%PDF-1.3 1 0 obj << /Kids [ 4 0 R 5 0 R 6 0 R 7 0 R 8 0 R 9 0 R 10 0 R 11 0 R 12 0 R 13 0 R 14 0 R ] /Type /Pages /Count 11 >> endobj 2 0 obj << /Subject (Neural Information Processing Systems http\072\057\057nips\056cc\057) /Publisher (Curran Associates\054 Inc\056) /Language (en\055US) /Created (2018) /EventType (Poster) /Description-Abstract (In this paper\054 we consider the problem of linear regression with heavy\055tailed distributions\056 Different from previous studies that use the squared loss to measure the performance\054 we choose the absolute loss\054 which is capable of estimating the conditional median\056 To address the challenge that both the input and output could be heavy\055tailed\054 we propose a truncated minimization problem\054 and demonstrate that it enjoys an \044O\050\134sqrt\173d\057n\175\051\044 excess risk\054 where \044d\044 is the dimensionality and \044n\044 is the number of samples\056 Compared with traditional work on \044\134ell\1371\044\055regression\054 the main advantage of our result is that we achieve a high\055probability risk bound without exponential moment conditions on the input and output\056 Furthermore\054 if the input is bounded\054 we show that the classical empirical risk minimization is competent for \044\134ell\1371\044\055regression even when the output is heavy\055tailed\056) /Producer (PyPDF2) /Title (\044\134ell\1371\044\055regression with Heavy\055tailed Distributions) /Date (2018) /ModDate (D\07220190218211348\05508\04700\047) /Published (2018) /Type (Conference Proceedings) /firstpage (1076) /Book (Advances in Neural Information Processing Systems 31) /Description (Paper accepted and presented at the Neural Information Processing Systems Conference \050http\072\057\057nips\056cc\057\051) /Editors (S\056 Bengio and H\056 Wallach and H\056 Larochelle and K\056 Grauman and N\056 Cesa\055Bianchi and R\056 Garnett) /Author (Lijun Zhang\054 Zhi\055Hua Zhou) /lastpage (1086) >> 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