[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84342-en":3,"doc-seo-84342-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},84342,1099514068365,"Aurelia","https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068",8,"Research & Report","CASL-VAE: Learning Structured Latent Variables from Unpaired Data","CASL-VAE is a deep contrastive latent variable model designed to quantify variability of a target population relative to a reference population when paired data are unavailable. It learns structured generative factors from unpaired data by decomposing variation into continuous common latent factors shared across populations and a hierarchical target-specific latent. The hierarchical latent captures discrete subtypes and continuous within-subtype heterogeneity. Variational inference enables approximate joint likelihood optimization across reference and target domains, supporting paired-sample generation and cross-domain analysis, validated on neuroimaging and Alzheimer’s heterogeneity.","CASL-VAE: Learning Structured Latent Variables from Unpaired Data for Semi-supervised Clustering and Paired Sample Generation  \nSai Spandana Chintapalli 1 2 Pratik Chaudhari 3 Christos Davatzikos 1 2 4  \nAbstract  \nQuantifying variability in a target population relative to a reference population is central to many scientific and clinical problems (e.g., diseased vs.  \nhealthy) . Yet, without paired data and in the presence of heterogeneous target variation, existing methods struggle to separate multiple modes of target-specific variation. We propose CASL-VAE, a deep contrastive latent variable model that learns structured latent generative factors from unpaired data. CASL-VAE factorizes variation into continuous common latent factors shared across populations and hierarchical salient latent factors that model target-specific heterogeneity as discrete subtypes and continuous within-subtype variation. Using variational inference, we show how approximate joint likelihood optimization over reference and target domains can be performed using unpaired data, providing a principled basis for paired-sample generation and cross-domain analysis. We validate CASL-VAE on semi-synthetic neuroimaging data, demonstrating improved subtype recovery and paired-sample generation compared to baseline clustering and generative mod  \nels. We also validate its ability to reveal biologically plausible heterogeneity in Alzheimer’s disease.  \n1. Introduction  \nMany scientific and applied problems involve understanding how a target population varies with respect to a reference population. For example, in medicine, researchers analyze pathological patterns in patient data relative to healthy controls (Fan et al., 2008) . Similar comparative analyses arise  \n1 Center for AI and Data Science for Integrated Diagnostics, University of Pennsylvania 2Department of Bioengineering, University of Pennsylvania 3Department of Electrical and Systems Engineering, University of Pennsylvania 4Department of Radiology, University of Pennsylvania. Correspondence to: Christos Davatzikos \u003C[christos.davatzikos@pennmedicine.upenn.edu](christos.davatzikos@pennmedicine.upenn.edu) >.  \nPreprint. July 9, 2026.  \nin genomics, drug discovery, and socio-economic studies, where contrasts between groups are often more informative than absolute measurements (Romero et al., 2012 ; Soneson & Robinson, 2018 ; Akhoon, 2021) .  \nIn practice, such comparisons are challenging for three reasons: (i) variation in the target domain is often entangled with variation present in the reference domain, obscuring subtle target-specific effects (for example, natural biological variation in healthy individuals could be mistaken for disease-related changes in patients); (ii) target-domain variation is frequently heterogeneous (Nunes et al., 2020), reflecting latent subtypes or context-dependent factors (for instance, patients with the same diagnosis may have diverse underlying pathologies, or cell populations may respond differently to the same treatment); and (iii) paired observations across domains—where each target sample has a corresponding reference sample—are rarely available, preventing direct supervision for learning cross-domain relationships. As a result, existing methods often struggle to disentangle heterogeneous, target-specific variation in unpaired data (Marquand et al., 2016 ; Feczko et al., 2019) .  \nGenerative representation learning can help address these challenges by learning latent representations that model the data generation process (Bercea et al., 2025) . In principle, such representations can differentiate between domains, capture heterogeneous subpopulations, and support downstream generative analyses (Kopf & Claassen, 2021) . However, standard generative models applied to multi-domain data typically entangle shared and domain-specific factors, leading to unstable or difficult-to-interpret representations (Higgins et al., 2017 ; Chen et al., 2016) . Contrastive Analysis (CA) methods aim","cbCairlgNleH1b5b","https://ap.wps.com/l/cbCairlgNleH1b5b","pdf",981941,5,1,19,"English","en",105,"# Abstract\n# Introduction\n## Variability across reference and target populations\n## Challenges with unpaired comparative learning\n## Generative and contrastive representation learning\n## Proposed CASL-VAE framework","[{\"question\":\"What problem does CASL-VAE address?\",\"answer\":\"CASL-VAE targets learning how a target population differs from a reference population when paired observations are not available and target variation is heterogeneous.\"},{\"question\":\"How does CASL-VAE represent shared versus target-specific variation?\",\"answer\":\"It factorizes latent variables into continuous common factors shared across domains and a hierarchical salient latent that models target-specific heterogeneity via discrete subtypes and continuous within-subtype variation.\"},{\"question\":\"How does CASL-VAE enable paired-sample generation without paired training data?\",\"answer\":\"Through variational inference, it performs approximate joint likelihood optimization across reference and target domains using only marginal observations, which supports paired-sample generation and cross-domain comparison.\"}]",1784194944,48,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"casl-vae-learning-structured-latent-variables-from-unpaired-data","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/casl-vae-learning-structured-latent-variables-from-unpaired-data/84342/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-28","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What 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