%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 ] /Type /Pages /Count 10 >> 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 (2017) /EventType (Poster) /Description-Abstract (We establish the consistency of an algorithm of Mondrian Forests\176\134cite\173lakshminarayanan2014mondrianforests\054lakshminarayanan2016mondrianuncertainty\175\054 a randomized classification algorithm that can be implemented online\056 First\054 we amend the original Mondrian Forest algorithm proposed in\176\134cite\173lakshminarayanan2014mondrianforests\175\054 that considers a \134emph\173fixed\175 lifetime parameter\056 Indeed\054 the fact that this parameter is fixed actually hinders statistical consistency of the original procedure\056 Our modified Mondrian Forest algorithm grows trees with increasing lifetime parameters \044\134lambda\137n\044\054 and uses an alternative updating rule\054 allowing to work also in an online fashion\056 Second\054 we provide a theoretical analysis establishing simple conditions for consistency\056 Our theoretical analysis also exhibits a surprising fact\072 our algorithm achieves the minimax rate \050optimal rate\051 for the estimation of a Lipschitz regression function\054 which is a strong extension of previous results\176\134cite\173arlot2014purf\137bias\175 to an \134emph\173arbitrary dimension\175\056) /Producer (PyPDF2) /Title (Universal consistency and minimax rates for online Mondrian Forests) /Date (2017) /ModDate (D\07220180212230709\05508\04700\047) /Published (2017) /Type (Conference Proceedings) /firstpage (3758) /Book (Advances in Neural Information Processing Systems 30) /Description (Paper accepted and presented at the Neural Information Processing Systems Conference \050http\072\057\057nips\056cc\057\051) /Editors (I\056 Guyon and U\056V\056 Luxburg and S\056 Bengio and H\056 Wallach and R\056 Fergus and S\056 Vishwanathan and R\056 Garnett) /Author (Jaouad Mourtada\054 St\351phane Ga\357ffas\054 Erwan Scornet) /lastpage (3767) >> endobj 3 0 obj << /Type /Catalog /Pages 1 0 R >> endobj 4 0 obj << /Parent 1 0 R /Contents 14 0 R /Resources 15 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 50 0 R 51 0 R 52 0 R 53 0 R 54 0 R 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 66 0 R 67 0 R 68 0 R 69 0 R 70 0 R 71 0 R 72 0 R 73 0 R 74 0 R 75 0 R 76 0 R 77 0 R 78 0 R ] /Type /Page >> endobj 5 0 obj << /Parent 1 0 R /Contents 79 0 R /Resources 80 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 85 0 R 86 0 R 87 0 R 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 97 0 R 98 0 R 99 0 R 100 0 R 101 0 R 102 0 R 103 0 R 104 0 R 105 0 R 106 0 R 107 0 R 108 0 R 109 0 R 110 0 R ] /Type /Page >> endobj 6 0 obj << /Parent 1 0 R /Contents 111 0 R /Resources 112 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 161 0 R 162 0 R 163 0 R 164 0 R 165 0 R 166 0 R ] /Type /Page >> endobj 7 0 obj << /Parent 1 0 R /Contents 167 0 R /Resources 168 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 169 0 R 170 0 R 171 0 R 172 0 R 173 0 R ] /Type /Page >> endobj 8 0 obj << /Parent 1 0 R /Contents 174 0 R /Resources 175 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 176 0 R 177 0 R 178 0 R 179 0 R 180 0 R 181 0 R 182 0 R ] /Type /Page >> endobj 9 0 obj << /Parent 1 0 R /Contents 183 0 R /Resources 184 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 197 0 R 198 0 R 199 0 R 200 0 R 201 0 R 202 0 R 203 0 R 204 0 R 205 0 R 206 0 R 207 0 R 208 0 R 209 0 R 210 0 R 211 0 R 212 0 R 213 0 R 214 0 R 215 0 R ] /Type /Page >> endobj 10 0 obj << /Parent 1 0 R /Contents 216 0 R /Resources 217 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 222 0 R 223 0 R 224 0 R 225 0 R 226 0 R 227 0 R 228 0 R 229 0 R 230 0 R 231 0 R 232 0 R 233 0 R 234 0 R 235 0 R 236 0 R 237 0 R 238 0 R 239 0 R 240 0 R 241 0 R 242 0 R 243 0 R 244 0 R ] /Type /Page >> endobj 11 0 obj << /Parent 1 0 R /Contents 245 0 R /Resources 246 0 R /Group 343 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 345 0 R 346 0 R 347 0 R 348 0 R 349 0 R 350 0 R 351 0 R 352 0 R 353 0 R 354 0 R 355 0 R 356 0 R 357 0 R 358 0 R 359 0 R 360 0 R 361 0 R ] /Type /Page >> endobj 12 0 obj << /Parent 1 0 R /Contents 362 0 R /Resources 363 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 372 0 R 373 0 R 374 0 R ] /Type /Page >> endobj 13 0 obj << /Parent 1 0 R /Contents 375 0 R /Type /Page /Resources 376 0 R /MediaBox [ 0 0 612 792 ] >> endobj 14 0 obj << /Length 3572 /Filter /FlateDecode >> stream xڵZM{ܶWܧK|ͥvlc'4[j i~XV~}g0 v 0fl_$Wgv,%$i2XmBY]ܝ.Z0snXKeڤqX~%K6mY^pDj˶>UA/۲*'j4yg[z[r 5jSVvysqT/.Xg\Ѫohʼї~*K#v-N;{y=XK &Y"3 :%$*\;ML,tc41㒩(K./r`Hc&V]cinonA(ͻ~ϳnMND s)U֛ή9ǛlmoM^,,yȳ30 q[/?vȒE:-z/~>.e̵\'Uy~swGhx'*_TXlLw^>/Q/J0fd
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