mlsanityData to 14 Oct 2026

Data-Induced Interactions of Sparse Sensors Using Statistical Physics

arXiv 2307.11838 ↗First posted 21 Jul 2023cond-mat.stat-mech cs.LG eess.SPcited by 3

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Abstract (arXiv)

Large-dimensional empirical data in science and engineering frequently have a low-rank structure and can be represented as a combination of just a few eigenmodes. Because of this structure, we can use just a few spatially localized sensor measurements to reconstruct the full state of a complex system. The quality of this reconstruction, especially in the presence of sensor noise, depends significantly on the spatial configuration of the sensors. Multiple algorithms based on gappy interpolation and QR factorization have been proposed to optimize sensor placement. Here, instead of an algorithm that outputs a single "optimal" sensor configuration, we take a statistical mechanics view to compute the full landscape of sensor interactions induced by the training data. The two key advances of this paper are the recasting of the sensor placement landscape in an Ising model form and a regularized reconstruction that significantly decreases reconstruction error for few sensors. In addition, we provide first uncertainty quantification of the sparse sensing reconstruction and open questions about the shape of reconstruction risk curve. Mapping out these data-induced sensor interactions allows combining them with external selection criteria and anticipating sensor replacement impacts.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 16 of its 57 references that are in the map. First posted on arXiv 21 Jul 2023.

Builds on

16 of 57 references.

References · 16

  1. 2013Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Mapscited by 2,371
  2. 2018Reconciling modern machine learning practice and the bias-variance trade-offcited by 927
  3. 2023Modern Bayesian Experimental Designcited by 125
  4. 2020Optimal Regularization Can Mitigate Double Descentcited by 109
  5. 2020Double Trouble in Double Descent : Bias and Variance(s) in the Lazy Regimecited by 95
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  7. 2020A Brief Prehistory of Double Descentcited by 44
  8. 2020Learning a Probabilistic Strategy for Computational Imaging Sensor Selectioncited by 8
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  11. 2023Constrained optimization of sensor placement for nuclear digital twinscited by 6
  12. 2018Greedy Sensor Placement with Cost Constraintscited by 5
4 more
  1. 2018Optimal Sensor and Actuator Selection using Balanced Model Reductioncited by 3
  2. 2021Inadequacy of Linear Methods for Minimal Sensor Placement and Feature Selection in Nonlinear Systems; a New Approach Using Secantscited by 3
  3. 2021Dynamic Compressed Sensing of Unsteady Flows with a Mobile Robotcited by 2
  4. 2018Surges of collective human activity emerge from simple pairwise correlationscited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 0; 2026: 2.

3 papers.

  1. 2024State Estimation Using Sparse DEIM and Recurrent Neural Networkscited by 1
  2. 2026Christoffel-DPS: Optimal sensor placement in diffusion posterior sampling for arbitrary distributionscited by 0
  3. 2026Origins and mitigation of double descent in reduced order modelingcited by 0