Adversarially-Robust Inference on Trees via Belief Propagation

arXiv:2404.00768v1 Announce Type: cross
Abstract: We introduce and study the problem of posterior inference on tree-structured graphical models in the presence of a malicious adversary who can corrupt some observed nodes. In the well-studied broadcasting on trees model, corresponding to the ferromagnetic Ising model on a $d$-regular tree with zero external field, when a natural signal-to-noise ratio exceeds one (the celebrated Kesten-Stigum threshold), the posterior distribution of the root given the leaves is bounded away from $\mathrm{Ber}(1/2)$, and carries nontrivial …

abstract arxiv belief broadcasting cs.ds inference math.pr math.st nodes posterior propagation robust stat.ml stat.th study tree trees type via