Abstract | ||
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We revisit the problem of learning from untrusted batches introduced by Qiao and Valiant [QV17]. Recently, Jain and Orlitsky [JO19] gave a simple semidefinite programming approach based on the cut-norm that achieves essentially information-theoretically optimal error in polynomial time. Concurrently, Chen et al. [CLM19] considered a variant of the problem where $\mu$ is assumed to be structured, e.g. log-concave, monotone hazard rate, $t$-modal, etc. In this case, it is possible to achieve the same error with sample complexity sublinear in $n$, and they exhibited a quasi-polynomial time algorithm for doing so using Haar wavelets. In this paper, we find an appealing way to synthesize the techniques of [JO19] and [CLM19] to give the best of both worlds: an algorithm which runs in polynomial time and can exploit structure in the underlying distribution to achieve sublinear sample complexity. Along the way, we simplify the approach of [JO19] by avoiding the need for SDP rounding and giving a more direct interpretation of it through the lens of soft filtering, a powerful recent technique in high-dimensional robust estimation. |
Year | Venue | DocType |
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2020 | NIPS 2020 | Conference |
Volume | Citations | PageRank |
33 | 0 | 0.34 |
References | Authors | |
0 | 3 |
Name | Order | Citations | PageRank |
---|---|---|---|
Sitan Chen | 1 | 1 | 6.46 |
Jerry Li | 2 | 229 | 22.67 |
Ankur Moitra | 3 | 892 | 56.19 |