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[Submitted on 16 Sep 2026] Title:Sparse Priors for Efficient Distribution Learning View a PDF of the paper titled Sparse Priors for Efficient Distribution Learning, by Saumya Goyal and 1 other authors View PDF HTML (experimental) Abstract:Despite the widespread use and success of generative AI techniques today, theoretical guarantees on learning a distribution supported in $d$ dimensions from $n$ samples degrade as $O(n^{-1/\Theta(d)})$, though shown to be minimax optimal. We hypothesize that present bounds are too pessimistic because smoothness assumptions are not enough to capture the structure of distributions that often appear in real applications. Consequently, we introduce the class of sparse priors and define the "Sparse Dimension" as a measure of sparsity of a prior over the space of all distributions. We show that distribution learning under a $k$-sparse prior achieves a Bayesian risk lower bound of $\Omega(\sqrt{k/n})$ under common distance metrics, and show a matching (up to logarithmic terms asymptotically in $n,k$) upper bound for the TV distance under mild additional assumptions. We show the statistical equivalence of distribution learning and learning to sample in the Bayesian setting so that our results apply to learning to sample as well. While $k$ can still depend on the dimension $d$, or a notion of intrinsic dimension, our results show that learning under an appropriate prior overcomes the curse of dimensionality with respect to the dependence on $n$. Subjects: Machine Learning (cs.LG); Statistics Theory (math.ST) Cite as: arXiv:2609.20883 [cs.LG] (or arXiv:2609.20883v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2609.20883 arXiv-issued DOI via DataCite (pending registration) Submission history From: Saumya Goyal [view email] [v1] Wed, 16 Sep 2026 21:13:14 UTC (71 KB) Full-text links: Access Paper: View a PDF of the paper titled Sparse Priors for Efficient Distribution Learning, by Saumya Goyal 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 math math.ST stat stat.TH 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?)