# Data-Induced Interactions of Sparse Sensors Using Statistical Physics

arXiv: https://arxiv.org/abs/2307.11838 · HTML: https://mlsanity.com/paper/2307.11838/

## 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 (most cited first, 16 of 16)

- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Optimal Regularization Can Mitigate Double Descent](https://mlsanity.com/paper/2003.01897/) (2020)
- [Double Trouble in Double Descent : Bias and Variance(s) in the Lazy Regime](https://mlsanity.com/paper/2003.01054/) (2020)
- [Data-Driven Sparse Sensor Placement for Reconstruction](https://mlsanity.com/paper/1701.07569/) (2017)
- [A Brief Prehistory of Double Descent](https://mlsanity.com/paper/2004.04328/) (2020)
- [Learning a Probabilistic Strategy for Computational Imaging Sensor Selection](https://mlsanity.com/paper/2003.10424/) (2020)
- [PySensors: A Python Package for Sparse Sensor Placement](https://mlsanity.com/paper/2102.13476/) (2021)
- [Sensor Placement for Optimal Kalman Filtering: Fundamental Limits, Submodularity, and Algorithms](https://mlsanity.com/paper/1509.08146/) (2015)
- [Constrained optimization of sensor placement for nuclear digital twins](https://mlsanity.com/paper/2306.13637/) (2023)
- [Greedy Sensor Placement with Cost Constraints](https://mlsanity.com/paper/1805.03717/) (2018)
- [Optimal Sensor and Actuator Selection using Balanced Model Reduction](https://mlsanity.com/paper/1812.01574/) (2018)
- [Inadequacy of Linear Methods for Minimal Sensor Placement and Feature Selection in Nonlinear Systems; a New Approach Using Secants](https://mlsanity.com/paper/2101.11162/) (2021)
- [Dynamic Compressed Sensing of Unsteady Flows with a Mobile Robot](https://mlsanity.com/paper/2110.08658/) (2021)
- [Surges of collective human activity emerge from simple pairwise correlations](https://mlsanity.com/paper/1803.00118/) (2018)

## Built on by (most cited first, 3 of 3)

- [State Estimation Using Sparse DEIM and Recurrent Neural Networks](https://mlsanity.com/paper/2410.15982/) (2024)
- [Christoffel-DPS: Optimal sensor placement in diffusion posterior sampling for arbitrary distributions](https://mlsanity.com/paper/2605.06861/) (2026)
- [Origins and mitigation of double descent in reduced order modeling](https://mlsanity.com/paper/2607.26414/) (2026)

## 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.