{"id":255558,"date":"2015-12-10T02:28:27","date_gmt":"2015-12-10T10:28:27","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=255558"},"modified":"2018-10-16T20:20:08","modified_gmt":"2018-10-17T03:20:08","slug":"alternating-minimization-regression-problems-vector-valued-outputs","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/alternating-minimization-regression-problems-vector-valued-outputs\/","title":{"rendered":"Alternating Minimization for Regression Problems with Vector-valued Outputs"},"content":{"rendered":"
In regression problems involving vector-valued outputs (or equivalently, multiple responses), it is well known that the maximum likelihood estimator (MLE), which takes noise covariance structure into account, can be significantly more accurate than the ordinary least squares (OLS) estimator. However, existing literature compares OLS and MLE in terms of their asymptotic, not finite sample, guarantees. 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