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Learning Entangled Single-Sample Gaussians in the Subset-of-Signals Model | | Yingyu Liang
; Hui Yuan
; | | Date: |
10 Jul 2020 | | Abstract: | In the setting of entangled single-sample distributions, the goal is to
estimate some common parameter shared by a family of $n$ distributions, given
one single sample from each distribution. This paper studies mean estimation
for entangled single-sample Gaussians that have a common mean but different
unknown variances. We propose the subset-of-signals model where an unknown
subset of $m$ variances are bounded by 1 while there are no assumptions on the
other variances. In this model, we analyze a simple and natural method based on
iteratively averaging the truncated samples, and show that the method achieves
error $O left(frac{sqrt{nln n}}{m}
ight)$ with high probability when
$m=Omega(sqrt{nln n})$, matching existing bounds for this range of $m$. We
further prove lower bounds, showing that the error is
$Omegaleft(left(frac{n}{m^4}
ight)^{1/2}
ight)$ when $m$ is between
$Omega(ln n)$ and $O(n^{1/4})$, and the error is
$Omegaleft(left(frac{n}{m^4}
ight)^{1/6}
ight)$ when $m$ is between
$Omega(n^{1/4})$ and $O(n^{1 - epsilon})$ for an arbitrarily small
$epsilon>0$, improving existing lower bounds and extending to a wider range of
$m$. | | Source: | arXiv, 2007.5557 | | Services: | Forum | Review | PDF | Favorites | |
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