Interaction Screening: Efficient and Sample-Optimal Learning of Ising Models
This addresses the challenge of efficient and sample-optimal graph recovery in Ising models, which is incremental but improves upon prior bounds.
The paper tackles the problem of learning the underlying graph of an unknown Ising model from samples, proposing a new estimator that is computationally efficient and achieves near-optimal sample complexity, requiring samples logarithmic in system size and exponential in coupling intensity and node-degree.
We consider the problem of learning the underlying graph of an unknown Ising model on p spins from a collection of i.i.d. samples generated from the model. We suggest a new estimator that is computationally efficient and requires a number of samples that is near-optimal with respect to previously established information-theoretic lower-bound. Our statistical estimator has a physical interpretation in terms of "interaction screening". The estimator is consistent and is efficiently implemented using convex optimization. We prove that with appropriate regularization, the estimator recovers the underlying graph using a number of samples that is logarithmic in the system size p and exponential in the maximum coupling-intensity and maximum node-degree.