Private Center Points and Learning of Halfspaces
| Autor: | Beimel, Amos, Moran, Shay, Nissim, Kobbi, Stemmer, Uri |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We present a private learner for halfspaces over an arbitrary finite domain $X\subset \mathbb{R}^d$ with sample complexity $mathrm{poly}(d,2^{\log^*|X|})$. The building block for this learner is a differentially private algorithm for locating an approximate center point of $m>\mathrm{poly}(d,2^{\log^*|X|})$ points -- a high dimensional generalization of the median function. Our construction establishes a relationship between these two problems that is reminiscent of the relation between the median and learning one-dimensional thresholds [Bun et al.\ FOCS '15]. This relationship suggests that the problem of privately locating a center point may have further applications in the design of differentially private algorithms. We also provide a lower bound on the sample complexity for privately finding a point in the convex hull. For approximate differential privacy, we show a lower bound of $m=\Omega(d+\log^*|X|)$, whereas for pure differential privacy $m=\Omega(d\log|X|)$. Comment: 14 pages |
| Databáze: | arXiv |
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