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- W2922433720 abstract "We provide high-probability sample complexity guarantees for exact structure recovery of tree-structured graphical models, when only noisy observations of the respective vertex emissions are available. We assume that the hidden variables follow either an Ising model or a Gaussian graphical model, and the observables are noise-corrupted versions of the hidden variables: We consider multiplicative $pm 1$ binary noise for Ising models, and additive Gaussian noise for Gaussian models. Such hidden models arise naturally in a variety of applications such as physics, biology, computer science, and finance. We study the impact of measurement noise on the task of learning the underlying tree structure via the well-known textit{Chow-Liu algorithm} and provide formal sample complexity guarantees for exact recovery. In particular, for a tree with $p$ vertices and probability of failure $delta>0$, we show that the number of necessary samples for exact structure recovery is of the order of $mc{O}(log(p/delta))$ for Ising models (which remains the textit{same as in the noiseless case}), and $mc{O}(mathrm{polylog}{(p/delta)})$ for Gaussian models." @default.
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- W2922433720 date "2019-04-11" @default.
- W2922433720 modified "2023-09-28" @default.
- W2922433720 title "Learning Tree Structures from Noisy Data" @default.
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