[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83326-en":3,"doc-seo-83326-105":30,"detail-sidebar-cat-0-en-105":91},{"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},83326,1374391974585,"Genevieve","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Workload-Preserving Differentially Private Synthetic Data for Causal Inference via Maximum-Entropy Calibration","Workload-based differentially private (DP) synthetic data methods privately measure aggregate queries and convert noisy answers into synthetic records. While generic workloads can match distributions, causal estimands such as the average treatment effect (ATE) also require preserving treatment-arm balance and causal moment structure. The paper introduces causal workloads built from orthogonal moments used by doubly robust estimators, and analyzes ATE error via sampling, privacy, workload-approximation, Monte Carlo, and calibration terms. It also proposes CAUSAL-AIM and a noise-aware multiple-imputation method to obtain confidence intervals. ","Workload-Preserving Differentially Private Synthetic Data for Causal Inference via Maximum-Entropy Calibration  \nAmir Asiaee 1 Kaveh Aryan2  \n1Department of Biostatistics, Vanderbilt University Medical Center, Nashville, Tennessee, USA  \n2Department of Informatics, King’s College London, London, UK  \narXiv :2607 .08 122v 1 [ cs .LG] 9 Jul 2026  \nAbstract  \nWorkload-based differentially private (DP) synthetic data methods privately measure aggregate queries and post-process the noisy answers into synthetic records. Generic workloads can achieve strong distributional fidelity, but causal estimands such as the average treatment effect (ATE) depend on treatment-arm balance and outcome moments that generic marginals need not preserve. We propose causal workloads: DP query sets designed around the orthogonal moments used by doubly robust causal estimators. The released workload can be used directly by stable moment-map estimators or reconstructed by maximum-entropy calibration into reusable synthetic data; our theory decomposes ATE error into sampling, privacy, workload-approximation, Monte Carlo, and calibration terms. We also introduce CAUSAL-AIM, an adaptive workload selector, and a noise-aware multiple-imputation (NA+MI) procedure for confidence intervals from DP synthetic data. Because the workload is released once, the same DP synthetic table can support ATE, ATT, and subgroup analyses without additional privacy spending. Empirically, causal workloads are most useful at strict privacy budgets and for calibrated uncertainty, while generic workloads often retain an advantage for point RMSE as privacy relaxes. The broader lesson is a tradeoff: distributional fidelity can help point accuracy, but valid causal inference requires preserving causal moments and propagating DP noise rather than treating synthetic rows as real.  \n1 INTRODUCTION  \nDifferential privacy is increasingly used for public release of sensitive tabular datasets in domains such as health, educa-  \ntion, and social science [Dwork and Roth, 2014] . A common deployment pattern is to release DP synthetic microdata so that downstream analysts can reuse existing statistical and machine learning workflows [Liang et al., 2026] . State-ofthe-art DP synthesis methods often follow a select–measure– reconstruct pipeline: select a set of low-dimensional queries, measure them privately, and reconstruct a distribution (often maximum entropy / graphical model) from the noisy answers [McKenna et al., 2021, 2022] . However, causal inference introduces additional structure and fragility. Even if synthetic data match many marginals, causal estimandscan be biased by subtle distortions in overlap, confounding structure, or conditional outcome models. Recent work emphasizes that DP noise inflates the variance of causal estimators and invalidates naive confidence intervals unless it is explicitly modeled [Farzam and Sapiro, 2024, Schröder et al., 2025a,b, Ohnishi and Awan, 2024] .  \nThis paper asks a concrete question:  \nWhich DP queries must a synthetic data mechanism preserve to enable valid causal inference, and what are the fundamental privacy–causal tradeoffs?  \nWe answer by designing causal workloads and giving explicit bounds for stable workload-based estimators and for the calibrated synthetic-data route.  \nKey idea: causal workloads as orthogonal moments.  \nModern causal estimators, including doubly robust (DR) estimators [Robins et al., 1994] and double/debiased machine learning [Chernozhukov et al., 2018], rely on score functions whose expectation identifies the target estimand. We propose to choose a workload that directly measures these orthogonal moments, or a basis approximation thereof, under DP. The released workload can then be used in two ways: the direct q-route evaluates a stable estimator as a function of the released moments, while the synthetic-data route reconstructs a maximum-entropy distribution matched to those moments and samples reusable synthetic records. ","cbCainzhOZD5ZLck","https://ap.wps.com/l/cbCainzhOZD5ZLck","pdf",751059,2,1,28,"English","en",105,"# Abstract\n# Introduction\n## Problem framing: privacy–causal tradeoffs\n## Key idea: causal workloads as orthogonal moments\n## Why synthetic data at all\n## Contributions\n# Related Work\n## DP-synthesis primer","[{\"question\":\"What problem does the paper address in DP synthetic data for causal inference?\",\"answer\":\"Generic DP synthetic-data workloads can preserve many marginals yet still bias causal estimands like the ATE due to distortions in overlap, confounding structure, or conditional outcome models. The paper targets which DP query information must be preserved to support valid causal inference.\"},{\"question\":\"How does the proposed method define causal workloads?\",\"answer\":\"Causal workloads are DP query sets constructed from orthogonal-score moments underlying doubly robust and debiased causal estimators. These moments are measured privately and then used directly by stable moment-map estimators or reconstructed via maximum-entropy calibration.\"},{\"question\":\"How is ATE error decomposed for the synthetic-data route?\",\"answer\":\"The theory decomposes ATE error into multiple components: sampling, privacy, workload approximation, Monte Carlo, and calibration terms, to explain where causal inaccuracy originates under DP synthesis.\"}]",1784186747,71,{"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":86,"head_meta":88,"extra_data":90,"updated_unix":28},"workload-preserving-differentially-private-synthetic-data-for-causal-inference-via-maximum-entropy-calibration","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/workload-preserving-differentially-private-synthetic-data-for-causal-inference-via-maximum-entropy-calibration/83326/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-25","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the paper address in DP synthetic data for causal inference?","Question",{"text":75,"@type":76},"Generic DP synthetic-data workloads can preserve many marginals yet still bias causal estimands like the ATE due to distortions in overlap, confounding structure, or conditional outcome models. The paper targets which DP query information must be preserved to support valid causal inference.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed method define causal workloads?",{"text":80,"@type":76},"Causal workloads are DP query sets constructed from orthogonal-score moments underlying doubly robust and debiased causal estimators. These moments are measured privately and then used directly by stable moment-map estimators or reconstructed via maximum-entropy calibration.",{"name":82,"@type":73,"acceptedAnswer":83},"How is ATE error decomposed for the synthetic-data route?",{"text":84,"@type":76},"The theory decomposes ATE error into multiple components: sampling, privacy, workload approximation, Monte Carlo, and calibration terms, to explain where causal inaccuracy originates under DP synthesis.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]