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Bayesian D-Optimal Experimental Designs via Column Subset Selection

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arxiv 2402.16000 v3 pith:HLG5KAGX submitted 2024-02-25 math.NA cs.NA

Srinivas Eswar , Vishwas Rao , Arvind K. Saibaba This is my paper · ORCID
classification math.NAcs.NA
keywords problemalgorithmsinversebayesiancolumnexperimentallinearnumerical
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This paper tackles optimal sensor placement for Bayesian linear inverse problems, a popular version of the more general Optimal Experimental Design (OED) problem, using the D-optimality criterion. This is done by establishing connections between sensor placement and Column Subset Selection Problem (CSSP), which is a well-studied problem in Numerical Linear Algebra (NLA). In particular, we use the Golub-Klema-Stewart (GKS) approach which involves computing the truncated Singular Value Decomposition (SVD) followed by a pivoted QR factorization on the right singular vectors. The algorithms are further accelerated by using randomization to compute the low-rank approximation as well as for sampling the indices. The resulting algorithms are robust, computationally efficient, amenable to parallelization, require virtually no parameter tuning, and come with strong theoretical guarantees. One of the proposed algorithms is also adjoint-free which is beneficial in situations, where the adjoint is expensive to evaluate or is not available. Additionally, we develop a method for data completion without solving the inverse problem. Numerical experiments on model inverse problems involving the heat equation and seismic tomography in two spatial dimensions demonstrate the performance of our approaches.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Submodularity of the expected information gain in infinite-dimensional linear inverse problems

    math.OC 2026-02 accept novelty 6.0 of 10

    In infinite-dimensional linear Gaussian Bayesian inverse problems, expected information gain is monotone submodular, so greedy sensor placement retains its (1-1/e) approximation guarantee.

  2. Variance-Preserving Orthogonal Selection (VPOS): Greedy Feature Selection via Orthogonal Deflation in PCA Loading Space

    cs.LG 2026-07 conditional novelty 5.0 of 10

    VPOS greedily selects the feature with the largest weighted PCA loading norm, deflates that direction, and reports the lowest reconstruction MSE on eight benchmarks under a minimum-MSE d-selection rule.

  3. Multifidelity sensor placement in Bayesian state estimation problems

    math.NA 2026-02 conditional novelty 5.0 of 10

    A budget-constrained greedy plus iterative algorithm selects cheap/expensive sensors to maximize Bayesian D-optimality and beats random designs in benchmark state estimation.

  4. Structured Column Subset Selection for Bayesian Optimal Experimental Design

    math.NA 2025-05 conditional novelty 5.0 of 10

    A tensor-based framework selects structured subsets of experimental design variables by applying column subset selection to mode unfoldings of the design matrix.

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