{"id":164231,"date":"2013-04-02T00:00:00","date_gmt":"2013-04-02T07:00:00","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/msr-research-item\/classifier-selection-using-the-predicate-depth\/"},"modified":"2018-10-16T20:25:59","modified_gmt":"2018-10-17T03:25:59","slug":"classifier-selection-using-the-predicate-depth","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/classifier-selection-using-the-predicate-depth\/","title":{"rendered":"Classifier Selection using the Predicate Depth"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Typically, one approaches a supervised machine learning problem by writing down an objective function and finding a hypothesis that minimizes it. This is equivalent to finding the Maximum A Posteriori (MAP) hypothesis for a Boltzmann distribution. However, MAP is not a robust statistic. We present an alternative approach by defining a median of the distribution, which we show is both more robust, and has good generalization guarantees. We present algorithms to approximate this median.<\/p>\n<p>One contribution of this work is an efficient method for approximating the Tukey median. The Tukey median, which is often used for data visualization and outlier detection, is a special case of the family of medians we define: however, computing it exactly is exponentially slow in the dimension. Our algorithm approximates such medians in polynomial time while making weaker assumptions than those required by previous work.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Typically, one approaches a supervised machine learning problem by writing down an objective function and finding a hypothesis that minimizes it. This is equivalent to finding the Maximum A Posteriori (MAP) hypothesis for a Boltzmann distribution. However, MAP is not a robust statistic. We present an alternative approach by defining a median of the distribution, [&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":"rang","user_id":"33341"},{"type":"user_nicename","value":"cburges","user_id":"31351"}],"msr_publishername":"Microsoft Technical 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