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首页> 外文期刊>Journal of statistical mechanics: Theory and Experiment >A statistical physics approach to learning curves for the inverse Ising problem
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A statistical physics approach to learning curves for the inverse Ising problem

机译：一种统计物理方法对逆误区的学习曲线

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摘要

Using methods of statistical physics, we analyse the error of learning couplings in large Ising models from independent data (the inverse Ising problem). We concentrate on learning based on local cost functions, such as the pseudo-likelihood method for which the couplings are inferred independently for each spin. Assuming that the data are generated from a true Ising model, we compute the reconstruction error of the couplings using a combination of the replica method with the cavity approach for densely connected systems. We show that an explicit estimator based on a quadratic cost function achieves minimal reconstruction error, but requires the length of the true coupling vector as prior knowledge. A simple mean field estimator of the couplings which does not need such knowledge is asymptotically optimal, i.e. when the number of observations is much larger than the number of spins. Comparison of the theory with numerical simulations shows excellent agreement for data generated from two models with random couplings in the high temperature region: a model with independent couplings (Sherrington-Kirkpatrick model), and a model where the matrix of couplings has a Wishart distribution.
机译：使用统计物理方法，我们从独立数据（逆误差问题）分析了大型型号中的学习耦合的误差。我们专注于基于本地成本函数的学习，例如对每个旋转独立推断耦合的伪似然方法。假设数据是从真实的insing模型生成的，我们使用副本方法的组合来计算耦合的重建误差，其中具有用于密集连接的系统的腔方法。我们表明，基于二次成本函数的显式估算器实现了最小的重建误差，但需要真正耦合向量的长度作为先验知识。不需要这些知识的联轴器的简单平均场估计是渐近最佳的，即，当观察的数量远远大于旋转的数量时。具有数值模拟的理论的比较显示了从高温区域中随机耦合的两种模型产生的良好协议：具有独立耦合的模型（Sherrington-Kirkpatrick模型），以及耦合矩阵具有Wiskart分布的模型。

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