تقرير
Better Locally Private Sparse Estimation Given Multiple Samples Per User
| العنوان: | Better Locally Private Sparse Estimation Given Multiple Samples Per User |
|---|---|
| المؤلفون: | Ma, Yuheng, Jia, Ke, Yang, Hanfang |
| المصدر: | ICML2024 Proceedings |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Statistics |
| مصطلحات موضوعية: | Statistics - Machine Learning, Computer Science - Machine Learning, Statistics - Methodology |
| الوصف: | Previous studies yielded discouraging results for item-level locally differentially private linear regression with $s^*$-sparsity assumption, where the minimax rate for $nm$ samples is $\mathcal{O}(s^{*}d / nm\varepsilon^2)$. This can be challenging for high-dimensional data, where the dimension $d$ is extremely large. In this work, we investigate user-level locally differentially private sparse linear regression. We show that with $n$ users each contributing $m$ samples, the linear dependency of dimension $d$ can be eliminated, yielding an error upper bound of $\mathcal{O}(s^{*2} / nm\varepsilon^2)$. We propose a framework that first selects candidate variables and then conducts estimation in the narrowed low-dimensional space, which is extendable to general sparse estimation problems with tight error bounds. Experiments on both synthetic and real datasets demonstrate the superiority of the proposed methods. Both the theoretical and empirical results suggest that, with the same number of samples, locally private sparse estimation is better conducted when multiple samples per user are available. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2408.04313 |
| رقم الأكسشن: | edsarx.2408.04313 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |