Abstract Adaptive mesh refinement (AMR) is the art of solving PDEs on a mesh hierarchy with increasing mesh refinement at each level of the hierarchy. Accurate treatment on AMR hierarchies requires accurate prolongation of the solution from a coarse mesh to a newly defined finer mesh. For scalar variables, suitably highorder finite volume WENO methods can carry out such a prolongation. However, classes of PDEs, such as computational electrodynamics (CED) and magnetohydrodynamics (MHD), require that vector fields preserve a divergence constraint. The primal variables in such schemes consist of normal components of the vector field that are collocated at the faces of the mesh. As a result, the reconstruction and prolongation strategies for divergence constraintpreserving vector fields are necessarily more intricate. In this paper we present a fourthorder divergence constraintpreserving prolongation strategy that is analytically exact. Extension to higher orders using analytically exact methods is very challenging. To overcome that challenge, a novel WENOlike reconstruction strategy is invented that matches the moments of the vector field in the faces, where the vector field components are collocated. This approach is almost divergence constraintpreserving, therefore, we call it WENOADP. To make it exactly divergence constraintpreserving, a touchup procedure is developed that ismore »
FLAME: A Fast Largescale Almost Matching Exactly Approach to Causal Inference
A classical problem in causal inference is that of matching, where treatment units need to be matched to control units based on covariate information. In this work, we propose a method that computes high quality almostexact matches for highdimensional categorical datasets. This method, called FLAME (Fast Largescale Almost Matching Exactly), learns a distance metric for matching using a holdout training data set. In order to perform matching efficiently for large datasets, FLAME leverages techniques that are natural for query processing in the area of database management, and two implementations of FLAME are provided: the first uses SQL queries and the second uses bitvector techniques. The algorithm starts by constructing matches of the highest quality (exact matches on all covariates), and successively eliminates variables in order to match exactly on as many variables as possible, while still maintaining interpretable highquality matches and balance between treatment and control groups. We leverage these high quality matches to estimate conditional average treatment effects (CATEs). Our experiments show that FLAME scales to huge datasets with millions of observations where existing stateoftheart methods fail, and that it achieves significantly better performance than other matching methods.
 Award ID(s):
 1703431
 Publication Date:
 NSFPAR ID:
 10291692
 Journal Name:
 Journal of machine learning research
 Volume:
 22
 Issue:
 31
 Page Range or eLocationID:
 141
 ISSN:
 15337928
 Sponsoring Org:
 National Science Foundation
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