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001 978-3-319-32774-7
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020 _a9783319327747
_9978-3-319-32774-7
024 7 _a10.1007/978-3-319-32774-7
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
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072 7 _aPBT
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082 0 4 _a519.2
_223
100 1 _avan de Geer, Sara.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aEstimation and Testing Under Sparsity
_h[electronic resource] :
_bÉcole d'Été de Probabilités de Saint-Flour XLV – 2015 /
_cby Sara van de Geer.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2016.
300 _aXIII, 274 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aÉcole d'Été de Probabilités de Saint-Flour,
_x0721-5363 ;
_v2159
505 0 _a1 Introduction.- The Lasso.- 3 The square-root Lasso.- 4 The bias of the Lasso and worst possible sub-directions.- 5 Confidence intervals using the Lasso.- 6 Structured sparsity -- 7 General loss with norm-penalty -- 8 Empirical process theory for dual norms.- 9 Probability inequalities for matrices.- 10 Inequalities for the centred empirical risk and its derivative.- 11 The margin condition.- 12 Some worked-out examples.- 13 Brouwer’s fixed point theorem and sparsity.- 14 Asymptotically linear estimators of the precision matrix.- 15 Lower bounds for sparse quadratic forms.- 16 Symmetrization, contraction and concentration.- 17 Chaining including concentration.- 18 Metric structure of convex hulls.
520 _aTaking the Lasso method as its starting point, this book describes the main ingredients needed to study general loss functions and sparsity-inducing regularizers. It also provides a semi-parametric approach to establishing confidence intervals and tests. Sparsity-inducing methods have proven to be very useful in the analysis of high-dimensional data. Examples include the Lasso and group Lasso methods, and the least squares method with other norm-penalties, such as the nuclear norm. The illustrations provided include generalized linear models, density estimation, matrix completion and sparse principal components. Each chapter ends with a problem section. The book can be used as a textbook for a graduate or PhD course.
650 0 _aDistribution (Probability theory.
650 0 _aMathematical statistics.
650 0 _aComputer science.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aStatistical Theory and Methods.
_0http://scigraph.springernature.com/things/product-market-codes/S11001
650 2 4 _aProbability and Statistics in Computer Science.
_0http://scigraph.springernature.com/things/product-market-codes/I17036
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319327730
776 0 8 _iPrinted edition:
_z9783319327754
830 0 _aÉcole d'Été de Probabilités de Saint-Flour,
_x0721-5363 ;
_v2159
856 4 0 _uhttps://doi.org/10.1007/978-3-319-32774-7
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c10381
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