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REVIEW 4 major objections 5 minor 32 references

Multifidelity sensor placement in Bayesian state estimation problems

T0 review · 4 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read The paper claims that a new iterative refinement algorithm for budget-constrained multifidelity sensor placement matches or beats a Sherman–Morrison-accelerated greedy algorithm on D-optimality benchmarks, with both clearly outperforming ra

desk verdict Genuinely novel iterative multifidelity greedy and a useful Sherman-Morrison implementation, with clean theory; but the experiments are undercut by the truncated-SVD error floor and reduced-space-only evaluation. read the letter →

arxiv 2602.07269 v2 pith:VBI7Q4OU submitted 2026-02-06 math.NA cs.NAmath.OC

Gabriela Ramon , Geena Sarnoski , Vasishta Tumuluri , Hugo Díaz , Arvind K. Saibaba This is my paper · ORCID
classification math.NAcs.NAmath.OC MSC 62K0593E1065F3049N45
keywords BayesianstateestimationsensorplacementD-optimalitymultifidelitygreedyalgorithmsoptimalexperimentaldesigncolumnsubsetselectionSherman–Morrisonupdate
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tackles the problem of where to place sensors of different quality—cheap, noisy ones and expensive, accurate ones—when there is a fixed budget, with the goal of minimizing posterior uncertainty in a Bayesian state estimate. The authors formulate the problem as a budget-constrained multifidelity D-optimal experimental design and link it to column subset selection. They contribute a greedy algorithm accelerated by Sherman–Morrison rank-one updates and a new iterative algorithm that alternately refines the positions of each sensor fidelity for every feasible budget allocation. On sea surface temperature and flow-past-a-cylinder benchmarks, the iterative algorithm matches or beats greedy in D-optimality, and both clearly beat random sensor placement while keeping reconstruction errors low. The practical point is that a budget can be spent on a mix of fidelities in a principled way that scales to large candidate sets.

What carries the argument

The D-optimality objective written as a log-determinant of a rank-one sum, B(S)=I+Σ_j (A_j S_j)(A_j S_j)^T; the marginal gain of adding a sensor collapses to log(1 + [A_j]_:^i B^{-1} [A_j]_:i), so Sherman–Morrison updates maintain B^{-1}A_j dictionaries at O(Mℓ) per step. This converts the combinatorial search into an efficient greedy/iterative sweep. The allocation pruning rests on monotonicity and the 'expensive-sensors-are-more-informative' proposition.

What would settle it

Compute the exact D-optimal solution by exhaustive search on a small problem (M ≤ 20 candidate locations, two fidelities) and show either that the iterative algorithm's final design has lower Φ_D than the greedy design, or run the iterative algorithm on a problem where the true state is a localized traveling pulse absent from the training snapshots and show the chosen sensors yield higher average reconstruction error than randomly placed sensors.

Watch

Extended reading notes

Core claim

Using the Bayesian D-optimality criterion, the paper expresses the objective as Φ_D(S)=log det(I + Σ_j (A_j S_j)(A_j S_j)^T), where A_j = σ_j^{-1} Σ_pr^{1/2} Ψ^T are scaled restrictions of the reduced-order basis to candidate locations. Because adding a sensor is a rank-one update, the matrix determinant lemma and the Sherman–Morrison formula let the marginal information gain be computed in O(ℓ) flops, giving a greedy algorithm with total O(kMℓ) complexity. The paper proves monotonicity and submodularity of the multifidelity objective, shows expensive sensors are always at least as informative as cheap ones at the same location, and uses these properties to prune the set of budget-feasible (

Load-bearing premise

The true state is assumed to be well approximated by the leading POD modes of the training data, u ≈ Φm, and the truncation error from the SVD is ignored when computing the D-optimality objective.

Editorial extensions

If this is right

  • If the empirical ordering holds, the iterative algorithm is a drop-in replacement for greedy multifidelity selection, giving better D-optimality at comparable cost.
  • The O(kMℓ) complexity makes budgeted sensor placement feasible for large spatial grids (tens of thousands of candidate locations), as demonstrated on a 44,219-point SST grid.
  • The cost-to-noise ratio c_ch/c_exp compared to σ²_exp/σ²_ch gives a practical rule for which fidelity a greedy search will favor.
  • Because no constant-factor guarantee exists, users should run both algorithms and choose the best, or use the iterative output as a warm start.
  • The same rank-one update machinery carries over to other budgeted submodular objectives with a log-det structure, such as information-theoretic sensor placement.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's critical-ratio condition suggests a testable design rule: when c_ch/c_exp < σ²_exp/σ²_ch, cheap sensors dominate; a practitioner could validate this against exhaustive search on small instances.
  • If the POD truncation error is significant (e.g., localized features absent from training data), the D-optimal designs for the reduced model may not improve true-state reconstruction; the paper flags but does not test this.
  • The alternating greedy refinement is coordinate ascent on the combinatorial selection space and may converge to different local optima depending on initialization; starting from the greedy solution instead of all-expensive might change outcomes.
  • The approach generalizes to more than two fidelities by extending the allocation pruning; the complexity bound would scale with the number of fidelities.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The manuscript formulates a budget-constrained multifidelity D-optimal sensor placement problem for Bayesian state estimation using a reduced-order dictionary model. It proposes a cost-normalized greedy algorithm accelerated by Sherman–Morrison rank-one updates (Algorithm 2), an iterative allocation-refinement algorithm (Algorithm 4), proves monotonicity/submodularity of the objective, gives a counterexample showing that the greedy method has no constant-factor approximation guarantee, and reports experiments on sea surface temperature and flow-past-a-cylinder benchmarks.

Significance. If the claims hold, the paper makes a useful contribution to an underexplored area: efficient multifidelity sensor selection under a budget. The Sherman–Morrison updating scheme in Section 3.4 is correctly derived and reduces the per-iteration cost from O(kMℓ^2(k+ℓ)) to O(kMℓ), a genuine practical improvement. The extension of monotonicity/submodularity to the multifidelity setting (Proposition 3.2) is correct, and the explicit counterexample in Lemma 3.4 is a valuable negative result. However, the experimental validation is conducted entirely inside the truncated-reduced model, the theoretical corroboration in Appendix B contains an invalid inference, and the iterative algorithm has feasibility gaps in its pruning or termination logic. These issues are fixable but currently affect load-bearing claims.

major comments (4)
  1. [§2.1, Table 2, §5.2.3] The observation model (2) explicitly ignores truncation error from the SVD basis. All D-optimality comparisons and all reported reconstruction errors are therefore computed inside the reduced model. The relative errors in Table 2 (0.1038 for SST, 0.0864 for cylinder) are of the same magnitude as the ~10% relative-error floor expected from retaining 99% of the singular-value energy. As a result, the experiments do not establish that the selected sensors improve state estimation for the true system; they only demonstrate improvement of the reduced-model objective. Section 5.2.3 compares greedy and iterative against random designs only in Φ_D, not in true-state reconstruction error. Please quantify the truncation error for the two datasets, report true-state reconstruction comparisons against random designs (and, if feasible, against existing multifidelity methods such as [6,19]), and tempe
  2. [Appendix B] The derivation of the critical cost/noise ratio is invalid. The text claims that the displayed inequalities imply a_ch^T B^{-1} a_ch = a_exp^T B^{-1} a_exp. From log(1+σ_ch^{-2} a_ch^T B^{-1} a_ch) ≤ log(1+σ_exp^{-2} a_exp^T B^{-1} a_exp) one can only conclude σ_ch^{-2} a_ch^T B^{-1} a_ch ≤ σ_exp^{-2} a_exp^T B^{-1} a_exp, not equality of the quadratic forms. A concrete counterexample is B=I, σ_ch=1, σ_exp=0.1, a_ch^T a_ch=100, a_exp^T a_exp=1, which satisfies both displayed inequalities while the quadratic forms are 100 and 1. Thus the subsequent Taylor approximation and the claimed theoretical corroboration of the empirical regimes are not supported. Either correct the derivation or remove the claim in Section 1.1 bullet 5 that the experiments are 'theoretically corroborated.'
  3. [Algorithms 1 and 2, Lemma 3.4] The main loops in Algorithms 1 and 2 terminate only when b_curr < c_ch; they do not check whether any candidate location remains. In the proof of Lemma 3.4, M=1, and after the greedy step selects the only location, b_curr = 1 − ε/2 ≥ c_ch = ε/2 for ε ∈ (0,1), so the next iteration would attempt argmax over J × ∅. This makes the counterexample formally dependent on undefined behavior. The pseudocode should include the condition I ≠ ∅ (or an equivalent break) in the while loop.
  4. [§4.1, Algorithm 4, Phase I] The pruning step sets k_ch = floor((b − c_exp k_exp)/c_ch) but does not enforce k_ch ≤ M − k_exp. When k_ch + k_exp exceeds the number of candidate locations, the allocation is infeasible. Moreover, the dominance argument based on monotonicity assumes that an additional sensor can always be placed; if k_ch + k_exp = M, that assumption fails, so smaller-k_ch allocations cannot be discarded by this argument. Please cap k_ch by M − k_exp and revisit the pruning claims; otherwise the iterative algorithm may return infeasible sensor configurations.
minor comments (5)
  1. [§3.5, §3.2] Typographical/numbering inconsistencies: 'Theorem 3.4' should be 'Lemma 3.4'; 'Theorem 2.3' and 'Theorem 2.4' should be 'Lemma 2.3' and 'Corollary 2.4'; Section 4.1 and Algorithm 4 refer to 'Theorems 3.2 and 3.3' though these are propositions.
  2. [Table 3, §5.2.1] Case (3d): 1/3.85 ≈ 0.2597, which is slightly above the critical value 0.25, not 'slightly below' as stated in the table caption. The text should also clarify the meaning of the symbol ⪅ in Figure 3(d).
  3. [§5.2.3, Figure 5] The comparison against random designs reports only point values of Φ_D in Table 4. Please report the spread of the random-design histograms (e.g., interquartile range or standard deviation) so that 'considerably better' is substantiated quantitatively.
  4. [§2.1, Eq. (3)] The prior-scaling parameter λ is set to 0.01 without any sensitivity study. Since the D-optimality objective and the selected sensors can depend on the prior scale, a brief sensitivity check or a statement of how λ was chosen would strengthen the empirical claims.
  5. [Algorithm 4] The termination condition in lines 14 and 19 compares the new objective with the previous one and breaks on decrease. Since equal objective values also indicate no progress, the condition could be '≤' rather than '<' for consistency with the stated 'objective function decreases' criterion.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the D-optimality objective and algorithms are derived in-line; self-citations frame but do not force the results.

full rationale

The derivation chain is self-contained. The D-optimality objective is derived algebraically in Proposition 3.1, with a proof supplied: Phi_D(S) = log det(I + (A_ch S_ch)(A_ch S_ch)^T + (A_exp S_exp)(A_exp S_exp)^T). The Sherman-Morrison implementation in Section 3.4 follows from the matrix determinant lemma and is a routine algebraic update, not a fitted parameter renamed as a prediction. Monotonicity and submodularity are proven in Proposition 3.2 using standard determinant inequalities, and Proposition 3.3 (expensive sensors are more informative) is also proven in-line. Algorithm 4 is a heuristic search over allocations whose objective is the same Phi_D; comparing it to greedy and to random designs is a benchmark evaluation, not a prediction that reduces to its inputs. The self-citations [7] (CSSP/NP-hardness) and [13] (POD-based dictionary model) overlap with the authors, but neither is invoked as an external uniqueness theorem; the dictionary ansatz u approximately equal to Phi m is explicitly stated as an assumption and is tested on holdout data. The acknowledged truncation error ('Note here we have ignored the error coming from the truncated SVD') is a genuine validity limitation: if the true state has significant energy outside span(Phi), maximizing reduced-model Phi_D may not improve the true Bayesian estimator. That is a robustness/correctness concern, not a circular reduction, because the reported comparisons are not constructed to equal their own inputs.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. The main hand-chosen inputs are experimental hyperparameters (lambda and the energy threshold). The modeling axioms are standard for linear-Gaussian Bayesian inverse problems with a reduced-order dictionary basis; the least defensible is the ignored SVD truncation error, which is load-bearing for the whole reduced-model formulation.

free parameters (2)
  • Prior scaling lambda = 0.01
    The prior covariance Sigma_pr = lambda^2/(p-1) Sigma_l^2 uses lambda=0.01 in all experiments (Section 2.1, Section 5); this hand-chosen constant affects D-optimality scores and the resulting sensor selections.
  • Truncation energy threshold = 99%
    The reduced basis dimension l is chosen as the smallest dimension capturing 99% cumulative singular value energy (Section 5); this modeling threshold determines the dictionary basis and hence the sensor placement objective.
assumptions (5)
  • domain assumption The state u lies approximately in the span of Phi, the leading l left singular vectors of training data; truncation error from the SVD is ignored.
    Invoked in Section 2.1 when substituting u approx Phi m into the observation model; if the true state has components outside this subspace, D-optimal designs for the reduced model may not be informative for the true field.
  • domain assumption Linear-Gaussian observation model with diagonal noise covariance and Gaussian prior on reduced coordinates.
    Used throughout Sections 2.1 and 3.1 to obtain a closed-form posterior covariance; sensor selection is performed for this model rather than for general nonlinear observation operators.
  • domain assumption D-optimality (log-determinant of the information matrix) is the design objective.
    The paper optimizes Phi_D; if a different optimality criterion (A-, E-optimality, or direct reconstruction error) is desired, the proposed algorithms do not directly apply.
  • standard math Sherman-Morrison formula, matrix determinant lemma, Minkowski determinant theorem, and NP-hardness of D-optimal design and knapsack are used as background results.
    Used in proofs and complexity discussion in Sections 2.3 and 3.
  • domain assumption For iterative Phase-I pruning, monotonicity and 'expensive sensors are more informative' are used to discard allocations; this assumes unused candidate locations exist and that swapping fidelity at an already-selected location is feasible.
    Phase I in Section 4.1 discards allocations by adding a cheap sensor or replacing a cheap sensor with an expensive one; if M is small and all locations are used, pruning can discard optimal allocations.

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Cite this review

Pith. "Pith review of Multifidelity sensor placement in Bayesian state estimation problems." pith.science (2026). https://pith.science/paper/VBI7Q4OU

@misc{pith2026260207269,
  author       = {Pith},
  title        = {Pith review of: Multifidelity sensor placement in Bayesian state estimation problems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VBI7Q4OU}},
  note         = {Machine review of arXiv:2602.07269}
}
read the original abstract

We study optimal sensor placement for Bayesian state estimation problems in which sensors vary in cost and fidelity, resulting in a budget-constrained multifidelity optimal experimental design problem. Sensor placement optimality is quantified using the D-optimality criterion, and the problem is approached by leveraging connections with the column subset selection problem in numerical linear algebra. We implement a greedy approach for this problem, whose computational efficiency we improve using rank-one updates via the Sherman-Morrison formula. We additionally present an iterative algorithm that, for each feasible allocation of sensors, greedily optimizes over each sensor fidelity subject to previous sensor choices, repeating this process until a termination criterion is satisfied. To our knowledge, these algorithms are novel in the context of cost-constrained multifidelity sensor placement. We evaluate our methods on several benchmark state estimation problems, including reconstructions of sea surface temperature and flow around a cylinder, and empirically demonstrate improved performance over random designs.

Figures

Figures reproduced from arXiv: 2602.07269 by the authors.

Figure 1
Figure 1. MAP reconstructions of sea surface temperature us￾ing sensors selected by the greedy (top) and the iterative (bottom) algorithms. Both methods employ the same settings, yielding com￾parable relative errors of about 11%. For the iterative method, the candidate set contained |K| = 11 allocations, and the algorithm performed a total of t = 2 greedy refinement iterations across all candidates. Markers indicate sensor lo… view at source ↗
Figure 2
Figure 2. MAP reconstructions of flow past a cylinder obtained using greedy (top) and iterative (bottom) sensor selection. Both approaches achieve comparable relative errors of approximately 9%. For the iterative method, the candidate set consists of |K| = 11 sensor allocations, and the algorithm performed a total of t = 9 greedy refinement iterations across all candidates. The zoomed insets highlight sensor placements concen… view at source ↗
Figure 3
Figure 3. Greedy sensor selection results for different costs and measurement noise standard deviations. Case cch/cexp σch/σexp kch/kexp Description (3a) 1/4 0.02/0.01 100/0 Critical (balanced) ratio (3b) 1/6 0.02/0.01 100/0 Cheap sensors dominates (3c) 1/5 0.05/0.01 0/20 Expensive sensors dominates (3d) 1/3.85 0.02/0.01 19/21 Slightly below critical ratio [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Sensor placement results for the greedy (left) and it￾erative (right) algorithms. Rows correspond to increasing budgets b = 50, 100, 200 from top to bottom. The corresponding (kch, kexp) values are indicated below each image, with cheap sensors shown in red and expensi…
Figure 5
Figure 5. Figure 5: D-optimality comparison of random, greedy, and itera￾tive sensor selection at b = 500. Both greedy and iterative selection outperform random selection. 6. Conclusion. Optimal data collection has applications in many areas of science and engineering, including medicine,…

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Works this paper leans on

32 extracted references · 8 canonical work pages

  1. [1]

    #1 @plain#1#2#3 #1 \@ifnotempty #1 \@upn #2 (#3) @plain#1#2#3 \@upn #2 \@ifnotempty #2

    \@testbibitem #1 (#2) MR #1 (#2) http://www.ams.org/mathscinet-getitem?mr=#1&return=pdf #1 \@ifundefined href arxiv:#1 http://arxiv.org/pdf/#1 arXiv:#1 \@cite#1#2 @th [ #1 @tempswa, #2 ] \@ifundefined cite cite \@nx \@xp\@nx cite @plain#1#2#3 @oremn@me #1 #1 \@ifnotempty #1 \@upn #2 @notefont(#3) @plain #1 #1 \@d@mmy\@currentlabel \@currentlabel @oremn@me...

    1996

  2. [2]

    ތ jr ̼6 -(VSg\߰ b endstream endobj 16 0 obj <</Filter/FlateDecode/Length 585>>stream HTK-7 Dw @ 58#?Aמt] 3s D3,YKǟOHlC KP= UB >

    \@testbibitem \@testbibitem#1 \@ifnextchar( \@mrtestbibitem #1 \@doitestbibitem #1 \@ltestbibitem[#1]#2 \@ifnextchar( \@mrtestbibitem #2 \@doitestbibitem #2 \@doitestbibitem#1 \@ifnextchar[ \@doibibitem #1 \@bibitem #1 \@mrtestbibitem#1(#2) \@ifnextchar[ \@mrdoibibitem#1(#2) \@mrbibitem#1(#2) \@doibibitem#1[#2] \@tempa \@tempb #2 \@tempa\@tempb #2 [1] ##1...

    arXiv 2021

  3. [3]

    Alexanderian , A brief note on the Bayesian D-optimality criterion , 2023, https://arxiv.org/abs/2212.11466, https://arxiv.org/abs/2212.11466

    A. Alexanderian , A brief note on the Bayesian D-optimality criterion , 2023, https://arxiv.org/abs/2212.11466, https://arxiv.org/abs/2212.11466

    arXiv 2023

  4. [4]

    Attia, S

    A. Attia, S. Leyffer, and T. S. Munson , Stochastic Learning Approach for Binary Optimization: Application to B ayesian Optimal Design of Experiments , SIAM Journal on Scientific Computing, 44 (2022), p. B395–B427, https://doi.org/10.1137/21m1404363, http://dx.doi.org/10.1137/21M1404363

    doi:10.1137/21m1404363 2022

  5. [5]

    Bakker, H

    T. Bakker, H. van Hoof, and M. Welling , Experimental design for MRI by greedy policy search , in Proceedings of the 34th International Conference on Neural Information Processing Systems, NIPS '20, Red Hook, NY, USA, 2020, Curran Associates Inc

    2020

  6. [6]

    Barklage, M

    A. Barklage, M. Stradtner, and P. Bekemeyer , Sensor placement for optimal aerodynamic data fusion , Aerospace Science and Technology, 155 (2024), p. 109598, https://doi.org/https://doi.org/10.1016/j.ast.2024.109598, https://www.sciencedirect.com/science/article/pii/S1270963824007272

    arXiv 2024

  7. [7]

    Chakkor, E

    S. Chakkor, E. Cheikh, B. Mostafa, and A. Hajraoui , Efficiency Evaluation Metrics for Wireless Intelligent Sensors Applications , International Journal of Intelligent Systems and Application, 6 (2014), pp. 1--10, https://doi.org/10.5815/ijisa.2014.10.01

    work page doi:10.5815/ijisa.2014.10.01 2014

  8. [8]

    Clark, S

    E. Clark, S. L. Brunton, and J. N. Kutz , Multi-Fidelity Sensor Selection: Greedy Algorithms to Place Cheap and Expensive Sensors With Cost Constraints , IEEE Sensors Journal, 21 (2021), pp. 600--611, https://doi.org/10.1109/JSEN.2020.3013094

    arXiv 2021

Show all 32 references
  1. [9]

    Eswar, V

    S. Eswar, V. Rao, and A. K. Saibaba , Bayesian D -Optimal Experimental Designs via Column Subset Selection , 2025, https://arxiv.org/abs/2402.16000, https://arxiv.org/abs/2402.16000

    2025 arXiv

  2. [10]

    Ferrolino, J

    A. Ferrolino, J. E. Lope, and R. Mendoza , Optimal Location of Sensors for Early Detection of Tsunami Waves , Springer International Publishing, 06 2020, pp. 562--575, https://doi.org/10.1007/978-3-030-50417-5_42

    2020 doi

  3. [11]

    G. H. Golub and C. F. V. Loan , Matrix Computations , Johns Hopkins University Press, Baltimore, MD, 4th ed., 2013

    2013

  4. [12]

    G \"u nther, M

    T. G \"u nther, M. Gross, and H. Theisel , Generic Objective Vortices for Flow Visualization , ACM Transactions on Graphics (Proc. SIGGRAPH), 36 (2017), pp. 141:1--141:11

    2017

  5. [13]

    Haber, L

    E. Haber, L. Horesh, and L. Tenorio , Numerical methods for experimental design of large-scale linear ill-posed inverse problems , Inverse Problems, 24 (2008), p. 055012, https://doi.org/10.1088/0266-5611/24/5/055012

    2008 doi

  6. [14]

    R. A. Horn and C. R. Johnson , Matrix Analysis , Cambridge University Press, Cambridge, UK; New York, NY, USA, 2nd ed., 2012

    2012

  7. [15]

    Kakasenko, A

    L. Kakasenko, A. Alexanderian, M. Farazmand, and A. K. Saibaba , Bridging the Gap Between Deterministic and Probabilistic Approaches to State Estimation , 2025, https://arxiv.org/abs/2505.04004, https://arxiv.org/abs/2505.04004

    2025 arXiv

  8. [16]

    Kandasamy, G

    K. Kandasamy, G. Dasarathy, J. Oliva, J. Schneider, and B. P\' o czos , Gaussian process bandit optimisation with multi-fidelity evaluations , in Proceedings of the 30th International Conference on Neural Information Processing Systems, NIPS'16, Red Hook, NY, USA, 2016, Curran...

    2016

  9. [17]

    Khuller, A

    S. Khuller, A. Moss, and J. S. Naor , The budgeted maximum coverage problem , Inf. Process. Lett., 70 (1999), p. 39–45, https://doi.org/10.1016/S0020-0190(99)00031-9, https://doi.org/10.1016/S0020-0190(99)00031-9

    1999 doi

  10. [18]

    Korte and J

    B. Korte and J. Vygen , The Knapsack Problem , Springer Berlin Heidelberg, Berlin, Heidelberg, 2008, pp. 439--448, https://doi.org/10.1007/978-3-540-71844-4_17, https://doi.org/10.1007/978-3-540-71844-4_17

    2008 doi

  11. [19]

    Krause, A

    A. Krause, A. Singh, and C. Guestrin , Near-Optimal Sensor Placements in Gaussian Processes: Theory, Efficient Algorithms and Empirical Studies , Journal of Machine Learning Research, 9 (2008), pp. 235--284, http://jmlr.org/papers/v9/krause08a.html

    2008

  12. [20]

    Kumar Kundu , Chapter 1 - Introduction to sensors and types of biosensors , in Multifaceted Bio-sensing Technology , L

    B. Kumar Kundu , Chapter 1 - Introduction to sensors and types of biosensors , in Multifaceted Bio-sensing Technology , L. Singh, D. Mahapatra, and S. Kumar, eds., vol. 4 of Bioelectrochemical Systems: The way forward, Academic Press, 2023, pp. 1--12, https://doi.org/https://d...

    2023 doi

  13. [21]

    Leskovec, A

    J. Leskovec, A. Krause, C. Guestrin, C. Faloutsos, J. Vanbriesen, and N. Glance , Cost-effective outbreak detection in networks , Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 420-429 (2007), pp. 420--429, https://doi.org/10.114...

    2007

  14. [22]

    Lin, Y.-L

    J.-F. Lin, Y.-L. Xu, and S.-S. Law , Structural damage detection-oriented multi-type sensor placement with multi-objective optimization , Journal of Sound and Vibration, 422 (2018), pp. 568--589, https://doi.org/https://doi.org/10.1016/j.jsv.2018.01.047, https://www.sciencedir...

    2018 doi

  15. [23]

    Loose and P

    N. Loose and P. Heimbach , Leveraging Uncertainty Quantification to Design Ocean Climate Observing Systems , Journal of Advances in Modeling Earth Systems, 13 (2021), p. e2020MS002386, https://doi.org/https://doi.org/10.1029/2020MS002386, https://agupubs.onlinelibrary.wiley.co...

    2021 doi

  16. [24]

    Marcus and H

    M. Marcus and H. Minc , A Survey of Matrix Theory and Matrix Inequalities , The American Mathematical Monthly, (1965), https://api.semanticscholar.org/CorpusID:121044889

    1965

  17. [25]

    Minoux , Accelerated greedy algorithms for maximizing submodular set functions , in Optimization Techniques, J

    M. Minoux , Accelerated greedy algorithms for maximizing submodular set functions , in Optimization Techniques, J. Stoer, ed., Berlin, Heidelberg, 1978, Springer Berlin Heidelberg, pp. 234--243

    1978

  18. [26]

    https://www.ncei.noaa.gov/products/optimum-interpolation-sst, 2021

    National Oceanic and Atmospheric Administration (NOAA) , NOAA Optimal Interpolation (OI) Sea Surface Temperature (SST) v2 . https://www.ncei.noaa.gov/products/optimum-interpolation-sst, 2021. Accessed: 2025-06-17

    2021

  19. [27]

    G. L. Nemhauser, L. A. Wolsey, and M. L. Fisher , An analysis of approximations for maximizing submodular set functions—I , Mathematical Programming, 14 (1978), pp. 265--294, https://doi.org/10.1007/BF01588971

    1978 doi

  20. [28]

    Nishida, N

    T. Nishida, N. Ueno, S. Koyama, and H. Saruwatari , Region-Restricted Sensor Placement Based on Gaussian Process for Sound Field Estimation , IEEE Transactions on Signal Processing, 70 (2022), pp. 1718--1733, https://doi.org/10.1109/TSP.2022.3156012

    2022

  21. [29]

    Paredes-Ahumada, P

    J. Paredes-Ahumada, P. Ferrer-Cid, J. M. Barcelo-Ordinas, and J. Garcia-Vidal , Convex Relaxation Method for Sensor Placement in Multiclass Monitoring Networks , IEEE Transactions on Instrumentation and Measurement, 73 (2024), pp. 1--13, https://doi.org/10.1109/TIM.2024.3461788

    2024

  22. [30]

    T. G. Robertazzi and S. C. Schwartz , An Accelerated Sequential Algorithm for Producing D-Optimal Designs , SIAM Journal on Scientific and Statistical Computing, 10 (1989), pp. 341--358, https://doi.org/10.1137/0910022, https://doi.org/10.1137/0910022, https://arxiv.org/abs/ht...

    1989 doi

  23. [31]

    Shamaiah, S

    M. Shamaiah, S. Banerjee, and H. Vikalo , Greedy sensor selection: Leveraging submodularity , in 49th IEEE Conference on Decision and Control (CDC), 2010, pp. 2572--2577, https://doi.org/10.1109/CDC.2010.5717225

    2010

  24. [32]

    Sviridenko , A note on maximizing a submodular set function subject to a knapsack constraint , Operations Research Letters, 32 (2004), pp

    M. Sviridenko , A note on maximizing a submodular set function subject to a knapsack constraint , Operations Research Letters, 32 (2004), pp. 41--43, https://doi.org/https://doi.org/10.1016/S0167-6377(03)00062-2, https://www.sciencedirect.com/science/article/pii/S0167637703000622

    2004 doi

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.