An extensible statistical framework for detecting anomalous time series including those with heavy-tailed distributions and nonstationarity in higher-order moments is introduced based on penalized likelihood distributional regression. Specifically, generalized additive models for location, scale, and shape are used to infer sample path representations defined by a parametric distribution with parameters comprised of basis functions. Akaike weights are then applied to each model and time series, yielding a probability measure that can be effectively used to classify and rank anomalous time series. A mathematical exposition is also given to justify the proposed Akaike weight scoring under a suitable model embedding as a way to asymptotically identify anomalous time series. Studies evaluating the methodology on both multiple simulations and a real-world dataset also confirm that anomalies can be detected with high accuracy. Both code implementing the algorithm for running on a local machine and the datasets referenced in this article are available online.<\/p>\n","protected":false},"excerpt":{"rendered":"
An extensible statistical framework for detecting anomalous time series including those with heavy-tailed distributions and nonstationarity in higher-order moments is introduced based on penalized likelihood distributional regression. Specifically, generalized additive models for location, scale, and shape are used to infer sample path representations defined by a parametric distribution with parameters comprised of basis functions. Akaike […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13556,13558],"msr-publication-type":[193715],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[263677,246790,246694,246691,246682,263674,256363,261697],"msr-conference":[],"msr-journal":[263680],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-826105","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-artificial-intelligence","msr-research-area-security-privacy-cryptography","msr-locale-en_us","msr-field-of-study-akaike-information-criterion","msr-field-of-study-anomaly-detection","msr-field-of-study-artificial-intelligence","msr-field-of-study-computer-science","msr-field-of-study-pattern-recognition","msr-field-of-study-penalized-likelihood","msr-field-of-study-scale-ratio","msr-field-of-study-series-mathematics"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2021-2-11","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"doi","viewUrl":"false","id":"false","title":"10.1080\/10618600.2020.1868306","label_id":"243106","label":0},{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/ui.adsabs.harvard.edu\/abs\/2020arXiv200200499S\/abstract","label_id":"243109","label":0},{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/www.tandfonline.com\/doi\/full\/10.1080\/10618600.2020.1868306","label_id":"243109","label":0}],"msr_related_uploader":"","msr_attachments":[],"msr-author-ordering":[{"type":"guest","value":"cole-sodja","user_id":826108,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=cole-sodja"}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[740044],"msr_project":[],"publication":[],"video":[],"download":[],"msr_publication_type":"article","related_content":[],"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/826105"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-research-item"}],"version-history":[{"count":1,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/826105\/revisions"}],"predecessor-version":[{"id":826111,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/826105\/revisions\/826111"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=826105"}],"wp:term":[{"taxonomy":"msr-content-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-content-type?post=826105"},{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=826105"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=826105"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=826105"},{"taxonomy":"msr-product-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-product-type?post=826105"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=826105"},{"taxonomy":"msr-platform","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-platform?post=826105"},{"taxonomy":"msr-download-source","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-download-source?post=826105"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=826105"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=826105"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=826105"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=826105"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=826105"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=826105"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=826105"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}