[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117834-en":3,"doc-seo-117834-105":30,"detail-sidebar-cat-0-en-105":96},{"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":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},117834,962075006959,"Anda","https://ap-avatar.wpscdn.com/avatar/e0002397efbe92a78e?_k=1776741047341049297",8,"Research & Report","Beyond Convergence - Identifiability of Machine Learning and Deep Learning Models","Machine learning and deep learning models can fit data through optimization, yet the underlying inverse problems are not always identifiable, meaning model parameters may not be uniquely determined by observed inputs and the data’s input–output relationship. This work examines identifiability via parameter estimation from motion sensor signals, using a bipedal spring-mass human walk dynamics model to generate synthetic gait data. A deep neural network estimates subject-specific parameters, showing that some parameters are identifiable while others remain unidentifiable. Unidentifiability is treated as an intrinsic experimental limitation, requiring changes in data collection, data fusion, and model-based machine learning to improve reliability and generalizability across domains.","Beyond Convergence: Identifiability of Machine Learning and Deep Learning Models  \nReza Sameni*  \narXiv :2307 . 1 1332v 1 [ cs .LG] 21 Jul 2023  \nAbstract—Machine learning (ML) and deep learning models are extensively used for parameter optimization and regression problems. However, not all inverse problems in ML are “identifiable,” indicating that model parameters may not be uniquely determined from the available data and the data model's inputoutput relationship.  \nIn this study, we investigate the notion of model parameter identifiability through a case study focused on parameter estimation from motion sensor data. Utilizing a bipedal-spring mass human walk dynamics model, we generate synthetic data representing diverse gait patterns and conditions. Employing a deep neural network, we attempt to estimate subject-wise parameters, including mass, stiffness, and equilibrium leg length. The results show that while certain parameters can be identified from the observation data, others remain unidentifiable, highlighting that unidentifiability is an intrinsic limitation of the experimental setup, necessitating a change in data collection and experimental scenarios.  \nBeyond this specific case study, the concept of identifiability has broader implications in ML and deep learning. Addressing unidentifiability requires proven identifiable models (with theoretical support), multimodal data fusion techniques, and advancements in model-based machine learning. Understanding and resolving unidentifiability challenges will lead to more reliable and accurate applications across diverse domains, transcending mere model convergence and enhancing the reliability of machine learning models.  \nIndex Terms—Identifiability, Machine Learning, Deep Learning, Parameter Estimation, Model Reliability  \nI. INTRODUCTION  \nMachine learning (ML) and deep learning models have demonstrated remarkable capacity to train and optimize model parameters based on data. The quality of adaptation in these models is commonly assessed using standard convergence measures such as mean squared error (MSE), mean absolute error (MAE), accuracy, etc. However, even with abundant training data and successful convergence, not all inverse problems are “identifiable,” in the sense that the model parameters may be uniquely determined from the available data.  \nIdentifiability, a fundamental concept in system and control theory [1] and stochastic inference [2], rigorously examines the possibility of uniquely determining model parameters based on the (mathematical) description of the input-output relationship. Certain models may remain unidentifiable regardless of data volume, quality, and model accuracy due to the data-parameter relationship. Unidentifiable problems appear at the heart of  \nR. Sameni is with the Department of Biomedical Informatics, Emory University, Atlanta, GA, USA. Email: [rsameni@dbmi.emory.edu](rsameni@dbmi.emory.edu)[ ](rsameni@dbmi.emory.edu)[Supplementary material for the](Supplementary material for the) “[BMI-532: Model-based machine learning](BMI-532: Model-based machine learning)”course presented at Emory University, Spring 2023 .  \nmany data modeling and stochastic inference problems, including retrieving time-series data from noisy measurements, estimating likelihoods or log-likelihoods in Bayesian inference problems, or training the weights of shallow and deep neural networks [3], [4] . Although unidentifiability is an intrinsic property of the data model that relates the measurements and parameters, it may go unnoticed, particularly in complex MLand deep learning models with thousands or millions of hidden parameters. This often occurs when models exhibit successful convergence during training or when the framework is fully data-driven without explicit data models. Despite the apparent training convergence, unidentifiable models can pose potential misinterpretation, especially when the underlying data models are not analytically available or easy to study.  \nIn this ","cbCaimUZa63Iuruh","https://ap.wps.com/l/cbCaimUZa63Iuruh","pdf",499212,1,5,"English","en",105,"# Introduction\n## Identifiability in ML and control theory\n## Case study objective and modeling approach\n## Organization of the paper\n# Gait model and synthetic data\n# Deep learning architecture and training\n# Results and conclusions","[{\"question\":\"What does identifiability mean in the context of machine learning models?\",\"answer\":\"Identifiability determines whether model parameters can be uniquely determined from the available data given the input–output relationship. Even with abundant data and convergence, some inverse problems may remain unidentifiable.\"},{\"question\":\"How does the paper test identifiability in practice?\",\"answer\":\"It performs a case study using human gait dynamics, generating synthetic motion-sensor data with a bipedal spring-mass model, then training a deep neural network to estimate subject-wise parameters.\"},{\"question\":\"What are the key findings about which parameters can be identified?\",\"answer\":\"The results indicate that certain subject-wise parameters can be identified from the observation data, while others remain unidentifiable, reflecting an intrinsic limitation of the experimental setup.\"},{\"question\":\"How can unidentifiability be addressed according to the paper?\",\"answer\":\"The paper argues for using theoretically supported identifiable models, applying multimodal data fusion, and advancing model-based machine learning. It also emphasizes considering identifiability during model development and analysis.\"}]","Beyond Convergence - Identifiability of Machine Learning and Deep Learning Models | PDF",1785679906,13,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":91,"head_meta":93,"extra_data":95,"updated_unix":28},"beyond-convergence-identifiability-of-machine-learning-and-deep-learning-models","",{"@graph":36,"@context":90},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"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/beyond-convergence-identifiability-of-machine-learning-and-deep-learning-models/117834/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"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","2026-08-05","2026-08-02",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82,86],{"name":73,"@type":74,"acceptedAnswer":75},"What does identifiability mean in the context of machine learning models?","Question",{"text":76,"@type":77},"Identifiability determines whether model parameters can be uniquely determined from the available data given the input–output relationship. Even with abundant data and convergence, some inverse problems may remain unidentifiable.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does the paper test identifiability in practice?",{"text":81,"@type":77},"It performs a case study using human gait dynamics, generating synthetic motion-sensor data with a bipedal spring-mass model, then training a deep neural network to estimate subject-wise parameters.",{"name":83,"@type":74,"acceptedAnswer":84},"What are the key findings about which parameters can be identified?",{"text":85,"@type":77},"The results indicate that certain subject-wise parameters can be identified from the observation data, while others remain unidentifiable, reflecting an intrinsic limitation of the experimental setup.",{"name":87,"@type":74,"acceptedAnswer":88},"How can unidentifiability be addressed according to the paper?",{"text":89,"@type":77},"The paper argues for using theoretically supported identifiable models, applying multimodal data fusion, and advancing model-based machine learning. 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