基于Quantization约束的分散数据约简
Decentralized Data Reduction with Quantization Constraints
摘要：
在统计推断中，数据简化的一个指导原则是充分性原则。本文将经典的充分性原理扩展到分散推理，即，数据减少需要以分散的方式实现。我们研究了局部和全局充分统计量的概念，以及在不同的观测模型下，分散推理两者之间的关系。然后，我们考虑的影响，量化分散的数据减少时，传感器之间的通信往往需要有限的容量限制。我们要问的中心问题是：如果分散式推理系统中的每个节点都必须使用有限数量的比特来总结其数据，那么在量化之前使用全局充分统计来实现数据简化仍然是最优的吗？我们表明，答案是否定的，使用一个简单的例子，并继续确定条件下，充分的数据减少，然后量化确实是最佳的。它们包括众所周知的情况下，在分散节点的数据是条件独立的，以及一类问题的条件相关的意见，承认条件独立的结构，通过引入一个适当选择的隐藏变量。
英文摘要：
A guiding principle for data reduction in statistical inference is the sufficiency principle. This paper extends the classical sufficiency principle to decentralized inference, i.e., data reduction needs to be achieved in a decentralized manner. We examine the notions of local and global sufficient statistics and the relationship between the two for decentralized inference under different observation models. We then consider the impacts of quantization on decentralized data reduction which is often needed when communications among sensors are subject to finite capacity constraints. The central question we intend to ask is: if each node in a decentralized inference system has to summarize its data using a finite number of bits, is it still optimal to implement data reduction using global sufficient statistics prior to quantization? We show that the answer is negative using a simple example and proceed to identify conditions under which sufficiency based data reduction followed by quantization is indeed optimal. They include the well known case when the data at decentralized nodes are conditionally independent as well as a class of problems with conditionally dependent observations that admit conditional independence structure through the introduction of an appropriately chosen hidden variable.
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