Inverse Ising inference from high-temperature re-weighting of observations
This provides a computationally efficient method for statistical physicists and machine learning practitioners dealing with high-dimensional stochastic systems, though it appears incremental as it builds on existing inference frameworks.
The authors tackled the problem of inferring Ising models from data without computing partition functions, by re-weighting observed configurations to approximate a flat distribution, achieving accurate inference for large systems where other methods are intractable.
Maximum Likelihood Estimation (MLE) is the bread and butter of system inference for stochastic systems. In some generality, MLE will converge to the correct model in the infinite data limit. In the context of physical approaches to system inference, such as Boltzmann machines, MLE requires the arduous computation of partition functions summing over all configurations, both observed and unobserved. We present here a conceptually and computationally transparent data-driven approach to system inference that is based on the simple question: How should the Boltzmann weights of observed configurations be modified to make the probability distribution of observed configurations close to a flat distribution? This algorithm gives accurate inference by using only observed configurations for systems with a large number of degrees of freedom where other approaches are intractable.