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Existing generative models of genetic variation, however, struggle to faithfully express dependencies in the data while retaining tractability and preserving privacy. We introduce Genetic Probabilistic Circuits (\n                    <jats:sc>GPC<\/jats:sc>\n                    ), a deep generative model for genetic variation data based on hidden Chow-Liu trees represented as probabilistic circuits.\n                    <jats:sc>GPC<\/jats:sc>\n                    generalizes traditional hidden Markov models by allowing arbitrary tree structures over latent variables, enabling it to capture long-range dependencies among SNPs.\n                    <jats:sc>GPC<\/jats:sc>\n                    is tractable, supporting exact computation of marginal and conditional probabilities that enables both AG generation and direct genotype imputation (avoiding the need for simulating AGs). We show that\n                    <jats:sc>GPC<\/jats:sc>\n                    generates AGs that accurately reproduce population structure and linkage disequilibrium patterns across a range of length scales. Compared to other deep generative approaches,\n                    <jats:sc>GPC<\/jats:sc>\n                    consistently improves imputation accuracy, with particularly strong gains for low-frequency variants and in populations that are not well-represented in public reference panels. Finally, we show that\n                    <jats:sc>GPC<\/jats:sc>\n                    better preserves privacy of the training data, thereby providing a practical framework for AG generation in settings with limited data access.\n                  <\/jats:p>","DOI":"10.1371\/journal.pgen.1012321","type":"journal-article","created":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T17:50:21Z","timestamp":1791309021000},"page":"e1012321","update-policy":"https:\/\/doi.org\/10.1371\/journal.pgen.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["GPC: An expressive and tractable deep generative model for genetic variation data"],"prefix":"10.1371","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-8455-1308","authenticated-orcid":true,"given":"Prateek","family":"Anand","sequence":"first","affiliation":[{"name":"University of California","place":["Los Angeles, California, United States of America"],"department":["Department of Computer Science"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anji","family":"Liu","sequence":"additional","affiliation":[{"name":"National University of Singapore","place":["Singapore, Singapore"],"department":["Department of Computer Science"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8241-1943","authenticated-orcid":true,"given":"Meihua","family":"Dang","sequence":"additional","affiliation":[{"name":"Stanford University","place":["Stanford, California, United States of America"],"department":["Department of Computer Science"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Boyang","family":"Fu","sequence":"additional","affiliation":[{"name":"Harvard Medical School","place":["Boston, Massachusetts, United States of America"],"department":["Department of Biomedical Informatics"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8184-7016","authenticated-orcid":true,"given":"Xinzhu","family":"Wei","sequence":"additional","affiliation":[{"name":"Cornell University","place":["Ithaca, New York, United States of America"],"department":["Department of Computational Biology"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guy","family":"Van den Broeck","sequence":"additional","affiliation":[{"name":"University of California","place":["Los Angeles, California, United States of America"],"department":["Department of Computer Science"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1586-9641","authenticated-orcid":true,"given":"Sriram","family":"Sankararaman","sequence":"additional","affiliation":[{"name":"University of California","place":["Los Angeles, California, United States of America"],"department":["Department of Computer Science"]},{"name":"University of California","place":["Los Angeles, California, United States of America"],"department":["Department of Human Genetics"]},{"name":"University of California","place":["Los Angeles, California, United States of America"],"department":["Department of Computational Medicine"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2026,10,6]]},"reference":[{"key":"pgen.1012321.ref001","doi-asserted-by":"crossref","unstructured":"Nordborg M. 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Class-conditional vae-gan for local-ancestry simulation. arXiv preprint. 2019;arXiv:1911.13220."},{"issue":"2","key":"pgen.1012321.ref006","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1093\/bioinformatics\/18.2.337","article-title":"Generating samples under a Wright-Fisher neutral model of genetic variation","volume":"18","author":"RR Hudson","year":"2002","journal-title":"Bioinformatics"},{"issue":"4","key":"pgen.1012321.ref007","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1093\/bioinformatics\/btl622","article-title":"msHOT: modifying Hudson\u2019s ms simulator to incorporate crossover and gene conversion hotspots","volume":"23","author":"G Hellenthal","year":"2007","journal-title":"Bioinformatics"},{"issue":"9","key":"pgen.1012321.ref008","doi-asserted-by":"crossref","first-page":"1332","DOI":"10.1093\/bioinformatics\/btr124","article-title":"fastsimcoal: a continuous-time coalescent simulator of genomic diversity under arbitrarily complex evolutionary scenarios","volume":"27","author":"L Excoffier","year":"2011","journal-title":"Bioinformatics"},{"issue":"5","key":"pgen.1012321.ref009","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1004842","article-title":"Efficient Coalescent Simulation and Genealogical Analysis for Large Sample Sizes","volume":"12","author":"J Kelleher","year":"2016","journal-title":"PLoS Comput Biol"},{"key":"pgen.1012321.ref010","article-title":"Efficient ancestry and mutation simulation with msprime 1.0","author":"F Baumdicker","year":"2021","journal-title":"bioRxiv"},{"issue":"2","key":"pgen.1012321.ref011","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/0040-5809(83)90013-8","article-title":"Properties of a neutral allele model with intragenic recombination","volume":"23","author":"RR Hudson","year":"1983","journal-title":"Theor Popul Biol"},{"key":"pgen.1012321.ref012","first-page":"257","article-title":"Griffiths and Paul Marjoram. An Ancestral Recombination Graph.","volume-title":"Progress in Population Genetics and Human Evolution, IMA Volumes in Mathematics and its Applications","author":"RC Griffiths","year":"1997"},{"issue":"3","key":"pgen.1012321.ref013","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1006\/tpbi.1998.1403","article-title":"Recombination as a point process along sequences","volume":"55","author":"C Wiuf","year":"1999","journal-title":"Theor Popul Biol"},{"issue":"1459","key":"pgen.1012321.ref014","doi-asserted-by":"crossref","first-page":"1387","DOI":"10.1098\/rstb.2005.1673","article-title":"Approximating the coalescent with recombination","volume":"360","author":"GAT McVean","year":"2005","journal-title":"Philos Trans R Soc Lond B Biol Sci"},{"key":"pgen.1012321.ref015","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1186\/1471-2156-7-16","article-title":"Fast \u201ccoalescent\u201d simulation","volume":"7","author":"P Marjoram","year":"2006","journal-title":"BMC Genet"},{"issue":"4","key":"pgen.1012321.ref016","doi-asserted-by":"crossref","first-page":"2213","DOI":"10.1093\/genetics\/165.4.2213","article-title":"Modeling linkage disequilibrium and identifying recombination hotspots using single-nucleotide polymorphism data","volume":"165","author":"N Li","year":"2003","journal-title":"Genetics"},{"issue":"1","key":"pgen.1012321.ref017","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1109\/MASSP.1986.1165342","article-title":"An introduction to hidden Markov models","volume":"3","author":"L Rabiner","year":"1986","journal-title":"IEEE ASSP Mag"},{"issue":"4","key":"pgen.1012321.ref018","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1086\/502802","article-title":"A fast and flexible statistical model for large-scale population genotype data: applications to inferring missing genotypes and haplotypic phase","volume":"78","author":"P Scheet","year":"2006","journal-title":"Am J Hum Genet"},{"issue":"2","key":"pgen.1012321.ref019","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1038\/nmeth.1785","article-title":"A linear complexity phasing method for thousands of genomes","volume":"9","author":"O Delaneau","year":"2011","journal-title":"Nat Methods"},{"issue":"8","key":"pgen.1012321.ref020","doi-asserted-by":"crossref","first-page":"955","DOI":"10.1038\/ng.2354","article-title":"Fast and accurate genotype imputation in genome-wide association studies through pre-phasing","volume":"44","author":"B Howie","year":"2012","journal-title":"Nat Genet"},{"issue":"10","key":"pgen.1012321.ref021","doi-asserted-by":"crossref","first-page":"1359","DOI":"10.1093\/bioinformatics\/bts144","article-title":"Fast and accurate inference of local ancestry in latino populations","volume":"28","author":"Y Baran","year":"2012","journal-title":"Bioinformatics"},{"issue":"6","key":"pgen.1012321.ref022","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pgen.1000519","article-title":"Sensitive detection of chromosomal segments of distinct ancestry in admixed populations","volume":"5","author":"AL Price","year":"2009","journal-title":"PLoS Genet"},{"issue":"1","key":"pgen.1012321.ref023","doi-asserted-by":"crossref","DOI":"10.1093\/g3journal\/jkaa036","article-title":"Visualizing population structure with variational autoencoders","volume":"11","author":"CJ Battey","year":"2021","journal-title":"G3 (Bethesda)"},{"issue":"2","key":"pgen.1012321.ref024","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pgen.1009303","article-title":"Creating artificial human genomes using generative neural networks","volume":"17","author":"B Yelmen","year":"2021","journal-title":"PLoS Genet"},{"issue":"10","key":"pgen.1012321.ref025","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1011584","article-title":"Deep convolutional and conditional neural networks for large-scale genomic data generation","volume":"19","author":"B Yelmen","year":"2023","journal-title":"PLoS Comput Biol"},{"key":"pgen.1012321.ref026","unstructured":"Szatkownik A, Furtlehner CF, Charpiat G, Yelmen B, Jay F. Towards creating longer genetic sequences with gans: Generation in principal component space. In Knowles DA, Mostafavi S, editors. Proceedings of the 18th Machine Learning in Computational Biology meeting, volume 240 of Proceedings of Machine Learning Research. 2024. p. 110\u201322."},{"issue":"4","key":"pgen.1012321.ref027","doi-asserted-by":"crossref","DOI":"10.1093\/genetics\/iyae024","article-title":"Interpreting generative adversarial networks to infer natural selection from genetic data","volume":"226","author":"R Riley","year":"2024","journal-title":"Genetics"},{"key":"pgen.1012321.ref028","article-title":"Genome-AC-GAN: Enhancing synthetic genotype generation through auxiliary classification","author":"A Shaked","year":"2024","journal-title":"bioRxiv"},{"issue":"2","key":"pgen.1012321.ref029","first-page":"348","article-title":"Autoencoders for genomic variation analysis","volume":"36","author":"M Geleta","year":"2026","journal-title":"Genome Res"},{"issue":"3","key":"pgen.1012321.ref030","article-title":"Generating realistic artificial human genomes using adversarial autoencoders","volume":"7","author":"C Burnard","year":"2025","journal-title":"NAR Genom Bioinform"},{"issue":"1","key":"pgen.1012321.ref031","article-title":"Generating synthetic genotypes using diffusion models","volume":"41","author":"P Kenneweg","year":"2025","journal-title":"Bioinformatics"},{"issue":"11","key":"pgen.1012321.ref032","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pgen.1009049","article-title":"Genotype imputation using the Positional Burrows Wheeler Transform","volume":"16","author":"S Rubinacci","year":"2020","journal-title":"PLoS Genet"},{"issue":"3","key":"pgen.1012321.ref033","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/j.ajhg.2018.07.015","article-title":"A One-Penny Imputed Genome from Next-Generation Reference Panels","volume":"103","author":"BL Browning","year":"2018","journal-title":"Am J Hum Genet"},{"issue":"5","key":"pgen.1012321.ref034","doi-asserted-by":"crossref","first-page":"782","DOI":"10.1093\/bioinformatics\/btu704","article-title":"Minimac2: faster genotype imputation","volume":"31","author":"C Fuchsberger","year":"2014","journal-title":"Bioinformatics"},{"key":"pgen.1012321.ref035","unstructured":"Liu A, Van den Broeck G. Tractable regularization of probabilistic circuits. In: Advances in Neural Information Processing Systems 35 (NeurIPS). 2021."},{"issue":"1","key":"pgen.1012321.ref036","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1086\/321275","article-title":"Linkage disequilibrium in humans: models and data","volume":"69","author":"JK Pritchard","year":"2001","journal-title":"Am J Hum Genet"},{"key":"pgen.1012321.ref037","unstructured":"Vergari A, Choi YJ, Peharz R, Van den Broeck G. Probabilistic circuits: representations, inference, learning and applications. In: AAAI Tutorial. 2020."},{"key":"pgen.1012321.ref038","unstructured":"Choi YJ, Vergari A, Van den Broeck G. Probabilistic circuits: A unifying framework for tractable probabilistic models. 2020."},{"issue":"3","key":"pgen.1012321.ref039","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1109\/TIT.1968.1054142","article-title":"Approximating discrete probability distributions with dependence trees","volume":"14","author":"C Chow","year":"1968","journal-title":"IEEE Trans Inform Theory"},{"key":"pgen.1012321.ref040","unstructured":"Liu A, Ahmed K, Van den Broeck G. Scaling tractable probabilistic circuits: A systems perspective. In: Proceedings of the 41th International Conference on Machine Learning (ICML). 2024."},{"issue":"7571","key":"pgen.1012321.ref041","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1038\/nature15393","article-title":"A global reference for human genetic variation","volume":"526","author":"1000 Genomes Project Consortium","year":"2015","journal-title":"Nature"},{"issue":"7726","key":"pgen.1012321.ref042","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1038\/s41586-018-0579-z","article-title":"The UK Biobank resource with deep phenotyping and genomic data","volume":"562","author":"C Bycroft","year":"2018","journal-title":"Nature"},{"issue":"18","key":"pgen.1012321.ref043","doi-asserted-by":"crossref","DOI":"10.1016\/j.cell.2022.08.004","article-title":"High-coverage whole-genome sequencing of the expanded 1000 genomes project cohort including 602 trios","volume":"185","author":"M Byrska-Bishop","year":"2022","journal-title":"Cell"},{"issue":"6","key":"pgen.1012321.ref044","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1016\/j.ajhg.2022.04.002","article-title":"Meta-imputation: An efficient method to combine genotype data after imputation with multiple reference panels","volume":"109","author":"K Yu","year":"2022","journal-title":"Am J Hum Genet"},{"key":"pgen.1012321.ref045","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1016\/j.neucom.2019.12.136","article-title":"Generation and evaluation of privacy preserving synthetic health data","volume":"416","author":"A Yale","year":"2020","journal-title":"Neurocomputing"},{"key":"pgen.1012321.ref046","doi-asserted-by":"crossref","unstructured":"Shokri R, Stronati M, Song C, Shmatikov V. Membership Inference Attacks Against Machine Learning Models. In: 2017 IEEE Symposium on Security and Privacy (SP). IEEE; 2017. p. 3\u201318.","DOI":"10.1109\/SP.2017.41"},{"issue":"8","key":"pgen.1012321.ref047","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pgen.1000167","article-title":"Resolving individuals contributing trace amounts of dna to highly complex mixtures using high-density snp genotyping microarrays","volume":"4","author":"N Homer","year":"2008","journal-title":"PLoS Genetics"},{"key":"pgen.1012321.ref048","doi-asserted-by":"crossref","unstructured":"Fredrikson M, Jha S, Ristenpart T. Model Inversion Attacks that Exploit Confidence Information and Basic Countermeasures. In: Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security. 2015. p. 1322\u201333.","DOI":"10.1145\/2810103.2813677"},{"key":"pgen.1012321.ref049","unstructured":"Park M, Foulds J, Chaudhuri K, Welling M. Dp-em: Differentially private expectation maximization. 2016."},{"key":"pgen.1012321.ref050","first-page":"2672","article-title":"Generative adversarial nets","author":"I Goodfellow","year":"2014","journal-title":"Adv Neural Inform Process Syst"},{"key":"pgen.1012321.ref051","unstructured":"Kingma DP, Welling M. Auto-encoding variational bayes. arXiv preprint. 2013;arxiv:1312.6114."},{"key":"pgen.1012321.ref052","article-title":"Don\u2019t explain without verifying veracity: An evaluation of explainable AI with video activity recognition","author":"M Nourani","year":"2020","journal-title":"CoRR"},{"key":"pgen.1012321.ref053","unstructured":"Ahmed K, Zeng Z, Niepert M, Van den Broeck G. Simple: A gradient estimator for k-subset sampling. In: ICLR. 2023."},{"key":"pgen.1012321.ref054","first-page":"11169","article-title":"On tractable computation of expected predictions","volume":"32","author":"P Khosravi","year":"2019","journal-title":"Adv Neural Inform Process Syst"},{"issue":"10","key":"pgen.1012321.ref055","doi-asserted-by":"crossref","first-page":"12278","DOI":"10.1609\/aaai.v37i10.26447","article-title":"Certifying Fairness of Probabilistic Circuits","volume":"37","author":"NR Selvam","year":"2023","journal-title":"AAAI"},{"issue":"13","key":"pgen.1012321.ref056","doi-asserted-by":"crossref","first-page":"12051","DOI":"10.1609\/aaai.v35i13.17431","article-title":"Group Fairness by Probabilistic Modeling with Latent Fair Decisions","volume":"35","author":"Y Choi","year":"2021","journal-title":"AAAI"},{"key":"pgen.1012321.ref057","unstructured":"Correia A, Peharz R, de Campos CP. Joints in random forests. In: Advances in Neural Information Processing Systems 33 (NeurIPS). 2020."},{"key":"pgen.1012321.ref058","unstructured":"Li W, Zeng Z, Vergari A, Van den Broeck G. Tractable computation of expected kernels. In: Proceedings of the 37th Conference on Uncertainty in Artificial Intelligence (UAI). 2021."},{"key":"pgen.1012321.ref059","unstructured":"Dang M, Vergari A, Van den Broeck G. Strudel: Learning structured-decomposable probabilistic circuits. In: Proceedings of the 10th International Conference on Probabilistic Graphical Models (PGM). 2020."},{"key":"pgen.1012321.ref060","unstructured":"Zhang H, Juba B, Van den Broeck G. Probabilistic generating circuits. In: Proceedings of the 38th International Conference on Machine Learning (ICML). 2021."},{"key":"pgen.1012321.ref061","unstructured":"Darwiche A. A logical approach to factoring belief networks. In: Proceedings of KR. 2002. p. 409\u201320."},{"key":"pgen.1012321.ref062","doi-asserted-by":"crossref","unstructured":"Poon H, Domingos P. Sum-product networks: A new deep architecture. In: 2011 IEEE International Conference on Computer Vision Workshops (ICCV Workshops). 2011. p. 689\u201390.","DOI":"10.1109\/ICCVW.2011.6130310"},{"key":"pgen.1012321.ref063","doi-asserted-by":"crossref","first-page":"630","DOI":"10.1007\/978-3-662-44851-9_40","article-title":"Cutset Networks: A Simple, Tractable, and Scalable Approach for Improving the Accuracy of Chow-Liu Trees.","volume-title":"Joint European conference on machine learning and knowledge discovery in databases","author":"T Rahman","year":"2014"},{"key":"pgen.1012321.ref064","unstructured":"Vergari A, Choi YJ, Liu A, Teso S, Van den Broeck G. A compositional atlas of tractable circuit operations for probabilistic inference. In: Advances in Neural Information Processing Systems 35 (NeurIPS). 2021."},{"key":"pgen.1012321.ref065","unstructured":"Doga K, Van den Broeck G, Choi A, Darwiche A. Probabilistic sentential decision diagrams. In: Fourteenth International Conference on the Principles of Knowledge Representation and Reasoning. 2014."},{"key":"pgen.1012321.ref066","volume-title":"Probabilistic Graphical Models: Principles and Techniques - Adaptive Computation and Machine Learning","author":"Daphne Koller and Nir Friedman","year":"2009"}],"updated-by":[{"DOI":"10.1371\/journal.pgen.1012321","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T00:00:00Z","timestamp":1791504000000}}],"container-title":["PLOS Genetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pgen.1012321","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T18:07:30Z","timestamp":1791569250000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pgen.1012321"}},"subtitle":[],"editor":[{"given":"Yun","family":"Li","sequence":"first","affiliation":[{"name":"University of North Carolina at Chapel Hill","place":["UNITED STATES OF AMERICA"]}],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2026,10,6]]},"references-count":66,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2026,10,6]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pgen.1012321","relation":{},"ISSN":["1553-7404"],"issn-type":[{"value":"1553-7404","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,6]]}}}