Beyond identifiability: Learning causal representations with few environments and finite samples

Statistics > Machine Learning [Submitted on 26 Mar 2026] Beyond identifiability: Learning causal representations with few environments and finite samples Inbeom Lee, Tongtong Jin, Bryon Aragam We provide explicit, finite-sample guarantees for learning causal representations from data with a sublinear number of environments. Causal representation learning seeks to provide a rigourous foundation for the general representation learning problem by bridging causal models with latent factor models in order to learn interpretable representations with causal semantics. Despite a blossoming theory of identifiability in causal representation learning, estimation and finite-sample bounds are less well understood. We show that causal representations can be learned with only a logarithmic number of unknown, multi-node interventions, and that the intervention targets need not be carefully designed in advance. Through a careful perturbation analysis, we provide a new analysis of this problem that guarantees consistent recovery of (a) the latent causal graph, (b) the mixing matrix and representations, and (c) \emph{unknown} intervention targets. Subjects: Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Statistics Theory (math.ST) Cite as: arXiv:2603.25796 [stat.ML]   (or arXiv:2603.25796v1 [stat.ML] for this version)   https://doi.org/10.48550/arXiv.2603.25796 Focus to learn more Submission history From: Bryon Aragam [view email] [v1] Thu, 26 Mar 2026 18:03:57 UTC (24 KB) Access Paper: HTML (experimental) view license Current browse context: stat.ML < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.AI cs.LG math math.ST stat stat.TH References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)