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[Submitted on 4 Sep 2026] Title:Connecting Score Matching, Maximum Likelihood, and Expectation-Maximization in Mixed Linear Regression View a PDF of the paper titled Connecting Score Matching, Maximum Likelihood, and Expectation-Maximization in Mixed Linear Regression, by Zhankun Luo and 1 other authors View PDF HTML (experimental) Abstract:We study variance-preserving diffusion of the response in mixed linear regression (MLR) with unknown mixing weights. Our analysis separates the statistical guarantees of score matching from the loss geometry and optimization signal at a fixed diffusion noise level. The KL divergence links the denoising score matching objective integrated over the diffusion path with the likelihood and a terminal discrepancy. Under mild regularity conditions and terminal schedule, the resulting estimator converges up to the ground truth parameters of MLR, and its scaled error converges to the Gaussian limit of the maximum-likelihood estimator. At a fixed scale of the diffusion noise level, we derive a decomposition linking the score matching loss to cross-entropy and Expectation-Maximization (EM) operators. This decomposition yields an EM-related low-noise gradient expansion with additional correction terms of latent variance. In the high-noise limit, we further characterize gradient descent on this limiting loss under isotropic covariance. Along fixed high signal-to-noise ratio rays, the score matching imbalance gradient and the latent-variance term tend to zero pointwise. Numerical experiments illustrate our theoretical findings and statistical guarantees. Subjects: Machine Learning (cs.LG); Machine Learning (stat.ML) Cite as: arXiv:2609.05688 [cs.LG] (or arXiv:2609.05688v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2609.05688 arXiv-issued DOI via DataCite (pending registration) Submission history From: Zhankun Luo [view email] [v1] Fri, 4 Sep 2026 19:52:26 UTC (2,782 KB) Full-text links: Access Paper: View a PDF of the paper titled Connecting Score Matching, Maximum Likelihood, and Expectation-Maximization in Mixed Linear Regression, by Zhankun Luo and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG new | recent | 2026-09 Change to browse by: cs stat stat.ML References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: 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?) IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) 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?)