Inference of the sparse kinetic Ising model using the decimation method

TL;DR

This paper introduces a decimation-based inference method for the sparse kinetic Ising model, which automatically recovers network topology and outperforms traditional $ ext{l}_1$-optimization techniques in dynamical settings.

Contribution

The paper adapts the decimation method for dynamical inference of the kinetic Ising model, avoiding heuristic priors and demonstrating superior performance over $ ext{l}_1$ methods.

Findings

Decimation method accurately infers couplings in various topologies.

Decimation outperforms $ ext{l}_1$-optimization in dynamical inference.

Method operates automatically without manual parameter tuning.

Abstract

In this paper we study the inference of the kinetic Ising model on sparse graphs by the decimation method. The decimation method, which was first proposed in [Phys. Rev. Lett. 112, 070603] for the static inverse Ising problem, tries to recover the topology of the inferred system by setting the weakest couplings to zero iteratively. During the decimation process the likelihood function is maximized over the remaining couplings. Unlike the $\ell_1$-optimization based methods, the decimation method does not use the Laplace distribution as a heuristic choice of prior to select a sparse solution. In our case, the whole process can be done automatically without fixing any parameters by hand. We show that in the dynamical inference problem, where the task is to reconstruct the couplings of an Ising model given the data, the decimation process can be applied naturally into a maximum-likelihood optimization algorithm, as opposed to the static case where pseudo-likelihood method needs to be adopted. We also use extensive numerical studies to validate the accuracy of our methods in dynamical inference problems. Our results illustrate that on various topologies and with different distribution of couplings, the decimation method outperforms the widely-used $\ell _1$-optimization based methods.