Exponential Reduction in Sample Complexity with Learning of Ising Model Dynamics
This addresses the challenge of learning graphical models in applications where independent samples are hard to obtain due to slow mixing times, offering a significant efficiency improvement.
The paper tackles the problem of learning binary graphical models from correlated samples produced by a dynamical process, rather than independent samples, and finds that sample complexity reduces exponentially when the process is far from equilibrium compared to quickly mixing processes.
The usual setting for learning the structure and parameters of a graphical model assumes the availability of independent samples produced from the corresponding multivariate probability distribution. However, for many models the mixing time of the respective Markov chain can be very large and i.i.d. samples may not be obtained. We study the problem of reconstructing binary graphical models from correlated samples produced by a dynamical process, which is natural in many applications. We analyze the sample complexity of two estimators that are based on the interaction screening objective and the conditional likelihood loss. We observe that for samples coming from a dynamical process far from equilibrium, the sample complexity reduces exponentially compared to a dynamical process that mixes quickly.