{"id":886722,"date":"2022-10-14T02:25:10","date_gmt":"2022-10-14T09:25:10","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/"},"modified":"2022-11-06T22:01:18","modified_gmt":"2022-11-07T06:01:18","slug":"protobandit-efficient-prototype-selection-via-multi-armed-bandits","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/protobandit-efficient-prototype-selection-via-multi-armed-bandits\/","title":{"rendered":"ProtoBandit: Efficient Prototype Selection via Multi-Armed Bandits"},"content":{"rendered":"<p>In this work, we propose a multi-armed bandit-based framework for identifying a compact set of informative data instances (i.e., the prototypes) from a source dataset\u00a0<span id=\"MathJax-Element-1-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"texatom\"><span id=\"MathJax-Span-4\" class=\"mrow\"><span id=\"MathJax-Span-5\" class=\"mi\">S<\/span><\/span><\/span><\/span><\/span><\/span>\u00a0that best represents a given target set\u00a0<span id=\"MathJax-Element-2-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-6\" class=\"math\"><span id=\"MathJax-Span-7\" class=\"mrow\"><span id=\"MathJax-Span-8\" class=\"texatom\"><span id=\"MathJax-Span-9\" class=\"mrow\"><span id=\"MathJax-Span-10\" class=\"mi\">T<\/span><\/span><\/span><\/span><\/span><\/span>. Prototypical examples of a given dataset offer interpretable insights into the underlying data distribution and assist in example-based reasoning, thereby influencing every sphere of human decision-making. Current state-of-the-art prototype selection approaches require\u00a0<span id=\"MathJax-Element-3-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-11\" class=\"math\"><span id=\"MathJax-Span-12\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"mi\">O<\/span><span id=\"MathJax-Span-14\" class=\"mo\">(<\/span><span id=\"MathJax-Span-15\" class=\"texatom\"><span id=\"MathJax-Span-16\" class=\"mrow\"><span id=\"MathJax-Span-17\" class=\"mo\">|<\/span><\/span><\/span><span id=\"MathJax-Span-18\" class=\"texatom\"><span id=\"MathJax-Span-19\" class=\"mrow\"><span id=\"MathJax-Span-20\" class=\"mi\">S<\/span><\/span><\/span><span id=\"MathJax-Span-21\" class=\"texatom\"><span id=\"MathJax-Span-22\" class=\"mrow\"><span id=\"MathJax-Span-23\" class=\"mo\">|<\/span><\/span><\/span><span id=\"MathJax-Span-24\" class=\"texatom\"><span id=\"MathJax-Span-25\" class=\"mrow\"><span id=\"MathJax-Span-26\" class=\"mo\">|<\/span><\/span><\/span><span id=\"MathJax-Span-27\" class=\"texatom\"><span id=\"MathJax-Span-28\" class=\"mrow\"><span id=\"MathJax-Span-29\" class=\"mi\">T<\/span><\/span><\/span><span id=\"MathJax-Span-30\" class=\"texatom\"><span id=\"MathJax-Span-31\" class=\"mrow\"><span id=\"MathJax-Span-32\" class=\"mo\">|<\/span><\/span><\/span><span id=\"MathJax-Span-33\" class=\"mo\">)<\/span><\/span><\/span><\/span>\u00a0similarity comparisons between source and target data points, which becomes prohibitively expensive for large-scale settings. We propose to mitigate this limitation by employing stochastic greedy search in the space of prototypical examples and multi-armed bandits for reducing the number of similarity comparisons. Our randomized algorithm, ProtoBandit, identifies a set of\u00a0<span id=\"MathJax-Element-4-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-34\" class=\"math\"><span id=\"MathJax-Span-35\" class=\"mrow\"><span id=\"MathJax-Span-36\" class=\"mi\">k<\/span><\/span><\/span><\/span>\u00a0prototypes incurring\u00a0<span id=\"MathJax-Element-5-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-37\" class=\"math\"><span id=\"MathJax-Span-38\" class=\"mrow\"><span id=\"MathJax-Span-39\" class=\"mi\">O<\/span><span id=\"MathJax-Span-40\" class=\"mo\">(<\/span><span id=\"MathJax-Span-41\" class=\"mi\">k<\/span><span id=\"MathJax-Span-42\" class=\"texatom\"><span id=\"MathJax-Span-43\" class=\"mrow\"><span id=\"MathJax-Span-44\" class=\"mo\">|<\/span><\/span><\/span><span id=\"MathJax-Span-45\" class=\"texatom\"><span id=\"MathJax-Span-46\" class=\"mrow\"><span id=\"MathJax-Span-47\" class=\"mi\">S<\/span><\/span><\/span><span id=\"MathJax-Span-48\" class=\"texatom\"><span id=\"MathJax-Span-49\" class=\"mrow\"><span id=\"MathJax-Span-50\" class=\"mo\">|<\/span><\/span><\/span><span id=\"MathJax-Span-51\" class=\"mo\">)<\/span><\/span><\/span><\/span>\u00a0similarity comparisons, which is independent of the size of the target set. An interesting outcome of our analysis is for the\u00a0<span id=\"MathJax-Element-6-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-52\" class=\"math\"><span id=\"MathJax-Span-53\" class=\"mrow\"><span id=\"MathJax-Span-54\" class=\"mi\">k<\/span><\/span><\/span><\/span>-medoids clustering problem (<span id=\"MathJax-Element-7-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-55\" class=\"math\"><span id=\"MathJax-Span-56\" class=\"mrow\"><span id=\"MathJax-Span-57\" class=\"texatom\"><span id=\"MathJax-Span-58\" class=\"mrow\"><span id=\"MathJax-Span-59\" class=\"mi\">T<\/span><\/span><\/span><span id=\"MathJax-Span-60\" class=\"mo\">=<\/span><span id=\"MathJax-Span-61\" class=\"texatom\"><span id=\"MathJax-Span-62\" class=\"mrow\"><span id=\"MathJax-Span-63\" class=\"mi\">S<\/span><\/span><\/span><\/span><\/span><\/span>\u00a0setting) in which we show that our algorithm ProtoBandit approximates the BUILD step solution of the partitioning around medoids (PAM) method in\u00a0<span id=\"MathJax-Element-8-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-64\" class=\"math\"><span id=\"MathJax-Span-65\" class=\"mrow\"><span id=\"MathJax-Span-66\" class=\"mi\">O<\/span><span id=\"MathJax-Span-67\" class=\"mo\">(<\/span><span id=\"MathJax-Span-68\" class=\"mi\">k<\/span><span id=\"MathJax-Span-69\" class=\"texatom\"><span id=\"MathJax-Span-70\" class=\"mrow\"><span id=\"MathJax-Span-71\" class=\"mo\">|<\/span><\/span><\/span><span id=\"MathJax-Span-72\" class=\"texatom\"><span id=\"MathJax-Span-73\" class=\"mrow\"><span id=\"MathJax-Span-74\" class=\"mi\">S<\/span><\/span><\/span><span id=\"MathJax-Span-75\" class=\"texatom\"><span id=\"MathJax-Span-76\" class=\"mrow\"><span id=\"MathJax-Span-77\" class=\"mo\">|<\/span><\/span><\/span><span id=\"MathJax-Span-78\" class=\"mo\">)<\/span><\/span><\/span><\/span>\u00a0complexity. Empirically, we observe that ProtoBandit reduces the number of similarity computation calls by several orders of magnitudes (<span id=\"MathJax-Element-9-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-79\" class=\"math\"><span id=\"MathJax-Span-80\" class=\"mrow\"><span id=\"MathJax-Span-81\" class=\"mn\">100<\/span><span id=\"MathJax-Span-82\" class=\"mo\">\u2212<\/span><span id=\"MathJax-Span-83\" class=\"mn\">1000<\/span><\/span><\/span><\/span>\u00a0times) while obtaining solutions similar in quality to those from state-of-the-art approaches.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this work, we propose a multi-armed bandit-based framework for identifying a compact set of informative data instances (i.e., the prototypes) from a source dataset\u00a0S\u00a0that best represents a given target set\u00a0T. Prototypical examples of a given dataset offer interpretable insights into the underlying data distribution and assist in example-based reasoning, thereby influencing every sphere of [&hellip;]<\/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":"","msr-author-ordering":[{"type":"user_nicename","value":"Arghya Chaudhuri","user_id":"42360"},{"type":"user_nicename","value":"Pratik Jawanpuria","user_id":"39348"},{"type":"user_nicename","value":"Bamdev Mishra","user_id":"39006"}],"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"ACML 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