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Selecting n data points whose average is nearly as good as the mean
Find the worst-case loss ratio when the mean of a planar dataset is replaced by the best average of n of its points.
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| 1 | +{ | |
| 2 | + "domain": "computer-science", | |
| 3 | + "topics": [ | |
| 4 | + "learning-theory", | |
| 5 | + "discrete-geometry" | |
| 6 | + ], | |
| 7 | + "type": "proof", | |
| 8 | + "also": [ | |
| 9 | + "construction" | |
| 10 | + ], | |
| 11 | + "source": { | |
| 12 | + "key": "colt", | |
| 13 | + "name": "COLT open problems", | |
| 14 | + "url": "https://proceedings.mlr.press/v291/hanneke25e.html", | |
| 15 | + "id": "v291/hanneke25e", | |
| 16 | + "curator": "Conference on Learning Theory (COLT)", | |
| 17 | + "poser": "Steve Hanneke, Shay Moran, Alexander Shlimovich and Amir Yehudayoff", | |
| 18 | + "status": "open", | |
| 19 | + "as_of": "2026-10-20", | |
| 20 | + "catalog": "0521c19bbd38" | |
| 21 | + } | |
| 22 | +} | |