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D-optimal experimental design is a classical statistical problem in which one chooses a collection of data vectors, from some available large pool, in order to maximize a measure of predictive quality. In the classical formulation, the only constraint is on the cardinality of the collection, that is, the number of vectors chosen. We study a more general budget-constrained variant in which vectors have heterogeneous costs, and develop four new algorithms (two deterministic and two randomized) with approximation guarantees. Our methods handle heterogeneous costs using a novel exchange rule that interchanges packs of data vectors whose total costs are similar (up to some controlled amount of rounding error). The algorithms outperform the only existing method for this problem from both theoretical and empirical standpoints. Funding: The first and third authors gratefully acknowledge support from the National Science Foundation (NSF) Division of Civil, Mechanical and Manufacturing Innovation [Grant CMMI-2112828]. The second author gratefully acknowledges support from the NSF Division of Computing and Communication Foundations [Grant CCF-2246417] and Office of Naval Research [Grant N00014-24-1-2066]. 

Routing a Vehicle to Collect Data After an Earthquake In the immediate aftermath of a major earthquake, it is crucial to quickly and accurately assess structural damage throughout the region. It is especially important to identify buildings that have become unsafe in order to prioritize evacuation efforts. Only a very small number of building inspections can be feasibly performed in a narrow time frame; however, their results can then be combined with other data sources to predict damage at other locations that were not inspected. In “D-Optimal Orienteering for Postearthquake Reconnaissance Planning,” Wang, Xie, Ryzhov, Marković, and Ou present a novel nonlinear integer program that combines vehicle routing with a statistical objective, the goal being to maximize data quality. An exact method based on row and column generation is developed to solve problems with up to 200 buildings. The approach is validated in a realistic case study using real-world building data obtained from a state-of-the-art earthquake simulator. 

Abstract Gaussian process regression is widely used to model an unknown function on a continuous domain by interpolating a discrete set of observed design points. We develop a theoretical framework for proving new moderate deviations inequalities on different types of error probabilities that arise in GP regression. Two specific examples of broad interest are the probability of falsely ordering pairs of points (incorrectly estimating one point as being better than another) and the tail probability of the estimation error at an arbitrary point. Our inequalities connect these probabilities to the mesh norm, which measures how well the design points fill the space. 

We derive a new optimal sampling budget allocation for belief models based on linear regression with continuous covariates, where the expected response is interpreted as the value of the covariate vector, and an “error” occurs if a lower-valued vector is falsely identified as being better than a higher-valued one. Our allocation optimizes the rate at which the probability of error converges to zero using a large deviations theoretic characterization. This is the first large deviations-based optimal allocation for continuous decision spaces, and it turns out to be considerably simpler and easier to implement than allocations that use discretization. We give a practicable sequential implementation and illustrate its empirical potential. Funding: This work was supported by the National Science Foundation [Grant CMMI-2112828].