Robust Estimation of Tree Structured Ising Models
This addresses a robustness issue in statistical modeling for researchers in machine learning and statistics, though it is incremental as it builds on existing tree-structured Ising model work.
The paper tackles the problem of learning tree-structured Ising models when random variable signs are flipped with unknown probabilities, proving the problem is unidentifiable but limited to a small equivalence class, and proposes an algorithm with logarithmic sample complexity and polynomial runtime that correctly recovers this class.
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.