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Conference Paper: Learning Entangled Single-Sample Gaussians in the Subset-of-Signals Model
Title | Learning Entangled Single-Sample Gaussians in the Subset-of-Signals Model |
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Authors | |
Keywords | Entangled Gaussians Mean Estimation Subset-of-Signals |
Issue Date | 2020 |
Citation | Proceedings of Machine Learning Research, 2020, v. 125, p. 2712-2737 How to Cite? |
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 (√n ln n/m) with high probability when m = Ω(√n ln n), slightly improving existing bounds for this range of m. We further prove lower bounds, showing that the error is Ω ((n/m4)1/2) when m is between Ω(ln n) and O(n1/4), and the error is Ω ((n/m4)1/6) when m is between Ω(n1/4) and O(n1−ε) for an arbitrarily small ε > 0, improving existing lower bounds and extending to a wider range of m. |
Persistent Identifier | http://hdl.handle.net/10722/341401 |
DC Field | Value | Language |
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dc.contributor.author | Liang, Yingyu | - |
dc.contributor.author | Yuan, Hui | - |
dc.date.accessioned | 2024-03-13T08:42:32Z | - |
dc.date.available | 2024-03-13T08:42:32Z | - |
dc.date.issued | 2020 | - |
dc.identifier.citation | Proceedings of Machine Learning Research, 2020, v. 125, p. 2712-2737 | - |
dc.identifier.uri | http://hdl.handle.net/10722/341401 | - |
dc.description.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 (√n ln n/m) with high probability when m = Ω(√n ln n), slightly improving existing bounds for this range of m. We further prove lower bounds, showing that the error is Ω ((n/m4)1/2) when m is between Ω(ln n) and O(n1/4), and the error is Ω ((n/m4)1/6) when m is between Ω(n1/4) and O(n1−ε) for an arbitrarily small ε > 0, improving existing lower bounds and extending to a wider range of m. | - |
dc.language | eng | - |
dc.relation.ispartof | Proceedings of Machine Learning Research | - |
dc.subject | Entangled Gaussians | - |
dc.subject | Mean Estimation | - |
dc.subject | Subset-of-Signals | - |
dc.title | Learning Entangled Single-Sample Gaussians in the Subset-of-Signals Model | - |
dc.type | Conference_Paper | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.scopus | eid_2-s2.0-85158076811 | - |
dc.identifier.volume | 125 | - |
dc.identifier.spage | 2712 | - |
dc.identifier.epage | 2737 | - |
dc.identifier.eissn | 2640-3498 | - |