國立虎尾科技大學 |

Estimation and Testing Under Sparsity = École d'Été de Probabilités de Saint-Flour XLV – 2015 /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Estimation and Testing Under Sparsity/ by Sara van de Geer.
其他題名:	École d'Été de Probabilités de Saint-Flour XLV – 2015 /
作者:	van de Geer, Sara.
面頁冊數:	XIII, 274 p.online resource. :
Contained By:	Springer Nature eBook
標題:	Probabilities. -
電子資源:	https://doi.org/10.1007/978-3-319-32774-7
ISBN:	9783319327747

Estimation and Testing Under Sparsity = École d'Été de Probabilités de Saint-Flour XLV – 2015 /
van de Geer, Sara.

Estimation and Testing Under SparsityÉcole d'Été de Probabilités de Saint-Flour XLV – 2015 /[electronic resource] :by Sara van de Geer. - 1st ed. 2016. - XIII, 274 p.online resource. - École d'Été de Probabilités de Saint-Flour,21590721-5363 ;. - École d'Été de Probabilités de Saint-Flour,2151.

1 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.

Taking 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.

ISBN: 9783319327747

Standard No.: 10.1007/978-3-319-32774-7doiSubjects--Topical Terms:

527847
Probabilities.

LC Class. No.: QA273.A1-274.9

Dewey Class. No.: 519.2

Estimation and Testing Under Sparsity = École d'Été de Probabilités de Saint-Flour XLV – 2015 /
LDR:02952nam a22004335i 4500 001 981333
003 DE-He213
005 20200701170029.0
007 cr nn 008mamaa
008 201211s2016 gw | s |||| 0|eng d
020 $a 9783319327747 $9 978-3-319-32774-7
024 7 $a 10.1007/978-3-319-32774-7 $2 doi
035 $a 978-3-319-32774-7
050 4 $a QA273.A1-274.9
050 4 $a QA274-274.9
072 7 $a PBT $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
072 7 $a PBWL $2 thema
082 0 4 $a 519.2 $2 23
100 1 $a van de Geer, Sara. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1273788
245 1 0 $a Estimation and Testing Under Sparsity $h [electronic resource] : $b École d'Été de Probabilités de Saint-Flour XLV – 2015 / $c by Sara van de Geer.
250 $a 1st ed. 2016.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a XIII, 274 p. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a École d'Été de Probabilités de Saint-Flour, $x 0721-5363 ; $v 2159
505 0 $a 1 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 $a Taking 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 $a Probabilities. $3 527847
650 0 $a Statistics . $3 1253516
650 0 $a Mathematical statistics. $3 527941
650 1 4 $a Probability Theory and Stochastic Processes. $3 593945
650 2 4 $a Statistical Theory and Methods. $3 671396
650 2 4 $a Probability and Statistics in Computer Science. $3 669886
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319327730
776 0 8 $i Printed edition: $z 9783319327754
830 0 $a École d'Été de Probabilités de Saint-Flour, $x 0721-5363 ; $v 2151 $3 1256986
856 4 0 $u https://doi.org/10.1007/978-3-319-32774-7
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
912 $a ZDB-2-LNM
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)