%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 (2011) /Description-Abstract (Learning problems such as logistic regression are typically formulated as pure optimization problems defined on some loss function\056 We argue that this view ignores the fact that the loss function depends on stochastically generated data which in turn determines an intrinsic scale of precision for statistical estimation\056 By considering the statistical properties of the update variables used during the optimization \050e\056g\056 gradients\051\054 we can construct frequentist hypothesis tests to determine the reliability of these updates\056 We utilize subsets of the data for computing updates\054 and use the hypothesis tests for determining when the batch\055size needs to be increased\056 This provides computational benefits and avoids overfitting by stopping when the batch\055size has become equal to size of the full dataset\056 Moreover\054 the proposed algorithms depend on a single interpretable parameter \205 the probability for an update to be in the wrong direction \205 which is set to a single value across all algorithms and datasets\056 In this paper\054 we illustrate these ideas on three L1 regularized coordinate algorithms\072 L1 \055regularized L2 \055loss SVMs\054 L1 \055regularized logistic regression\054 and the Lasso\054 but we emphasize that the underlying methods are much more generally applicable\056) /Producer (Python PDF Library \055 http\072\057\057pybrary\056net\057pyPdf\057) /Title (Statistical Tests for Optimization Efficiency) /Date (2011) /Type (Conference Proceedings) /firstpage (2196) /Book (Advances in Neural Information Processing Systems 24) /Description (Paper accepted and presented at the Neural Information Processing Systems Conference \050http\072\057\057nips\056cc\057\051) /Editors (J\056 Shawe\055Taylor and R\056S\056 Zemel and P\056L\056 Bartlett and F\056 Pereira and K\056Q\056 Weinberger) /Author (Levi Boyles\054 Anoop Korattikara\054 Deva Ramanan\054 Max Welling) /lastpage (2204) >> endobj 3 0 obj << /Type /Catalog /Pages 1 0 R >> endobj 4 0 obj << /Parent 1 0 R /Rotate 0 /Contents 13 0 R /Resources << /ExtGState 14 0 R /ProcSet [ /PDF /Text ] /Font 16 0 R >> /MediaBox [ 0 0 612 792 ] /Type /Page >> endobj 5 0 obj << /Parent 1 0 R /Rotate 0 /Contents 38 0 R /Resources << /ExtGState 39 0 R /ProcSet [ /PDF /Text ] /Font 40 0 R >> /MediaBox [ 0 0 612 792 ] /Type /Page >> endobj 6 0 obj << /Parent 1 0 R /Rotate 0 /Contents 57 0 R /Resources << /ExtGState 58 0 R /ProcSet [ /PDF /Text ] /Font 59 0 R >> /MediaBox [ 0 0 612 792 ] /Type /Page >> endobj 7 0 obj << /Parent 1 0 R /Rotate 0 /Contents 74 0 R /Resources << /ExtGState 75 0 R /ProcSet [ /PDF /Text ] /Font 76 0 R >> /MediaBox [ 0 0 612 792 ] /Type /Page >> endobj 8 0 obj << /Parent 1 0 R /Rotate 0 /Contents 77 0 R /Resources << /ExtGState 78 0 R /ProcSet [ /PDF /Text ] /Font 79 0 R >> /MediaBox [ 0 0 612 792 ] /Type /Page >> endobj 9 0 obj << /Parent 1 0 R /Rotate 0 /Contents 98 0 R /Resources << /ExtGState 99 0 R /ProcSet [ /PDF /Text ] /Font 100 0 R >> /MediaBox [ 0 0 612 792 ] /Type /Page >> endobj 10 0 obj << /Parent 1 0 R /Rotate 0 /Contents 101 0 R /Resources << /ExtGState 102 0 R /ProcSet [ /PDF /Text ] /Font 103 0 R >> /MediaBox [ 0 0 612 792 ] /Type /Page >> endobj 11 0 obj << /Parent 1 0 R /Rotate 0 /Contents 108 0 R /Resources << /ExtGState 109 0 R /ProcSet [ /PDF /Text ] /Font 110 0 R >> /MediaBox [ 0 0 612 792 ] /Type /Page >> endobj 12 0 obj << /Parent 1 0 R /Rotate 0 /Contents 114 0 R /Resources << /ExtGState 115 0 R /ProcSet [ /PDF /Text ] /Font 116 0 R >> /MediaBox [ 0 0 612 792 ] /Type /Page >> endobj 13 0 obj << /Length 7302 /Filter /FlateDecode >> stream x][s7rG >Svz(%R%ڿT~oLsHK|}p>O|^}u8?3idzgjy4Ysv竳?CU@g\I+Ο+seU8>M37?_\Γ&iuxO?(W{x??\.KJ\$5%:7u)]*ݗ`bVޖkwwUrrΚN5rV&}mpid2%S^ߔa})\m]n2ʽp?qs'z哳?)%8|8%O