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About this paper
Eric Shen, Tony Wu, Mahbod Majid, Ankur Moitra
A polynomial-time algorithm recovers the sparsity pattern and estimates parameters of Gaussian Graphical Models from a single Glauber trajectory, sidestepping the challenge of slow mixing times and requiring only (alpha, d)-sparsity assumptions on the precision matrix. This approach also improves upon previous information-theoretic lower bounds.
Key insights
- Specific local update patterns within a single Glauber trajectory can provide sufficient information to learn GGM structure and parameters, even if the chain does not fully mix.
- Robust statistical estimators, like the median, are effective in handling contamination from unobserved neighbor updates and the inherent temporal dependence present in Glauber dynamics-generated samples.
- Normalizing the GGM by estimating and scaling its diagonal entries simplifies the estimation of off-diagonal parameters by standardizing the variance of noise terms.
Summary by alphaXiv.
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