论文标题
在信息约束下进行交互式高维估计的统一下限
Unified lower bounds for interactive high-dimensional estimation under information constraints
论文作者
论文摘要
我们考虑使用受局部信息约束的交互式协议（例如带宽限制，局部差异隐私和限制测量）的分布式参数估计。我们提供了一个统一的框架，使我们能够在任何$ \ ell_p $损失下得出各种（紧密的）minimax下限。我们的下限框架具有多功能性，并且产生了“插件”边界，这些边界广泛适用于各种估计问题，并且对于高斯家族的原型情况，它规避了先前技术的限制。特别是，我们的方法恢复了使用数据处理不平等和cramér-rao界限获得的界限，这是在我们感兴趣的环境中证明下限的另外两种替代方法。此外，对于所考虑的家庭，我们通过匹配的上限来补充下限。
We consider distributed parameter estimation using interactive protocols subject to local information constraints such as bandwidth limitations, local differential privacy, and restricted measurements. We provide a unified framework enabling us to derive a variety of (tight) minimax lower bounds for different parametric families of distributions, both continuous and discrete, under any $\ell_p$ loss. Our lower bound framework is versatile and yields "plug-and-play" bounds that are widely applicable to a large range of estimation problems, and, for the prototypical case of the Gaussian family, circumvents limitations of previous techniques. In particular, our approach recovers bounds obtained using data processing inequalities and Cramér--Rao bounds, two other alternative approaches for proving lower bounds in our setting of interest. Further, for the families considered, we complement our lower bounds with matching upper bounds.
