Adaptive and self-averaging Thouless-Anderson-Palmer mean-field theory for probabilistic modeling.
Adaptive and self-averaging Thouless-Anderson-Palmer mean-field theory for probabilistic modeling.
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用于概率建模的自适应和自平均 Thouless-Anderson-Palmer 平均场理论。
DOI：
10.1103/physreve.64.056131
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
O. Winther
中科院分区：
文献类型：
--
作者：
M. Opper;O. Winther
我们开发了一个推广的Thouless-Anderson-Palmer（TAP）平均场方法的无序物理，这使得该方法适用于计算近似平均值的概率模型的真实的数据。在传统的TAP方法，其中的随机变量之间的耦合分布的知识是必需的，我们的方法适应于具体的一组耦合。我们显示的方法的意义在两个方面：我们的方法再现副本对称的结果为广泛的一类玩具模型（假设一个非玻璃相）与给定的无序分布的热力学极限。另一方面，在真实的数据模型上的仿真表明，与传统的TAP方法相比，该方法实现了更准确的预测。
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.