Sensitivity-preserving of Fisher Information Matrix through random data down-sampling for experimental design

[2409.15906] Local sensitivity-preserving random data down-sampling for experimental design Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2409.15906 (math) [Submitted on 24 Sep 2024 ( v1 ), last revised 3 Aug 2026 (this version, v4)] Title: Local sensitivity-preserving random data down-sampling for experimental design Authors: Kathrin Hellmuth , Christian Klingenberg , Qin Li View a PDF of the paper titled Local sensitivity-preserving random data down-sampling for experimental design, by Kathrin Hellmuth and 2 other authors View PDF HTML (experimental) Abstract: The quality of numerical reconstructions for unknown parameters in inverse problems depends fundamentally on the selection of experimental data. To ensure a robust reconstruction, it is crucial to select data that are sensitive to the parameters, a property typically characterized by the conditioning of the Fisher Information Matrix (FIM). In this work, we propose a general framework for an efficient down-sampling strategy that selects experimental setups that preserve the information content of the full-data FIM. Our approach leverages matrix sketching techniques from randomized numerical linear algebra to achieve a sensitivity-preserving approximation. The method involves drawing samples from a sensitivity-informed distribution, which we execute using gradient-free ensemble sampling methods to handle potentially non-smooth or discrete design spaces. Numerical experiments demonstrate the effectiveness of this framework in selecting optimal sensor locations for a Schroedinger potential reconstruction problem. Subjects: Numerical Analysis (math.NA) ; Optimization and Control (math.OC) MSC classes: 49N45, 65N21, 65Fxx, 62Dxx, 49M41, 90C31 Cite as: arXiv:2409.15906 [math.NA] (or arXiv:2409.15906v4 [math.NA] for this version) https://doi.org/10.48550/arXiv.2409.15906 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Kathrin Hellmuth [ view email ] [v1] Tue, 24 Sep 2024 09:21:11 UTC (537 KB) [v2] Mon, 28 Jul 2025 17:06:44 UTC (571 KB) [v3] Sat, 11 Apr 2026 01:19:42 UTC (5,434 KB) [v4] Mon, 3 Aug 2026 22:39:57 UTC (5,436 KB) Full-text links: Access Paper: View a PDF of the paper titled Local sensitivity-preserving random data down-sampling for experimental design, by Kathrin Hellmuth and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2024-09 Change to browse by: cs cs.NA math math.OC References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Accurate Trace Estimation with Fewer Random Bits via Recursive TensorSketch#1012755
• Accurate Trace Estimation with Fewer Random Bits via Recursive TensorSketch#965442
• Fisher-information training of optical sensing front ends from natural fluctuations#1051311
• Multiparameter Maximum Information States for Coherent Diffraction Measurements#974444
• ADS-C: Antidistillation Sampling for Classification#381699