  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 polynomial 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.
