Partially Linear Additive Gaussian Graphical Models
This work addresses the issue of confounder distortion in graphical models for researchers in statistics and machine learning, representing an incremental improvement with a novel method for a known bottleneck.
The paper tackled the problem of estimating associations between random variables distorted by observed confounders by proposing a partially linear additive Gaussian graphical model (PLA-GGM), achieving superior performance in synthetic and real-world datasets compared to competing methods.
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 $\sqrt{n}$-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.