标题： L$_1$ 非平衡Ising模型重构的正则化方法 显示英文标题

标题： L$_1$ Regularization for Reconstruction of a non-equilibrium Ising Model

摘要： 使用精确学习算法重构稀疏非对称异步Ising网络中的耦合。 使用L$_1$正则化来消除虚假的弱连接，否则通过简单地最小化有限数据集的负似然性时会找到这些连接。 为了详细观察L$_1$正则化的工作原理，我们采用多种方法进行计算，包括（1）通过迭代最小化一个等于数据负对数似然加上L$_1$惩罚项的成本函数，以及（2）基于成本函数在其最小值附近的二次展开的近似方案。 在这些方案中，我们跟踪随着L$_1$惩罚强度从零增加到较大值时连接是如何被修剪的。 使用ROC曲线量化各种耦合强度下这些方法的性能。 显示英文摘要

摘要： The couplings in a sparse asymmetric, asynchronous Ising network are reconstructed using an exact learning algorithm. L$_1$ regularization is used to remove the spurious weak connections that would otherwise be found by simply minimizing the minus likelihood of a finite data set. In order to see how L$_1$ regularization works in detail, we perform the calculation in several ways including (1) by iterative minimization of a cost function equal to minus the log likelihood of the data plus an L$_1$ penalty term, and (2) an approximate scheme based on a quadratic expansion of the cost function around its minimum. In these schemes, we track how connections are pruned as the strength of the L$_1$ penalty is increased from zero to large values. The performance of the methods for various coupling strengths is quantified using ROC curves.