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We consider learning Ising tree models when the observations from the nodesare corrupted by independent but non-identically distributed noise with unknownstatistics. Katiyar et al. (2020) showed that although the exact tree structurecannot be recovered, one can recover a partial tree structure; that is, astructure belonging to the equivalence class containing the true tree. Thispaper presents a systematic improvement of Katiyar et al. (2020). First, wepresent a novel impossibility result by deriving a bound on the necessarynumber of samples for partial recovery. Second, we derive a significantlyimproved sample complexity result in which the dependence on the minimumcorrelation $\rho_{\min}$ is $\rho_{\min}^{-8}$ instead of $\rho_{\min}^{-24}$.Finally, we propose Symmetrized Geometric Averaging (SGA), a more statisticallyrobust algorithm for partial tree recovery. We provide error exponent analysesand extensive numerical results on a variety of trees to show that the samplecomplexity of SGA is significantly better than the algorithm of Katiyar et al.(2020). SGA can be readily extended to Gaussian models and is shown vianumerical experiments to be similarly superior.

SGA: A Robust Algorithm for Partial Recovery of Tree-Structured Graphical Models with Noisy Samples