%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 15 0 R ] /Type /Pages /Count 12 >> 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 (Valid causal inference in observational studies often requires controlling for confounders\056 However\054 in practice measurements of confounders may be noisy\054 and can lead to biased estimates of causal effects\056 We show that we can reduce bias induced by measurement noise using a large number of noisy measurements of the underlying confounders\056 We propose the use of matrix factorization to infer the confounders from noisy covariates\056 This flexible and principled framework adapts to missing values\054 accommodates a wide variety of data types\054 and can enhance a wide variety of causal inference methods\056 We bound the error for the induced average treatment effect estimator and show it is consistent in a linear regression setting\054 using Exponential Family Matrix Completion preprocessing\056 We demonstrate the effectiveness of the proposed procedure in numerical experiments with both synthetic data and real clinical data\056) /Producer (PyPDF2) /Title (Causal Inference with Noisy and Missing Covariates via Matrix Factorization) /Date (2018) /ModDate (D\07220190219000728\05508\04700\047) /Published (2018) /Type (Conference Proceedings) /firstpage (6921) /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 (Nathan Kallus\054 Xiaojie Mao\054 Madeleine Udell) /lastpage (6932) >> endobj 3 0 obj << /Type /Catalog /Pages 1 0 R >> endobj 4 0 obj << /Contents 16 0 R /Parent 1 0 R /Resources 17 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 44 0 R 45 0 R 46 0 R 47 0 R 48 0 R 49 0 R 50 0 R ] /Type /Page >> endobj 5 0 obj << /Contents 51 0 R /Parent 1 0 R /Resources 52 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 81 0 R 82 0 R 83 0 R 84 0 R 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 ] /Type /Page >> endobj 6 0 obj << /Contents 102 0 R /Parent 1 0 R /Resources 103 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 104 0 R 105 0 R 106 0 R 107 0 R 108 0 R ] /Type /Page >> endobj 7 0 obj << /Contents 109 0 R /Parent 1 0 R /Resources 110 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 139 0 R 140 0 R 141 0 R 142 0 R 143 0 R 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 154 0 R ] /Type /Page >> endobj 8 0 obj << /Contents 155 0 R /Parent 1 0 R /Resources 156 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 165 0 R 166 0 R 167 0 R 168 0 R 169 0 R 170 0 R 171 0 R 172 0 R 173 0 R 174 0 R 175 0 R ] /Type /Page >> endobj 9 0 obj << /Contents 176 0 R /Parent 1 0 R /Resources 177 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 178 0 R 179 0 R 180 0 R 181 0 R 182 0 R 183 0 R 184 0 R 185 0 R 186 0 R 187 0 R 188 0 R ] /Type /Page >> endobj 10 0 obj << /Contents 189 0 R /Parent 1 0 R /Resources 190 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 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 216 0 R 217 0 R ] /Type /Page >> endobj 11 0 obj << /Contents 218 0 R /Parent 1 0 R /Resources 219 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 229 0 R 230 0 R 231 0 R 232 0 R 233 0 R 234 0 R 235 0 R ] /Type /Page >> endobj 12 0 obj << /Contents 236 0 R /Parent 1 0 R /Resources 237 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 250 0 R 251 0 R 252 0 R 253 0 R ] /Type /Page >> endobj 13 0 obj << /Contents 254 0 R /Parent 1 0 R /Type /Page /Resources 255 0 R /MediaBox [ 0 0 612 792 ] >> endobj 14 0 obj << /Contents 256 0 R /Parent 1 0 R /Type /Page /Resources 257 0 R /MediaBox [ 0 0 612 792 ] >> endobj 15 0 obj << /Contents 258 0 R /Parent 1 0 R /Type /Page /Resources 259 0 R /MediaBox [ 0 0 612 792 ] >> endobj 16 0 obj << /Length 3364 /Filter /FlateDecode >> stream x}ZKϯ-TMHgk7Y')3r*=_)i|