[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-238739-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-238739-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","naomi-non-autoregressive-multiresolution-sequence-imputation","NAOMI: Non-Autoregressive Multiresolution Sequence Imputation","","Missing value imputation is a core challenge in spatiotemporal modeling, affecting tasks from motion tracking to physical system dynamics. Autoregressive deep generative approaches can suffer severe error propagation, which becomes catastrophic when imputing long-range sequences. NAOMI introduces a non-autoregressive deep generative model that leverages multiresolution structure and recursively decodes from coarse to fine resolutions under arbitrary missing patterns. Adversarial training further strengthens results, yielding markedly improved imputation accuracy and stronger generalization on benchmark datasets.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/naomi-non-autoregressive-multiresolution-sequence-imputation/238739/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/naomi-non-autoregressive-multiresolution-sequence-imputation/238739.png","ImageObject",300,407,{"name":42,"@type":43},"eBook King","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-31","2026-09-11",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",16,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"Why do autoregressive models struggle with long-range sequence imputation?","Question",{"text":63,"@type":64},"Autoregressive methods compound errors over time because each imputed value depends on previous (possibly predicted) values. For long-range sequences, this propagation can become catastrophic.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How does NAOMI impute missing values without autoregression?",{"text":68,"@type":64},"NAOMI models conditional distributions using both historical context and predicted future, then decomposes dependencies across multiple resolutions. It fills missing values recursively via a divide-and-conquer procedure from coarse to fine.",{"name":70,"@type":61,"acceptedAnswer":71},"What role does adversarial training play in NAOMI?",{"text":72,"@type":64},"NAOMI enhances the model with adversarial training to reduce variance, improving the realism and accuracy of imputed sequences under various missing patterns.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},238739,1789139310,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,111,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":97,"doc_module":4,"doc_module_name":25,"category_name":98,"show_sort_weight":99,"slug":100},5,"Comic",60,"comic",{"id":102,"doc_module":4,"doc_module_name":25,"category_name":103,"show_sort_weight":104,"slug":105},6,"Technology",50,"technology",{"id":107,"doc_module":4,"doc_module_name":25,"category_name":108,"show_sort_weight":109,"slug":110},7,"Healthcare",40,"healthcare",{"id":112,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":113,"slug":114},8,30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":97,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":112,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":140,"language":141,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":12,"update_tm":80,"read_time":145,"preview_page_count":4},962088006270,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","NAOMI: Non-Autoregressive Multiresolution Sequence Imputation  \nYukai Liu  \nCaltech  \n[yukai@caltech.edu](yukai@caltech.edu)  \nRose Yu  \nNortheastern University [roseyu@northeastern.edu](roseyu@northeastern.edu)  \nEric Zhan  \nCaltech [ezhan@caltech.edu](ezhan@caltech.edu)  \nStephan Zheng􀀃  \nCaltech, Salesforce [stephan.zheng@salesforce.com](stephan.zheng@salesforce.com)  \nYisong Yue  \nCaltech [yyue@caltech.edu](yyue@caltech.edu)  \nAbstract  \nMissing value imputation is a fundamental problem in spatiotemporal modeling, from motion tracking to the dynamics of physical systems. Deep autoregressive models suffer from error propagation which becomes catastrophic for imputing long-range sequences. In this paper, we take a non-autoregressive approach and propose a novel deep generative model: Non-AutOregressive Multiresolution Imputation (NAOMI) to impute long-range sequences given arbitrary missing patterns. NAOMI exploits the multiresolution structure of spatiotemporal data and decodes recursively from coarse to fine-grained resolutions using a divide-andconquer strategy. We further enhance our model with adversarial training. When evaluated extensively on benchmark datasets from systems of both deterministic and stochastic dynamics. In our experiments, NAOMI demonstrates significant improvement in imputation accuracy (reducing average error by 60% compared to autoregressive counterparts) and generalization for long-range sequences.  \n1 Introduction  \nThe problem of missing values often arises in real-life sequential data. For example, in motion tracking, trajectories often contain missing data due to object occlusion, trajectories crossing, and the instability of camera motion [1] . Missing values can introduce observational bias into training data, making the learning unstable. Hence, imputing missing values is of critical importance to the downstream sequence learning tasks. Sequence imputation has been studied for  \ndecades in statistics literature [2, 3, 4, 5] . Most statistical techniques are reliant on strong assumptions on missing patterns such as missing at random, and do not generalize well to unseen data. Moreover, existing methods do not work well when the proportion of missing data is high and the sequence is long.  \nRecent studies [6, 7, 8, 9] have proposed to use deep generative models for learning flexible missing patterns from sequence data. However, all existing deep generative imputation methods are autoregressive: they model the value at cur-  \nFigure 1: Imputation process of NAOMI in a basketball play given two players (purple and blue) and 5 known observations (black dots) . Missing values are imputed recursively from coarse resolution to fine-grained resolution (left to right) .  \n􀀃 This work was done while the author was at Caltech.  \n33rd Conference on Neural Information Processing Systems (NeurIPS 2019), Vancouver, Canada.  \nrent timestamp using the values from previous time-steps and impute missing data in a sequential manner. Hence, autoregressive models are highly susceptible to compounding error, which can become catastrophic for long-range sequence modeling. We observe in our experiments that existing autoregressive approaches struggle on sequence imputation tasks with long-range dynamics.  \nIn this paper, we introduce a novel non-autoregressive approach for long-range sequence imputation. Instead of conditioning only on the previous values, we model the conditional distribution on both the history and the (predicted) future. We exploit the multiresolution nature of spatiotemporal sequence, and decompose the complex dependency into simpler ones at multiple resolutions. Our model, Non-autoregressive Multiresolution Imputation (NAOMI), employs a divide and conquer strategy to fill in the missing values recursively. Our method is general and can work with various learning  \nobjectives. We release an implementation of our model as an open source project.2 In summary, our contributions are as follows:  \n􀀏 We pr","cbCaijyyDHdTjADp","https://ap.wps.com/l/cbCaijyyDHdTjADp","pdf",16475652,11,"English","# Introduction\n# Related Work","[{\"question\":\"Why do autoregressive models struggle with long-range sequence imputation?\",\"answer\":\"Autoregressive methods compound errors over time because each imputed value depends on previous (possibly predicted) values. For long-range sequences, this propagation can become catastrophic.\"},{\"question\":\"How does NAOMI impute missing values without autoregression?\",\"answer\":\"NAOMI models conditional distributions using both historical context and predicted future, then decomposes dependencies across multiple resolutions. It fills missing values recursively via a divide-and-conquer procedure from coarse to fine.\"},{\"question\":\"What role does adversarial training play in NAOMI?\",\"answer\":\"NAOMI enhances the model with adversarial training to reduce variance, improving the realism and accuracy of imputed sequences under various missing patterns.\"}]","NAOMI: Non-Autoregressive Multiresolution Sequence Imputation | PDF",28]