%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 (Using the \044\134ell\1371\044\055norm to regularize the estimation of the parameter vector of a linear model leads to an unstable estimator when covariates are highly correlated\056 In this paper\054 we introduce a new penalty function which takes into account the correlation of the design matrix to stabilize the estimation\056 This norm\054 called the trace Lasso\054 uses the trace norm of the selected covariates\054 which is a convex surrogate of their rank\054 as the criterion of model complexity\056 We analyze the properties of our norm\054 describe an optimization algorithm based on reweighted least\055squares\054 and illustrate the behavior of this norm on synthetic data\054 showing that it is more adapted to strong correlations than competing methods such as the elastic net\056) /Producer (Python PDF Library \055 http\072\057\057pybrary\056net\057pyPdf\057) /Title (Trace Lasso\072 a trace norm regularization for correlated designs) /Date (2011) /Type (Conference Proceedings) /firstpage (2187) /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 (Edouard Grave\054 Guillaume R\056 Obozinski\054 Francis R\056 Bach) /lastpage (2195) >> endobj 3 0 obj << /Type /Catalog /Pages 1 0 R >> endobj 4 0 obj << /Contents 13 0 R /Parent 1 0 R /Type /Page /Resources 14 0 R /MediaBox [ 0 0 612 792 ] >> endobj 5 0 obj << /Contents 36 0 R /Parent 1 0 R /Type /Page /Resources 37 0 R /MediaBox [ 0 0 612 792 ] >> endobj 6 0 obj << /Contents 74 0 R /Parent 1 0 R /Type /Page /Resources 75 0 R /MediaBox [ 0 0 612 792 ] >> endobj 7 0 obj << /Contents 80 0 R /Parent 1 0 R /Type /Page /Resources 81 0 R /MediaBox [ 0 0 612 792 ] >> endobj 8 0 obj << /Contents 82 0 R /Parent 1 0 R /Type /Page /Resources 83 0 R /MediaBox [ 0 0 612 792 ] >> endobj 9 0 obj << /Contents 91 0 R /Parent 1 0 R /Type /Page /Resources 92 0 R /MediaBox [ 0 0 612 792 ] >> endobj 10 0 obj << /Contents 93 0 R /Parent 1 0 R /Type /Page /Resources 94 0 R /MediaBox [ 0 0 612 792 ] >> endobj 11 0 obj << /Contents 95 0 R /Parent 1 0 R /Type /Page /Resources 96 0 R /MediaBox [ 0 0 612 792 ] >> endobj 12 0 obj << /Contents 103 0 R /Parent 1 0 R /Type /Page /Resources 104 0 R /MediaBox [ 0 0 612 792 ] >> endobj 13 0 obj << /Length 2812 /Filter /FlateDecode >> stream xYK[%" ϜbWI\DaU!9YC _~ ra%Uӯ .g$AWAQWQ`sC@EuN}pw x(M,xIFqEQGq1|/5}J8K+aäaZ;OPǶqk31}wuO?ue*:um=[ݛ}㞻v8J)CG5BlG=l8HTQUTA^QgƧHUE(K^{cDA>߃?4 j&} Ny>߽avN<֛a5ȧC6UZ5DJY{GE?>'RVQ^8G9djZiQ$!ؘmDŵ]Yt4Ӹ: T6~4mیGj, 87n]DYM{E;[N^UTAϤnG7bQ_--ރW&7ڱIy389$J7&T*}DQzۃE)+