  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).
