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Least squares regression is a ubiquitous tool for building emulators (a.k.a.surrogate models) of problems across science and engineering for purposes suchas design space exploration and uncertainty quantification. When the regressiondata are generated using an experimental design process (e.g., a quadraturegrid) involving computationally expensive models, or when the data size islarge, sketching techniques have shown promise to reduce the cost of theconstruction of the regression model while ensuring accuracy comparable to thatof the full data. However, random sketching strategies, such as those based onleverage scores, lead to regression errors that are random and may exhibitlarge variability. To mitigate this issue, we present a novel boosting approachthat leverages cheaper, lower-fidelity data of the problem at hand to identifythe best sketch among a set of candidate sketches. This in turn specifies thesketch of the intended high-fidelity model and the associated data. We providetheoretical analyses of this bi-fidelity boosting (BFB) approach and discussthe conditions the low- and high-fidelity data must satisfy for a successfulboosting. In doing so, we derive a bound on the residual norm of the BFBsketched solution relating it to its ideal, but computationally expensive,high-fidelity boosted counterpart. Empirical results on both manufactured andPDE data corroborate the theoretical analyses and illustrate the efficacy ofthe BFB solution in reducing the regression error, as compared to thenon-boosted solution.

Quadrature Sampling of Parametric Models with Bi-fidelity Boosting