Robust Estimation of Tree Structured Ising Models
Published:
Recommended citation: Ashish Katiyar, Vatsal Shah, and Constantine Caramanis. "Robust Estimation of Tree Structured Ising Models." arXiv preprint arXiv:2006.05601 (2020). https://arxiv.org/pdf/2006.05601.pdf
Abstract: We consider the task of learning Ising models when the signs of different random variables are flipped independently with possibly unequal, unknown probabilities. In this paper, we focus on the problem of robust estimation of tree-structured Ising models. Without any additional assumption of side information, this is an open problem. We first prove that this problem is unidentifiable, however, this unidentifiability is limited to a small equivalence class of trees formed by leaf nodes exchanging positions with their neighbors. Next, we propose an algorithm to solve the above problem with logarithmic sample complexity in the number of nodes and olynomial run-time complexity. Lastly, we empirically demonstrate that, as expected, existing algorithms are not inherently robust in the proposed setting whereas our algorithm correctly recovers the underlying equivalence class.