L$_1$ Regularization for Reconstruction of a non-equilibrium Ising Model
Abstract
The couplings in a sparse asymmetric, asynchronous Ising network are reconstructed using an exact learning algorithm. L 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 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 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 penalty is increased from zero to large values. The performance of the methods for various coupling strengths is quantified using ROC curves.
Cite
@article{arxiv.1211.3671,
title = {L$_1$ Regularization for Reconstruction of a non-equilibrium Ising Model},
author = {Hong-Li Zeng and John Hertz and Yasser Roudi},
journal= {arXiv preprint arXiv:1211.3671},
year = {2012}
}