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- W4385261738 abstract "Recently, Eldan, Koehler, and Zeitouni (2020) showed that Glauber dynamics mixes rapidly for general Ising models so long as the difference between the largest and smallest eigenvalues of the coupling matrix is at most $1 - epsilon$ for any fixed $epsilon > 0$. We give evidence that Glauber dynamics is in fact optimal for this general-purpose sampling task. Namely, we give an average-case reduction from hypothesis testing in a Wishart negatively-spiked matrix model to approximately sampling from the Gibbs measure of a general Ising model for which the difference between the largest and smallest eigenvalues of the coupling matrix is at most $1 + epsilon$ for any fixed $epsilon > 0$. Combined with results of Bandeira, Kunisky, and Wein (2019) that analyze low-degree polynomial algorithms to give evidence for the hardness of the former spiked matrix problem, our results in turn give evidence for the hardness of general-purpose sampling improving on Glauber dynamics. We also give a similar reduction to approximating the free energy of general Ising models, and again infer evidence that simulated annealing algorithms based on Glauber dynamics are optimal in the general-purpose setting." @default.
- W4385261738 created "2023-07-26" @default.
- W4385261738 creator A5044093947 @default.
- W4385261738 date "2023-07-24" @default.
- W4385261738 modified "2023-10-18" @default.
- W4385261738 title "Optimality of Glauber dynamics for general-purpose Ising model sampling and free energy approximation" @default.
- W4385261738 doi "https://doi.org/10.48550/arxiv.2307.12581" @default.
- W4385261738 hasPublicationYear "2023" @default.
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