Robust Estimation of Tree Structured Ising Models

Ashish Katiyar, Vatsal Shah, Constantine Caramanis

Abstract: We consider the task of learning Ising models when the signs of different random variablesare flipped independently with possibly unequal, unknown probabilities. In this paper, we focuson the problem of robust estimation of tree-structured Ising models. Without any additionalassumption of side information, this is an open problem. We first prove that this problem isunidentifiable, however, this unidentifiability is limited to a small equivalence class of treesformed by leaf nodes exchanging positions with their neighbors. Next, we propose an algorithmto solve the above problem with logarithmic sample complexity in the number of nodes andpolynomial run-time complexity. Lastly, we empirically demonstrate that, as expected, existingalgorithms are not inherently robust in the proposed setting whereas our algorithm correctlyrecovers the underlying equivalence class