000 | 03569nam a22005175i 4500 | ||
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001 | 978-3-319-32774-7 | ||
003 | DE-He213 | ||
005 | 20190213151343.0 | ||
007 | cr nn 008mamaa | ||
008 | 160628s2016 gw | s |||| 0|eng d | ||
020 |
_a9783319327747 _9978-3-319-32774-7 |
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024 | 7 |
_a10.1007/978-3-319-32774-7 _2doi |
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050 | 4 | _aQA274-274.9 | |
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_a519.2 _223 |
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_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. |
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300 |
_aXIII, 274 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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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 |
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_aÉcole d'Été de Probabilités de Saint-Flour, _x0721-5363 ; _v2159 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-319-32774-7 |
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