%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 ] /Type /Pages /Count 9 >> endobj 2 0 obj << /Subject (Neural Information Processing Systems http\072\057\057nips\056cc\057) /Publisher (Curran Associates) /Language (en\055US) /Created (2012) /Description-Abstract (We theoretically analyze and compare the following five popular multiclass classification methods\072 One vs\056 All\054 All Pairs\054 Tree\055based classifiers\054 Error Correcting Output Codes \050ECOC\051 with randomly generated code matrices\054 and Multiclass SVM\056 In the first four methods\054 the classification is based on a reduction to binary classification\056 We consider the case where the binary classifier comes from a class of VC dimension \044d\044\054 and in particular from the class of halfspaces over \044\134reals\136d\044\056 We analyze both the estimation error and the approximation error of these methods\056 Our analysis reveals interesting conclusions of practical relevance\054 regarding the success of the different approaches under various conditions\056 Our proof technique employs tools from VC theory to analyze the \134emph\173approximation error\175 of hypothesis classes\056 This is in sharp contrast to most\054 if not all\054 previous uses of VC theory\054 which only deal with estimation error\056) /Producer (Python PDF Library \055 http\072\057\057pybrary\056net\057pyPdf\057) /Title (Multiclass Learning Approaches\072 A Theoretical Comparison with Implications) /Date (2012) /Type (Conference Proceedings) /firstpage (485) /Book (Advances in Neural Information Processing Systems 25) /Description (Paper accepted and presented at the Neural Information Processing Systems Conference \050http\072\057\057nips\056cc\057\051) /Editors (F\056 Pereira and C\056J\056C\056 Burges and L\056 Bottou and K\056Q\056 Weinberger) /Author (Amit Daniely\054 Sivan Sabato\054 Shai S\056 Shwartz) /lastpage (493) >> endobj 3 0 obj << /Type /Catalog /Pages 1 0 R >> endobj 4 0 obj << /Parent 1 0 R /Contents 13 0 R /Resources 14 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 55 0 R 56 0 R 57 0 R 58 0 R 59 0 R 60 0 R 61 0 R 62 0 R 63 0 R 64 0 R 65 0 R ] /Type /Page >> endobj 5 0 obj << /Parent 1 0 R /Contents 66 0 R /Resources 67 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 76 0 R 77 0 R 78 0 R 79 0 R 80 0 R 81 0 R 82 0 R 83 0 R 84 0 R 85 0 R ] /Type /Page >> endobj 6 0 obj << /Parent 1 0 R /Contents 86 0 R /Resources 87 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 88 0 R 89 0 R 90 0 R 91 0 R 92 0 R 93 0 R 94 0 R 95 0 R 96 0 R ] /Type /Page >> endobj 7 0 obj << /Parent 1 0 R /Contents 97 0 R /Resources 98 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 103 0 R 104 0 R 105 0 R 106 0 R 107 0 R 108 0 R 109 0 R 110 0 R 111 0 R 112 0 R 113 0 R 114 0 R 115 0 R 116 0 R 117 0 R ] /Type /Page >> endobj 8 0 obj << /Parent 1 0 R /Contents 118 0 R /Resources 119 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 128 0 R 129 0 R 130 0 R 131 0 R 132 0 R 133 0 R 134 0 R 135 0 R ] /Type /Page >> endobj 9 0 obj << /Parent 1 0 R /Contents 136 0 R /Resources 137 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 138 0 R 139 0 R 140 0 R 141 0 R ] /Type /Page >> endobj 10 0 obj << /Parent 1 0 R /Contents 142 0 R /Resources 143 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 144 0 R 145 0 R 146 0 R 147 0 R 148 0 R 149 0 R 150 0 R 151 0 R 152 0 R 153 0 R ] /Type /Page >> endobj 11 0 obj << /Parent 1 0 R /Contents 154 0 R /Resources 155 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 160 0 R 161 0 R ] /Type /Page >> endobj 12 0 obj << /Parent 1 0 R /Contents 162 0 R /Type /Page /Resources 163 0 R /MediaBox [ 0 0 612 792 ] >> endobj 13 0 obj << /Length 3472 /Filter /FlateDecode >> stream xڽv6zak|Pdg{sR&!5GlC-_? D9aN @P{wyY~&xғAY*H{:=-4:ݞ뛳~#O&B(nn=j{q M_*/T?;TC.U M6/E(EFޅD"Fwgn51諭mxP {}8ְoڦGgn@}>JXDL?ж jz;PXRE:K,j` ^MeG&*I"M.K-_ 42]̮3(T87]_ D'P:Zt>+Mmi_0 OJ:^}|R_WEeAe=Q{ۥ9]Te7cIi WaU坱(*#/9exû?\\%?m2/h%b߶ͯ7%^5wyѲ(R̃ Efd*ˋLmdHAg"