UC Santa Barbara

Graphical models, which utilize graphs to encode conditional independencies between random variables, have proven to be versatile tools for encoding multivariate distributions. In addressing some practical considerations for using graphical models in applications, we developed two graphical model methods. Firstly, we develop the FROSTY method for directed graphical models focusing on scalability that performs well in simulation. FROSTY only requires observational data and user-specified confidence level as inputs and can estimate networks with thousands of variables. Notably, FROSTY does not require computationally expensive cross-validation for model selection. We learned that initial input and parameter tuning are important in estimation, and empirical evidence illustrates that other methods can be improved by adopting FROSTY's initial step. Secondly, we develop the ACCORD method for undirected graphical models based on pseudo-likelihood. For optimization, we propose a novel objective splitting that ensures linear convergence with a wide range of step size in both the objective values and the iterates despite the lack of strong convexity in ACCORD's objective function. Additionally, we implement a high-performance variant of ACCORD, named HP-ACCORD, that can scale up to 1 million variables utilizing communication-avoiding linear algebra on distributed computing environments.