[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120857-en":3,"doc-seo-120857-105":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":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},120857,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1782875107921204101",8,"Research & Report","Event-by-event Comparison between Machine-Learning and Transfer-Matrix-based Unfolding Methods","Event-by-event unfolding of detector effects enables quantitative comparisons between experimental measurements and theoretical predictions, as well as between datasets from different experiments. This work contrasts Machine-Learning–based and transfer-matrix–based unfolding strategies and introduces a procedure to obtain probabilistic single-event unfolded distributions with uncertainties and correlations within the transfer-matrix framework. The method is validated on a toy model and then applied to pseudo-data for the pp→Zγγ process. Iterative conditional invertible neural networks (IcINN) provide the ML comparison baseline.","Event-by-event Comparison between Machine-Learning– and Transfer-Matrix–based Unfolding Methods  \nMathias Backes 1,a, Anja Butter2,3,b, Monica Dunford 1,c, Bogdan Malaescu2,d  \n1 Kirchhoff-Institut für Physik, Universität Heidelberg, Germany  \n2 LPNHE, Sorbonne Université, Université Paris Cité, CNRS/IN2P3, Paris, France  \n3 Institut für Theoretische Physik, Universität Heidelberg, Germany  \narXiv:2310.17037v2 [[physics.data-an](physics.data-an)] 15 Dec 2024  \nAbstract The unfolding of detector effects is a key aspect of comparing experimental data with theoretical predictions. In recent years, different Machine-Learning methods have been developed to provide novel features, e.g. high dimensionality or a probabilistic single-event unfolding based on generative neural networks. Traditionally, many analyses unfold detector effects using transfer-matrix–based algorithms, which are well established in low-dimensional unfolding. They yield an unfolded distribution of the total spectrum, together with its covariance matrix. This paper proposes a method to obtain probabilistic single-event unfolded distributions, together with their uncertainties and correlations, for the transfer-matrix–based unfolding. The algorithm is first validated on a toy model and then applied to pseudo-data for thepp → Zγγ process. In both examples the performance is compared to the Machine-Learning– based single-event unfolding using an iterative approach with conditional invertible neural networks (IcINN) .  \n1 Introduction  \nUnfolding of detector effects has become one of the standard procedures in particle physics to enable quantitative comparisons between experimental data and theoretical predictions, as well as between data sets collected by different experiments.  \nMost common unfolding methods correct statistically (in the sense of an estimator) distributions parameterized as binned histograms. They employ response matrices  \na mathias.backes@kip.uni-heidelberg.de[b](b anja.butter@lpnhe.in2p3.fr)[ anja.butter@lpnhe.in2p3.fr](b anja.butter@lpnhe.in2p3.fr)[ ](b anja.butter@lpnhe.in2p3.fr)c monica.dunford@kip.uni-heidelberg.de[d](d malaescu@in2p3.fr)[ malaescu@in2p3.fr](d malaescu@in2p3.fr)  \nconnecting truth and reconstructed quantities, built using Monte Carlo simulations of the detector effects. A (pseudo-)inversion of the response matrix allows to convert measured distributions into unfolded ones, while possibly involving regularisation procedures too. Such“matrix–based” algorithms include e.g. a Simple Inversion [1], Singular Value Decomposition (SVD) [2], TUnfold [3], Iterative Bayesian Unfolding (IBU) [4, 5], Iterative Dynamically Stabilised (IDS) unfolding [6, 7], as well as other preceding iterative methods [8–13] .  \nMore recently, Machine-Learning (ML) techniques [14– 28] have enabled the development of a new class of unfolding methods in the context of particle physics. While allowing to perform a multidimensional unfolding (i.e. to simultaneously correct numerous observables for detector effects), such methods also enable an unbinned treatment of the data (see e.g. Ref. [29]) .  \nOne of the ML techniques for unfolding is provided by conditional Invertible Neural Networks (cINN) [20, 22– 24] . In contrast to many traditional methods the cINN operates on individual events, where the term ’event’refers to the detector response to particle interactions, e.g. at a particle collider, a fixed target experiment orin the context of astrophysical measurements like cosmic rays. The unfolding input is not a histogram of a reconstructed distribution, but rather one or several quantities reconstructed in a given event. The unfolding of individual events then leads to the notion of eventby-event unfolding, meaning that the overall unfolded distribution is obtained by combining the unfolding results of many individual events. Indeed, these methods yield an unfolded distribution for each quantity considered in a given event of an experimental data set. An i","cbCaikSdS4F1Frde","https://ap.wps.com/l/cbCaikSdS4F1Frde","pdf",2264692,1,25,"English","en",105,"# Introduction\n## Detector-effect unfolding in particle physics\n## Traditional matrix-based algorithms\n## Machine-Learning unfolding and event-by-event approaches\n## Goal: probabilistic single-event transfer-matrix unfolding","[{\"question\":\"What is unfolding of detector effects used for in particle physics?\",\"answer\":\"Unfolding corrects detector-induced distortions so that measured results can be quantitatively compared with theoretical predictions and with other experimental datasets.\"},{\"question\":\"How do traditional transfer-matrix–based unfolding methods work at a high level?\",\"answer\":\"They use response matrices built from Monte Carlo simulations to (pseudo-)invert the detector response, producing unfolded binned spectra and their covariance, often with regularization.\"},{\"question\":\"What does the paper propose for transfer-matrix unfolding beyond standard binned outputs?\",\"answer\":\"It proposes a method to obtain probabilistic single-event unfolded distributions, including uncertainties and correlations, and compares the performance against Machine-Learning single-event unfolding using an iterative approach with IcINN.\"}]","Event-by-event Comparison between Machine-Learning and Transfer-Matrix-based Unfolding Methods | 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is unfolding of detector effects used for in particle physics?","Question",{"text":75,"@type":76},"Unfolding corrects detector-induced distortions so that measured results can be quantitatively compared with theoretical predictions and with other experimental datasets.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How do traditional transfer-matrix–based unfolding methods work at a high level?",{"text":80,"@type":76},"They use response matrices built from Monte Carlo simulations to (pseudo-)invert the detector response, producing unfolded binned spectra and their covariance, often with regularization.",{"name":82,"@type":73,"acceptedAnswer":83},"What does the paper propose for transfer-matrix unfolding beyond standard binned outputs?",{"text":84,"@type":76},"It proposes a method to obtain probabilistic single-event unfolded distributions, including uncertainties and correlations, and compares the performance against Machine-Learning single-event unfolding using an iterative 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