Partially Linear Additive Gaussian Graphical Models

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Sinong Geng, Minhao Yan, Mladen Kolar, Sanmi Koyejo ;
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:2180-2190, 2019.

Abstract

We propose a partially linear additive Gaussian graphical model (PLA-GGM) for the estimation of associations between random variables distorted by observed confounders. Model parameters are estimated using an $L_1$-regularized maximal pseudo-profile likelihood estimator (MaPPLE) for which we prove a $\sqrt{n}$-sparsistency. Importantly, our approach avoids parametric constraints on the effects of confounders on the estimated graphical model structure. Empirically, the PLA-GGM is applied to both synthetic and real-world datasets, demonstrating superior performance compared to competing methods.

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