Optimizing the Union of Intersections LASSO ($UoI_{LASSO}$) and Vector Autoregressive ($UoI_{VAR}$) Algorithms for Improved Statistical Estimation at Scale

The analysis of scientific data of increasing size and complexity requires statistical machine learning methods that are both interpretable and predictive. Union of Intersections (UoI), a recently developed framework, is a two-step approach that separates model selection and model estimation. A linear regression algorithm based on UoI, $UoI_{LASSO}$, simultaneously achieves low false positives and low false negative feature selection as well as low bias and low variance estimates. Together, these qualities make the results both predictive and interpretable. In this paper, we optimize the $UoI_{LASSO}$ algorithm for single-node execution on NERSC's Cori Knights Landing, a Xeon Phi based supercomputer. We then scale $UoI_{LASSO}$ to execute on cores ranging from 68-278,528 cores on a range of dataset sizes demonstrating the weak and strong scaling of the implementation. We also implement a variant of $UoI_{LASSO}$, $UoI_{VAR}$ for vector autoregressive models, to analyze high dimensional time-series data. We perform single node optimization and multi-node scaling experiments for $UoI_{VAR}$ to demonstrate the effectiveness of the algorithm for weak and strong scaling. Our implementations enable to use estimate the largest VAR model (1000 nodes) we are aware of, and apply it to large neurophysiology data 192 nodes).