Network reconstruction for Ising models with asynchronous updates

by Hongli Zeng (Aalto University)

Tuesday 13 Nov 2012, 13:30 → 14:30 Europe/Stockholm

122:026

We investigate inference of the fully asymmetric Sherrington-Kirkpatrick (aSK) model using asynchronous update. The couplings are reconstructed from dynamical data by respectively naive mean field (nMF) and Thouless-Anderson-Palmer (TAP) approximations first. They can also be referred without approximations. In order to obtained algorithms with no approximation, two cases of the asynchronous update scheme are considered. One in which we know both the spin history (i.e., the times at which spins were actually flipped) and the update times (times at which an attempt was made to flip a spin), denoted as SUH and one in which we only know the spin history denoted as SOH. For both cases, maximizing the log-likelihood of the data leads to exact learning rules with respect to couplings in the model. For SUH case, there is a corresponding average version algorithm which we refer as AVE. The inference process by AVE and SOH need exactly the same data set. We study all methods numerically for fully connected aSK models, varying the data length, system size, temperature, and external field. Good convergence is observed in accordance with the theoretical expectations. We also studied the sparse network based on SUH algorithm with L1 regularization which is used to remove the spurious weak connections that be found by SUH algorithm. We perform the calculation in two ways: (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 both of these schemes, we are able to track how connections are pruned as the strength of the L1 penalty is increased from zero to large values. The performance of the methods is quantified using ROC curves.