Opper M, Winther O
Neural Computing Research Group, School of Engineering and Applied Science, Aston University, Birmingham B4 7ET, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Nov;64(5 Pt 2):056131. doi: 10.1103/PhysRevE.64.056131. Epub 2001 Oct 30.
We develop a generalization of the Thouless-Anderson-Palmer (TAP) mean-field approach of disorder physics, which makes the method applicable to the computation of approximate averages in probabilistic models for real data. In contrast to the conventional TAP approach, where the knowledge of the distribution of couplings between the random variables is required, our method adapts to the concrete set of couplings. We show the significance of the approach in two ways: Our approach reproduces replica symmetric results for a wide class of toy models (assuming a nonglassy phase) with given disorder distributions in the thermodynamic limit. On the other hand, simulations on a real data model demonstrate that the method achieves more accurate predictions as compared to conventional TAP approaches.
我们开发了一种无序物理中 Thouless-Anderson-Palmer（TAP）平均场方法的推广，这使得该方法适用于计算实际数据概率模型中的近似平均值。与传统的 TAP 方法不同，传统方法需要知道随机变量之间耦合分布的知识，而我们的方法适用于具体的耦合集。我们通过两种方式展示了该方法的重要性：在热力学极限下，对于具有给定无序分布的一大类玩具模型（假设为非玻璃态相），我们的方法重现了 replica 对称结果。另一方面，对实际数据模型的模拟表明，与传统的 TAP 方法相比，该方法能实现更准确的预测。
