基于配分函数的失配估计误差分析
Analysis of Mismatched Estimation Errors Using Gradients of Partition Functions
摘要：
我们考虑的问题，信号估计（去噪）从一个物理力学的角度来看，在最近的工作中的分析均方误差（MSE）估计使用最佳估计和某些分区函数之间的直接关系的延续。本文件主要由两部分组成。在第一部分中，使用上述关系，我们推导出一个码字（从随机选择的代码）的不匹配的MSE的单字母表达式，高斯矢量信道损坏。在第二部分中，我们提供了几个例子来演示MSE行为中的相变。这些例子使我们能够更深入地理解和收集关于真实和不匹配的概率度量在创建这些相变中的作用的直觉。
英文摘要：
We consider the problem of signal estimation (denoising) from a statistical-mechanical perspective, in continuation to a recent work on the analysis of mean-square error (MSE) estimation using a direct relationship between optimum estimation and certain partition functions. The paper consists of essentially two parts. In the first part, using the aforementioned relationship, we derive single-letter expressions of the mismatched MSE of a codeword (from a randomly selected code), corrupted by a Gaussian vector channel. In the second part, we provide several examples to demonstrate phase transitions in the behavior of the MSE. These examples enable us to understand more deeply and to gather intuition regarding the roles of the real and the mismatched probability measures in creating these phase transitions.
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