2012/11/15 by Hong-Li Zeng, Zeng, Hong-Li, John Hertz +3
Mathematics · Physics and Astronomy · #Data Analysis #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Computer and information sciences #FOS: Physical sciences #Methodology (stat.ME) #Statistics and Probability (physics.data-an) #cond-mat.dis-nn #physics.data-an #stat.ME
paper · pdf · doi:10.48550/arxiv.1211.3671
arxiv created 2012/11/15 · arxiv updated 2012/11/19
The couplings in a sparse asymmetric, asynchronous Ising network are reconstructed using an exact learning algorithm. L1 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 L1 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 L1 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 L1 penalty is increased from zero to large values. The performance of the methods for various coupling strengths is quantified using ROC curves.