution whose minimum non-zero mass is at least $ \frac{1}{k}$. Under the independent sampling model, we show that the sample complexity, i.e., the minimal sample size to achieve an additive error of $εk$ with probability at least 0.1 is within universal constant factors of $ \frac{k}{\log k}\log^2\frac{1}ε $, which improves the state-of-the-art result of $ \frac{k}{ε^2 \log k} $ in \cite{VV13}. Similar characterization of the minimax risk is also obtained. Our procedure is a linear estimator based on the Chebyshev polynomial and its approximation-theoretic properties, which can be evaluated in $O(n+\log^2 k)$ time and attains the sample complexity within a factor of six asymptotically. The superiority of the proposed estimator in terms of accuracy, computational efficiency and scalability is demonstrated in a variety of synthetic and real datasets.

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