{"id":534,"date":"2018-04-07T12:55:34","date_gmt":"2018-04-07T12:55:34","guid":{"rendered":"http:\/\/web.eecs.umich.edu\/~girasole\/?page_id=534"},"modified":"2018-04-07T12:55:34","modified_gmt":"2018-04-07T12:55:34","slug":"active-learning","status":"publish","type":"page","link":"https:\/\/web.eecs.umich.edu\/~girasole\/?page_id=534","title":{"rendered":"Active Learning"},"content":{"rendered":"<p>In many applications, it&#8217;s possible to take measurements repeatedly to use for inference. Examples include genetic experiments, environmental sensing, and crowdsourced image tasks. The problem of how to design sequential measurements for machine learning inference is called active learning. We can and should exploit expert knowledge about the signal of interest. However, if we trust a model too much, we may miss a true signal. We have studied active learning algorithms for image clustering\/classification and spatial environmental sampling.<\/p>\n<div id=\"zotpress-d70ea206773f7dabb5b249375036452b\" class=\"zp-Zotpress zp-Zotpress-Bib wp-block-group\">\n\n\t\t<span class=\"ZP_API_USER_ID ZP_ATTR\">1399621<\/span>\n\t\t<span class=\"ZP_ITEM_KEY ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_COLLECTION_ID ZP_ATTR\">E36HLPSJ<\/span>\n\t\t<span class=\"ZP_TAG_ID ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_AUTHOR ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_YEAR ZP_ATTR\"><\/span>\n        <span class=\"ZP_ITEMTYPE ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_INCLUSIVE ZP_ATTR\">1<\/span>\n\t\t<span class=\"ZP_STYLE ZP_ATTR\">chicago-author-date<\/span>\n\t\t<span class=\"ZP_LIMIT ZP_ATTR\">50<\/span>\n\t\t<span class=\"ZP_SORTBY ZP_ATTR\">date<\/span>\n\t\t<span class=\"ZP_ORDER ZP_ATTR\">desc<\/span>\n\t\t<span class=\"ZP_TITLE ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_SHOWIMAGE ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_SHOWTAGS ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_DOWNLOADABLE ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_NOTES ZP_ATTR\">1<\/span>\n\t\t<span class=\"ZP_ABSTRACT ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_CITEABLE ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_TARGET ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_URLWRAP ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_FORCENUM ZP_ATTR\"><\/span>\n        <span class=\"ZP_HIGHLIGHT ZP_ATTR\"><\/span>\n        <span class=\"ZP_POSTID ZP_ATTR\">534<\/span>\n\t\t<span class=\"ZOTPRESS_PLUGIN_URL ZP_ATTR\">https:\/\/web.eecs.umich.edu\/~girasole\/wp-content\/plugins\/zotpress\/<\/span>\n\n\t\t<div class=\"zp-List loading\">\n\t\t\t<div class=\"zp-SEO-Content\">\n\t\t\t\t<span class=\"ZP_JSON ZP_ATTR\">%7B%22status%22%3A%22success%22%2C%22updateneeded%22%3Afalse%2C%22instance%22%3Afalse%2C%22meta%22%3A%7B%22request_last%22%3A0%2C%22request_next%22%3A0%2C%22used_cache%22%3Atrue%7D%2C%22data%22%3A%5B%7B%22key%22%3A%22DTH4F5EN%22%2C%22library%22%3A%7B%22id%22%3A1399621%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Lipor%20et%20al.%22%2C%22parsedDate%22%3A%222017-10%22%2C%22numChildren%22%3A1%7D%2C%22bib%22%3A%22%26lt%3Bdiv%20class%3D%26quot%3Bcsl-bib-body%26quot%3B%20style%3D%26quot%3Bline-height%3A%201.35%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%26quot%3B%26gt%3B%5Cn%20%20%26lt%3Bdiv%20class%3D%26quot%3Bcsl-entry%26quot%3B%26gt%3BLipor%2C%20J.%2C%20B.%20P.%20Wong%2C%20D.%20Scavia%2C%20B.%20Kerkez%2C%20and%20L.%20Balzano.%202017.%20%26%23x201C%3BDistance-Penalized%20Active%20Learning%20Using%20Quantile%20Search.%26%23x201D%3B%20%26lt%3Bi%26gt%3BIEEE%20Transactions%20on%20Signal%20Processing%26lt%3B%5C%2Fi%26gt%3B%2065%20%2820%29%3A%205453%26%23x2013%3B65.%20%26lt%3Ba%20class%3D%26%23039%3Bzp-DOIURL%26%23039%3B%20href%3D%26%23039%3Bhttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1109%5C%2FTSP.2017.2731323%26%23039%3B%26gt%3Bhttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1109%5C%2FTSP.2017.2731323%26lt%3B%5C%2Fa%26gt%3B.%26lt%3B%5C%2Fdiv%26gt%3B%5Cn%26lt%3B%5C%2Fdiv%26gt%3B%22%2C%22data%22%3A%7B%22itemType%22%3A%22journalArticle%22%2C%22title%22%3A%22Distance-Penalized%20Active%20Learning%20Using%20Quantile%20Search%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%22%2C%22lastName%22%3A%22Lipor%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22B.%20P.%22%2C%22lastName%22%3A%22Wong%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%22%2C%22lastName%22%3A%22Scavia%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22B.%22%2C%22lastName%22%3A%22Kerkez%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22L.%22%2C%22lastName%22%3A%22Balzano%22%7D%5D%2C%22abstractNote%22%3A%22Adaptive%20sampling%20theory%20has%20shown%20that%2C%20with%20proper%20assumptions%20on%20the%20signal%20class%2C%20algorithms%20exist%20to%20reconstruct%20a%20signal%20in%20%24mathbb%20R%5Ed%24%20with%20an%20optimal%20number%20of%20samples.%20We%20generalize%20this%20problem%20to%20the%20case%20of%20spatial%20signals%2C%20where%20the%20sampling%20cost%20is%20a%20function%20of%20both%20the%20number%20of%20samples%20taken%20and%20the%20distance%20traveled%20during%20estimation.%20This%20is%20motivated%20by%20our%20work%20studying%20regions%20of%20low%20oxygen%20concentration%20in%20the%20Great%20Lakes.%20We%20show%20that%20for%20one-dimensional%20threshold%20classifiers%2C%20a%20tradeoff%20between%20the%20number%20of%20samples%20taken%20and%20distance%20traveled%20can%20be%20achieved%20using%20a%20generalization%20of%20binary%20search%2C%20which%20we%20refer%20to%20as%20quantile%20search.%20We%20characterize%20both%20the%20estimation%20error%20after%20a%20fixed%20number%20of%20samples%20and%20the%20distance%20traveled%20in%20the%20noiseless%20case%2C%20as%20well%20as%20the%20estimation%20error%20in%20the%20case%20of%20noisy%20measurements.%20We%20illustrate%20our%20results%20in%20both%20simulations%20and%20experiments%20and%20show%20that%20our%20method%20outperforms%20existing%20algorithms%20in%20a%20large%20range%20of%20sampling%20scenarios.%22%2C%22date%22%3A%22October%202017%22%2C%22section%22%3A%22%22%2C%22partNumber%22%3A%22%22%2C%22partTitle%22%3A%22%22%2C%22DOI%22%3A%2210.1109%5C%2FTSP.2017.2731323%22%2C%22citationKey%22%3A%22%22%2C%22url%22%3A%22%22%2C%22PMID%22%3A%22%22%2C%22PMCID%22%3A%22%22%2C%22ISSN%22%3A%221053-587X%22%2C%22language%22%3A%22%22%2C%22collections%22%3A%5B%22427SEM27%22%2C%22DZFDBB6V%22%2C%22E36HLPSJ%22%2C%22UIWU664R%22%5D%2C%22dateModified%22%3A%222018-02-16T18%3A44%3A47Z%22%7D%7D%2C%7B%22key%22%3A%2278Q9AHXX%22%2C%22library%22%3A%7B%22id%22%3A1399621%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Lipor%20and%20Balzano%22%2C%22parsedDate%22%3A%222015-12%22%2C%22numChildren%22%3A2%7D%2C%22bib%22%3A%22%26lt%3Bdiv%20class%3D%26quot%3Bcsl-bib-body%26quot%3B%20style%3D%26quot%3Bline-height%3A%201.35%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%26quot%3B%26gt%3B%5Cn%20%20%26lt%3Bdiv%20class%3D%26quot%3Bcsl-entry%26quot%3B%26gt%3BLipor%2C%20J.%2C%20and%20L.%20Balzano.%202015.%20%26%23x201C%3BMargin-Based%20Active%20Subspace%20Clustering.%26%23x201D%3B%20%26lt%3Bi%26gt%3B2015%20IEEE%206th%20International%20Workshop%20on%20Computational%20Advances%20in%20Multi-Sensor%20Adaptive%20Processing%20%28CAMSAP%29%26lt%3B%5C%2Fi%26gt%3B%2C%20December%2C%20377%26%23x2013%3B80.%20%26lt%3Ba%20class%3D%26%23039%3Bzp-DOIURL%26%23039%3B%20href%3D%26%23039%3Bhttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1109%5C%2FCAMSAP.2015.7383815%26%23039%3B%26gt%3Bhttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1109%5C%2FCAMSAP.2015.7383815%26lt%3B%5C%2Fa%26gt%3B.%26lt%3B%5C%2Fdiv%26gt%3B%5Cn%26lt%3B%5C%2Fdiv%26gt%3B%22%2C%22data%22%3A%7B%22itemType%22%3A%22conferencePaper%22%2C%22title%22%3A%22Margin-based%20active%20subspace%20clustering%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%22%2C%22lastName%22%3A%22Lipor%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22L.%22%2C%22lastName%22%3A%22Balzano%22%7D%5D%2C%22abstractNote%22%3A%22Subspace%20clustering%20has%20typically%20been%20approached%20as%20an%20unsupervised%20machine%20learning%20problem.%20However%20in%20several%20applications%20where%20the%20union%20of%20subspaces%20model%20is%20useful%2C%20it%20is%20also%20reasonable%20to%20assume%20you%20have%20access%20to%20a%20small%20number%20of%20labels.%20In%20this%20paper%20we%20investigate%20the%20benefit%20labeled%20data%20brings%20to%20the%20subspace%20clustering%20problem.%20We%20focus%20on%20incorporating%20labels%20into%20the%20k-subspaces%20algorithm%2C%20a%20simple%20and%20computationally%20efficient%20alternating%20estimation%20algorithm.%20We%20find%20that%20even%20a%20very%20small%20number%20of%20randomly%20selected%20labels%20can%20greatly%20improve%20accuracy%20over%20the%20unsupervised%20approach.%20We%20demonstrate%20that%20with%20enough%20labels%2C%20we%20get%20a%20significant%20improvement%20by%20using%20actively%20selected%20labels%20chosen%20for%20points%20that%20are%20nearly%20equidistant%20to%20more%20than%20one%20estimated%20subspace.%20We%20show%20this%20improvement%20on%20simulated%20data%20and%20face%20images.%22%2C%22proceedingsTitle%22%3A%222015%20IEEE%206th%20International%20Workshop%20on%20Computational%20Advances%20in%20Multi-Sensor%20Adaptive%20Processing%20%28CAMSAP%29%22%2C%22conferenceName%22%3A%222015%20IEEE%206th%20International%20Workshop%20on%20Computational%20Advances%20in%20Multi-Sensor%20Adaptive%20Processing%20%28CAMSAP%29%22%2C%22date%22%3A%22December%202015%22%2C%22eventPlace%22%3A%22%22%2C%22DOI%22%3A%2210.1109%5C%2FCAMSAP.2015.7383815%22%2C%22ISBN%22%3A%22%22%2C%22citationKey%22%3A%22%22%2C%22url%22%3A%22ieeexplore.ieee.org%5C%2Fxpl%5C%2FarticleDetails.jsp%3Farnumber%3D7383815%22%2C%22ISSN%22%3A%22%22%2C%22language%22%3A%22%22%2C%22collections%22%3A%5B%226JKB3X7P%22%2C%22DZFDBB6V%22%2C%22E36HLPSJ%22%2C%22ZA8QMDGD%22%5D%2C%22dateModified%22%3A%222016-06-13T15%3A59%3A42Z%22%7D%7D%2C%7B%22key%22%3A%22UUTZBDMJ%22%2C%22library%22%3A%7B%22id%22%3A1399621%7D%2C%22meta%22%3A%7B%22creatorSummary%22%3A%22Lipor%20et%20al.%22%2C%22parsedDate%22%3A%222015-09%22%2C%22numChildren%22%3A1%7D%2C%22bib%22%3A%22%26lt%3Bdiv%20class%3D%26quot%3Bcsl-bib-body%26quot%3B%20style%3D%26quot%3Bline-height%3A%201.35%3B%20padding-left%3A%201em%3B%20text-indent%3A-1em%3B%26quot%3B%26gt%3B%5Cn%20%20%26lt%3Bdiv%20class%3D%26quot%3Bcsl-entry%26quot%3B%26gt%3BLipor%2C%20J.%2C%20L.%20Balzano%2C%20B.%20Kerkez%2C%20and%20D.%20Scavia.%202015.%20%26%23x201C%3BQuantile%20Search%3A%20A%20Distance-Penalized%20Active%20Learning%20Algorithm%20for%20Spatial%20Sampling.%26%23x201D%3B%20%26lt%3Bi%26gt%3B2015%2053rd%20Annual%20Allerton%20Conference%20on%20Communication%2C%20Control%2C%20and%20Computing%20%28Allerton%29%26lt%3B%5C%2Fi%26gt%3B%2C%20September%2C%201241%26%23x2013%3B48.%20%26lt%3Ba%20class%3D%26%23039%3Bzp-DOIURL%26%23039%3B%20href%3D%26%23039%3Bhttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1109%5C%2FALLERTON.2015.7447150%26%23039%3B%26gt%3Bhttps%3A%5C%2F%5C%2Fdoi.org%5C%2F10.1109%5C%2FALLERTON.2015.7447150%26lt%3B%5C%2Fa%26gt%3B.%26lt%3B%5C%2Fdiv%26gt%3B%5Cn%26lt%3B%5C%2Fdiv%26gt%3B%22%2C%22data%22%3A%7B%22itemType%22%3A%22conferencePaper%22%2C%22title%22%3A%22Quantile%20search%3A%20A%20distance-penalized%20active%20learning%20algorithm%20for%20spatial%20sampling%22%2C%22creators%22%3A%5B%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22J.%22%2C%22lastName%22%3A%22Lipor%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22L.%22%2C%22lastName%22%3A%22Balzano%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22B.%22%2C%22lastName%22%3A%22Kerkez%22%7D%2C%7B%22creatorType%22%3A%22author%22%2C%22firstName%22%3A%22D.%22%2C%22lastName%22%3A%22Scavia%22%7D%5D%2C%22abstractNote%22%3A%22Adaptive%20sampling%20theory%20has%20shown%20that%2C%20with%20proper%20assumptions%20on%20the%20signal%20class%2C%20algorithms%20exist%20to%20reconstruct%20a%20signal%20in%20%3F%3F%3Fd%20with%20an%20optimal%20number%20of%20samples.%20We%20generalize%20this%20problem%20to%20when%20the%20cost%20of%20sampling%20is%20not%20only%20the%20number%20of%20samples%20but%20also%20the%20distance%20traveled%20between%20samples.%20This%20is%20motivated%20by%20our%20work%20studying%20regions%20of%20low%20oxygen%20concentration%20in%20the%20Great%20Lakes.%20We%20show%20that%20for%20one-dimensional%20threshold%20classifiers%2C%20a%20tradeoff%20between%20number%20of%20samples%20and%20distance%20traveled%20can%20be%20achieved%20using%20a%20generalization%20of%20binary%20search%2C%20which%20we%20refer%20to%20as%20quantile%20search.%20We%20derive%20the%20expected%20total%20sampling%20time%20for%20noiseless%20measurements%20and%20the%20expected%20number%20of%20samples%20for%20an%20extension%20to%20the%20noisy%20case.%20We%20illustrate%20our%20results%20in%20simulations%20relevant%20to%20our%20sampling%20application.%22%2C%22proceedingsTitle%22%3A%222015%2053rd%20Annual%20Allerton%20Conference%20on%20Communication%2C%20Control%2C%20and%20Computing%20%28Allerton%29%22%2C%22conferenceName%22%3A%222015%2053rd%20Annual%20Allerton%20Conference%20on%20Communication%2C%20Control%2C%20and%20Computing%20%28Allerton%29%22%2C%22date%22%3A%22Sept%202015%22%2C%22eventPlace%22%3A%22%22%2C%22DOI%22%3A%2210.1109%5C%2FALLERTON.2015.7447150%22%2C%22ISBN%22%3A%22%22%2C%22citationKey%22%3A%22%22%2C%22url%22%3A%22http%3A%5C%2F%5C%2Fieeexplore.ieee.org%5C%2Fxpl%5C%2FarticleDetails.jsp%3Farnumber%3D7447150%22%2C%22ISSN%22%3A%22%22%2C%22language%22%3A%22%22%2C%22collections%22%3A%5B%22DZFDBB6V%22%2C%22E36HLPSJ%22%2C%22UIWU664R%22%2C%22ZA8QMDGD%22%5D%2C%22dateModified%22%3A%222016-06-13T16%3A02%3A06Z%22%7D%7D%5D%7D<\/span>\n\n\t\t\t\t<div id=\"zp-ID-534-1399621-DTH4F5EN\" data-zp-author-date='Lipor-et-al.-2017-10' data-zp-date-author='2017-10-Lipor-et-al.' data-zp-date='2017-10' data-zp-year='2017' data-zp-itemtype='journalArticle' class=\"zp-Entry zpSearchResultsItem\">\n<div class=\"csl-bib-body\" style=\"line-height: 1.35; padding-left: 1em; text-indent:-1em;\">\n  <div class=\"csl-entry\">Lipor, J., B. P. Wong, D. Scavia, B. Kerkez, and L. Balzano. 2017. \u201cDistance-Penalized Active Learning Using Quantile Search.\u201d <i>IEEE Transactions on Signal Processing<\/i> 65 (20): 5453\u201365. <a class='zp-DOIURL' href='https:\/\/doi.org\/10.1109\/TSP.2017.2731323'>https:\/\/doi.org\/10.1109\/TSP.2017.2731323<\/a>.<\/div>\n<\/div>\n\t\t\t\t<\/div><!-- .zp-Entry .zpSearchResultsItem -->\t\t\t\t<div id=\"zp-ID-534-1399621-78Q9AHXX\" data-zp-author-date='Lipor-and-Balzano-2015-12' data-zp-date-author='2015-12-Lipor-and-Balzano' data-zp-date='2015-12' data-zp-year='2015' data-zp-itemtype='conferencePaper' class=\"zp-Entry zpSearchResultsItem\">\n<div class=\"csl-bib-body\" style=\"line-height: 1.35; padding-left: 1em; text-indent:-1em;\">\n  <div class=\"csl-entry\">Lipor, J., and L. Balzano. 2015. \u201cMargin-Based Active Subspace Clustering.\u201d <i>2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)<\/i>, December, 377\u201380. <a class='zp-DOIURL' href='https:\/\/doi.org\/10.1109\/CAMSAP.2015.7383815'>https:\/\/doi.org\/10.1109\/CAMSAP.2015.7383815<\/a>.<\/div>\n<\/div>\n\t\t\t\t<\/div><!-- .zp-Entry .zpSearchResultsItem -->\t\t\t\t<div id=\"zp-ID-534-1399621-UUTZBDMJ\" data-zp-author-date='Lipor-et-al.-2015-09' data-zp-date-author='2015-09-Lipor-et-al.' data-zp-date='2015-09' data-zp-year='2015' data-zp-itemtype='conferencePaper' class=\"zp-Entry zpSearchResultsItem\">\n<div class=\"csl-bib-body\" style=\"line-height: 1.35; padding-left: 1em; text-indent:-1em;\">\n  <div class=\"csl-entry\">Lipor, J., L. Balzano, B. Kerkez, and D. Scavia. 2015. \u201cQuantile Search: A Distance-Penalized Active Learning Algorithm for Spatial Sampling.\u201d <i>2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)<\/i>, September, 1241\u201348. <a class='zp-DOIURL' href='https:\/\/doi.org\/10.1109\/ALLERTON.2015.7447150'>https:\/\/doi.org\/10.1109\/ALLERTON.2015.7447150<\/a>.<\/div>\n<\/div>\n\t\t\t\t<\/div><!-- .zp-Entry .zpSearchResultsItem -->\n\t\t\t<\/div><!-- .zp-zp-SEO-Content -->\n\t\t<\/div><!-- .zp-List -->\n\t<\/div><!--.zp-Zotpress-->\n\n\n","protected":false},"excerpt":{"rendered":"<p>In many applications, it&#8217;s possible to take measurements repeatedly to use for inference. Examples include genetic experiments, environmental sensing, and crowdsourced image tasks. The problem of how to design sequential measurements for machine learning inference is called active learning. We can and should exploit expert knowledge about the signal of interest. However, if we trust [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":182,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/pages\/534"}],"collection":[{"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=534"}],"version-history":[{"count":1,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/pages\/534\/revisions"}],"predecessor-version":[{"id":535,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/pages\/534\/revisions\/535"}],"up":[{"embeddable":true,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/pages\/182"}],"wp:attachment":[{"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=534"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}