Papers › Maximum a Posteriori Estimation in Graphical Models Using Local Linear Approximation
Maximum a Posteriori Estimation in Graphical Models Using Local Linear Approximation
Ksheera Sagar, Jyotishka Datta, Sayantan Banerjee, Anindya Bhadra
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Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among variables. However, maximum a posteriori (MAP) estimation is challenging under hierarchical prior models, and traditional numerical optimization routines or expectation--maximization algorithms are difficult to implement. To this end, our contribution is a novel local linear approximation scheme that circumvents this issue using a very simple computational algorithm. Most importantly, the condition under which our algorithm is guaranteed to converge to the MAP estimate is explicitly stated and is shown to cover a broad class of completely monotone priors, including the graphical horseshoe. Further, the resulting MAP estimate is shown to be sparse and consistent in the ℓ₂-norm. Numerical results validate the speed, scalability, and statistical performance of the proposed method.
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