Inference by replication in densely connected systems.
Inference by replication in densely connected systems.
复制标题
在密集连接的系统中通过复制进行推理。
DOI：
10.1103/physreve.76.046121
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
D. Saad
中科院分区：
文献类型：
--
作者：
J. Neirotti;D. Saad
针对可映射到稠密图上的问题，提出了一种有效的贝叶斯推理方法。该方法基于消息传递，其中消息在暴露于相同证据节点的大量复制变量系统上被平均。求平均值需要假设解的对称性；在这里，我们扩展了以前基于类复制对称(RS)结构的推导，以包括更复杂的一步类复制对称破缺(1RSB-like)ansatz。为了验证该方法的潜力，将其用于研究不同噪声模型下的Ising线性感知器的临界特性和码分多址(CDMA)中的多用户检测。在非临界区的RS假设下得到的结果给出了在码分多址环境下的一种高效的信号检测算法；而在临界区，人们观察到一条结束于连续相变点的一阶转移线。还观察到了有限尺寸效应。虽然1RSB ansatz不是原始问题所必需的，但它被应用到具有更复杂的噪声模型的CDMA信号检测问题中，该模型表现出RSB行为，从而提高了性能。
An efficient Bayesian inference method for problems that can be mapped onto dense graphs is presented. The approach is based on message passing where messages are averaged over a large number of replicated variable systems exposed to the same evidential nodes. An assumption about the symmetry of the solutions is required for carrying out the averages; here we extend the previous derivation based on a replica-symmetric- (RS)-like structure to include a more complex one-step replica-symmetry-breaking-like (1RSB-like) ansatz. To demonstrate the potential of the approach it is employed for studying critical properties of the Ising linear perceptron and for multiuser detection in code division multiple access (CDMA) under different noise models. Results obtained under the RS assumption in the noncritical regime give rise to a highly efficient signal detection algorithm in the context of CDMA; while in the critical regime one observes a first-order transition line that ends in a continuous phase transition point. Finite size effects are also observed. While the 1RSB ansatz is not required for the original problems, it was applied to the CDMA signal detection problem with a more complex noise model that exhibits RSB behavior, resulting in an improvement in performance.