Learning Ising Models with Independent Failures
This addresses a practical issue in statistical modeling for fields like physics or biology where missing data is common, but it is incremental as it builds on existing methods.
The paper tackles the problem of learning the structure of Ising models when data entries are missing independently with unknown probability, and it presents an efficient algorithm that matches optimal runtime and sample complexity bounds from prior work.
We give the first efficient algorithm for learning the structure of an Ising model that tolerates independent failures; that is, each entry of the observed sample is missing with some unknown probability p. Our algorithm matches the essentially optimal runtime and sample complexity bounds of recent work for learning Ising models due to Klivans and Meka (2017). We devise a novel unbiased estimator for the gradient of the Interaction Screening Objective (ISO) due to Vuffray et al. (2016) and apply a stochastic multiplicative gradient descent algorithm to minimize this objective. Solutions to this minimization recover the neighborhood information of the underlying Ising model on a node by node basis.