Sensor Design for Accuracy-Bounded Estimation via Maximum-Entropy Likelihood Synthesis

• URL: http://arxiv.org/abs/2605.11120v1
• Date: Mon, 11 May 2026 18:28:45 GMT
• Title: Sensor Design for Accuracy-Bounded Estimation via Maximum-Entropy Likelihood Synthesis
• Abstract summary: Given an error budget, we synthesize the measurement likelihood that enforces it while injecting minimal information beyond the dynamical prior.<n>The framework accommodates arbitrary discrepancies and is instantiated for Wasserstein distance, mean discrepancy, $f$divergences, moment constraints, and hybrid metrics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Designing the sensing architecture for large-scale spatio-temporal systems is hard when accuracy requirements are specified but sensor models are uncertain or unavailable. Classical design treats sensor placement and estimation sequentially, requiring valid forward models for each sensing modality. This paper inverts the design flow: given an error budget, synthesize the measurement likelihood that enforces it while injecting minimal information beyond the dynamical prior. The likelihood is constructed by constrained optimization: among all posteriors satisfying a prescribed accuracy bound relative to a target, select the one minimizing Kullback-Leibler divergence from the prior. The solution is a maximum-entropy posterior in relative-entropy form, and the induced likelihood is the Radon-Nikodym derivative. The framework accommodates arbitrary discrepancies and is instantiated for Wasserstein distance, maximum mean discrepancy, $f$-divergences, moment constraints, and hybrid metrics. For each, we derive the discrete particle-level problem, analyze its convex or convex-relaxed structure, and present solvers with complexity scaling. A closed-form solution exists for the symmetric exponential-tilt case, and a distillation procedure converts nonparametric likelihood samples into parametric forms. A two-layer sensor design architecture embeds the synthesized likelihood in the recursive predict-update loop, connecting accuracy budgets to physical sensor placement, precision, and configuration. Numerical experiments comparing four metrics on unimodal and multimodal scenarios confirm the accuracy constraints are reliably enforced and reveal how metric choice determines the amount and spatial distribution of injected information.

Related papers

• Fitting Unknown Number of Hyperplanes with Manifold Optimization [57.48093263119306]
  Fitting unknown number of linearplanes to data is a fundamental yet challenging problem in machine learning.<n>Existing approaches often struggle with optimum optima or lack geometric consistency.
  arXiv  Detail & Related papers  (2026-05-27T14:02:20Z)
• A Unified Calibration Framework for Coordinate and Kinematic Parameters in Dual-Arm Robots [23.991712799218217]
  We present a novel framework for unified calibration of the coordinate transformations and kinematic parameters in both robot arms.<n>Our key idea is to unify all the tightly coupled parameters within a single Lie-algebraic formulation.<n>Our algorithm can yield a reliable estimate whose near-global optimality can be verified a posteriori.
  arXiv  Detail & Related papers  (2026-03-16T04:25:40Z)
• Slack More, Predict Better: Proximal Relaxation for Probabilistic Latent Variable Model-based Soft Sensors [12.346122868771118]
  Probabilistic Latent Variable Models (NPLVMs) are a cornerstone of soft sensor modeling.<n>NPLVMs are trained using amortized variational inference, where neural networks parameterize the variational posterior.<n>We introduce KProxNPLVM, a novel NPLVM that pivots to alleviate the objective itself and improving the NPLVM's performance.
  arXiv  Detail & Related papers  (2026-03-12T02:53:39Z)
• Geometry-Aware Optimal Transport: Fast Intrinsic Dimension and Wasserstein Distance Estimation [32.357350666094156]
  We introduce a tuning-free estimator of $textOT_c(, hat)$ that utilizes the semi-dual OT functional and, remarkably, requires no OT solver.<n>This framework unlocks significant computational and statistical advantages in practice.<n> Numerical experiments demonstrate that our geometry-aware pipeline effectively mitigates the discretization error bottleneck.
  arXiv  Detail & Related papers  (2026-02-04T08:56:28Z)
• On the Optimal Construction of Unbiased Gradient Estimators for Zeroth-Order Optimization [57.179679246370114]
  A potential limitation of existing methods is the bias inherent in most perturbation estimators unless a stepsize is proposed.<n>We propose a novel family of unbiased gradient scaling estimators that eliminate bias while maintaining favorable construction.
  arXiv  Detail & Related papers  (2025-10-22T18:25:43Z)
• Accelerated zero-order SGD under high-order smoothness and overparameterized regime [79.85163929026146]
  We present a novel gradient-free algorithm to solve convex optimization problems. Such problems are encountered in medicine, physics, and machine learning. We provide convergence guarantees for the proposed algorithm under both types of noise.
  arXiv  Detail & Related papers  (2024-11-21T10:26:17Z)
• SPARE: Symmetrized Point-to-Plane Distance for Robust Non-Rigid 3D Registration [77.13381026159111]
  We propose SPARE, a novel formulation that utilizes a symmetrized point-to-plane distance for robust non-rigid registration.<n>The proposed method greatly improves the accuracy of non-rigid registration problems and maintains relatively high solution efficiency.
  arXiv  Detail & Related papers  (2024-05-30T15:55:04Z)
• Dimension matters: precision and incompatibility in multi-parameter quantum estimation models [44.99833362998488]
  We study the role of probe dimension in determining the bounds of precision in quantum estimation problems. We also critically examine the performance of the so-called incompatibility (AI) in characterizing the difference between the Holevo-Cram'er-Rao bound and the Symmetric Logarithmic Derivative (SLD) one.
  arXiv  Detail & Related papers  (2024-03-11T18:59:56Z)
• Distributed Estimation and Inference for Semi-parametric Binary Response Models [8.309294338998539]
  This paper studies the maximum score estimator of a semi-parametric binary choice model under a distributed computing environment. An intuitive divide-and-conquer estimator is computationally expensive and restricted by a non-regular constraint on the number of machines.
  arXiv  Detail & Related papers  (2022-10-15T23:06:46Z)
• Information Entropy Initialized Concrete Autoencoder for Optimal Sensor Placement and Reconstruction of Geophysical Fields [58.720142291102135]
  We propose a new approach to the optimal placement of sensors for reconstructing geophysical fields from sparse measurements. We demonstrate our method on the two examples: (a) temperature and (b) salinity fields around the Barents Sea and the Svalbard group of islands. We find out that the obtained optimal sensor locations have clear physical interpretation and correspond to the boundaries between sea currents.
  arXiv  Detail & Related papers  (2022-06-28T12:43:38Z)
• Wasserstein Distributionally Robust Estimation in High Dimensions: Performance Analysis and Optimal Hyperparameter Tuning [2.4578723416255754]
  Distributionally robust optimization (DRO) has become a powerful framework for estimation under uncertainty.<n>We propose a DRO-based method for linear regression and address a central question: how to optimally choose the robustness radius.<n>We show that our method achieves the same effect as cross-validation, but at a fraction of the computational cost.
  arXiv  Detail & Related papers  (2022-06-27T13:02:59Z)
• Inverting brain grey matter models with likelihood-free inference: a tool for trustable cytoarchitecture measurements [62.997667081978825]
  characterisation of the brain grey matter cytoarchitecture with quantitative sensitivity to soma density and volume remains an unsolved challenge in dMRI. We propose a new forward model, specifically a new system of equations, requiring a few relatively sparse b-shells. We then apply modern tools from Bayesian analysis known as likelihood-free inference (LFI) to invert our proposed model.
  arXiv  Detail & Related papers  (2021-11-15T09:08:27Z)
• Manifold learning-based polynomial chaos expansions for high-dimensional surrogate models [0.0]
  We introduce a manifold learning-based method for uncertainty quantification (UQ) in describing systems. The proposed method is able to achieve highly accurate approximations which ultimately lead to the significant acceleration of UQ tasks.
  arXiv  Detail & Related papers  (2021-07-21T00:24:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.