分布式检测中线性数据融合的最大积算法
The Max-Product Algorithm Viewed as Linear Data-Fusion: A Distributed Detection Scenario
摘要：
在本文中，我们公开了最大乘积算法的统计行为，该算法被配置为解决分布式代理网络中的最大后验（MAP）估计问题。具体来说，我们首先建立一个分布式的假设检验进行的最大乘积迭代二进制值成对马尔可夫随机场，并表明所获得的决策变量是线性组合的局部对数似然比在网络中观察到的。然后，我们使用这些线性组合来制定系统的性能方面的虚警和检测概率。我们的研究结果表明，在有关的假设检验中，最大积算法的最佳性能是由一个最佳的线性数据融合方案，最大积算法的行为是非常相似的和-积算法的行为。因此，我们证明了最大乘积迭代的最佳性能是通过线性版本的和-积算法，该算法是基于在每个节点从其一跳邻居收到的统计数据进行优化。最后，我们通过计算机模拟验证了我们的观察。
英文摘要：
In this paper, we disclose the statistical behavior of the max-product algorithm configured to solve a maximum a posteriori (MAP) estimation problem in a network of distributed agents. Specifically, we first build a distributed hypothesis test conducted by a max-product iteration over a binary-valued pairwise Markov random field and show that the decision variables obtained are linear combinations of the local log-likelihood ratios observed in the network. Then, we use these linear combinations to formulate the system performance in terms of the false-alarm and detection probabilities. Our findings indicate that, in the hypothesis test concerned, the optimal performance of the max-product algorithm is obtained by an optimal linear data-fusion scheme and the behavior of the max-product algorithm is very similar to the behavior of the sum-product algorithm. Consequently, we demonstrate that the optimal performance of the max-product iteration is closely achieved via a linear version of the sum-product algorithm which is optimized based on statistics received at each node from its one-hop neighbors. Finally, we verify our observations via computer simulations.
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