Inference for Similarity and Alignability between Noisy High-Dimensional Datasets

[2511.21074] Inference for Similarity and Alignability between Noisy High-Dimensional Datasets Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Statistics Theory arXiv:2511.21074 (math) [Submitted on 26 Nov 2025 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: Inference for Similarity and Alignability between Noisy High-Dimensional Datasets Authors: Hongrui Chen , Rong Ma View a PDF of the paper titled Inference for Similarity and Alignability between Noisy High-Dimensional Datasets, by Hongrui Chen and Rong Ma View PDF HTML (experimental) Abstract: The rapid growth of high-dimensional datasets across a wide range of scientific domains has created an urgent need for new statistical methods to compare distributions with underlying low-dimensional structure. Assessing similarity between high-dimensional datasets whose observations concentrate near low-dimensional manifolds is particularly challenging due to the nontrivial effects of noise in high dimensions. We propose a principled framework for statistical inference on the similarity and alignability of high-dimensional datasets with low-dimensional smooth signals under heterogeneous noise. The key idea is to link the spectral properties of the observed data matrices to the geometry of their underlying signal distributions. Under a manifold signal-plus-noise model, we build on the principal variances associated to the underlying signals and develop a scale- and rotation-invariant dissimilarity measure between two datasets that may differ in sample size and noise structure. We further construct an estimator of the dissimilarity and a statistical test of dataset alignability, namely, whether the dissimilarity vanishes. The proposed methodology and its theoretical guarantees under high-dimensional asymptotic settings draw on recent advances in random matrix theory (RMT). The proposed framework accommodates heterogeneous noise across datasets and provides a fast, theoretically grounded approach to comparing high-dimensional datasets with low-dimensional structures. Through extensive simulations and analyses of multiple single-cell datasets, we demonstrate that the proposed method substantially outperforms existing approaches. Subjects: Statistics Theory (math.ST) ; Methodology (stat.ME); Machine Learning (stat.ML) Cite as: arXiv:2511.21074 [math.ST] (or arXiv:2511.21074v2 [math.ST] for this version) https://doi.org/10.48550/arXiv.2511.21074 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Rong Ma [ view email ] [v1] Wed, 26 Nov 2025 05:31:35 UTC (291 KB) [v2] Sat, 15 Aug 2026 01:53:21 UTC (39,416 KB) Full-text links: Access Paper: View a PDF of the paper titled Inference for Similarity and Alignability between Noisy High-Dimensional Datasets, by Hongrui Chen and Rong Ma View PDF HTML (experimental) TeX Source view license Current browse context: math.ST < prev | next > new | recent | 2025-11 Change to browse by: math stat stat.ME stat.ML stat.TH References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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