Fundamentals of high-dimensional statistics: with exercises and R labs
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham
Springer
[2022]
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| Series: | Springer texts in statistics
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 355 Seiten Diagramme |
| ISBN: | 9783030737917 9783030737948 |
| ISSN: | 2197-4136 |
Staff View
MARC
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| 245 | 1 | 0 | |a Fundamentals of high-dimensional statistics |b with exercises and R labs |c Johannes Lederer |
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Record in the Search Index
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| adam_text |
XIII Contents 1 Introduction. 1.1 Embracing High-Dimensionality. 1.2 1.3 1.4 1.5 Statistical Limitations of Classical Estimators. 1.6 1.7 Exercises. R Lab: Least-Squares vs. Ridge Estimation. 19 25 1.8 Notes and References. 34 2 Incorporating Prior Information. Regularization for Increasing the Numerical Stability*. Outlook. Linear Regression. ;. 1 2 5 10 13 18 37 38 41 45 48 53 63 71 77 2.1 2.2 Overview. 2.3 Post-Processing Methods. 2.4 2.5 2.6 2.7 2.8 Hôlder Inequality*. . . 3 Graphical
Models. 81 3.1 Overview. 82 3.2 3.3 Gaussian Graphical Models. 85 87 3.4 3.5 3.6 Neighborhood Selection. 91 Exercises. 95 R Lab: Estimating a Gene-Gene Coactivation Network. 98 3.7 Notes and References. 1°7 4 Tuning-Parameter Calibration. 1θ9 4.1 Overview. 4.2 4.3 4.4 Bounds on the Lasso's Effective Noise. HO 113 HO 1շ1 4.5 Exercises. 127 Sparsity-Inducing Prior Functions. Optimality Conditions*.
Exercises. R Lab: Overfitting. Notes and References. —· Maximum Regularized Likelihood Estimation. Cross-Validation. . . Adaptive Validation.
XIV Contents 46 R Lab: Cross-Validation. 4.7 Notes and References. 5 Inference. 5.1 5.2 One-Step Estimators. Confidence Intervals. 5.3 5.4 5.5 Exercises. R Lab: Confidence Intervals in Low and High Dimensions. 157 Notes and References. 166 6 Theory I: Prediction. 169 6.1 6.2 6.3 6.4 Overview. Basic Inequalities. Prediction Guarantees. Prediction Guarantees for Sparse and Weakly Correlated
Models. 170 175 182 192 6.5 6.6 Exercises. 204 Notes and References. 208 7 Theory 11: Estimation and Support Recovery. 211 7.1 7.2 7.3 7.4 7.5 7.6 Overview. Estimation Guarantees in tL·Ioss. Estimation Guarantees in Հ-Խտտ. Support Recovery Guarantees. Exercises. Notes and References. 212 213 218 231 235 237 A Supplementary Information. 239 Solutions. 240 A.l A.2 A.3 A.4 A.5 A.6 A.7 Solutions for ► Chap. 1 . Solutions
for ► Chap. 2. Solutions for ► Chap. 3. Solutions for ► Chap. 4. Solutions for ► Chap. 5. Solutions for ► Chap. 6. Solutions for ► Chap. 7. . 240 257 271 2g5 2gg 295 300 В Mathematical Background. 3θ9 B.1 B.2 Analysis. 3og Matrix Algebra . 131 135 139 140 146 153 Bibliography. . „„ Index. . . 345 |
| adam_txt |
XIII Contents 1 Introduction. 1.1 Embracing High-Dimensionality. 1.2 1.3 1.4 1.5 Statistical Limitations of Classical Estimators. 1.6 1.7 Exercises. R Lab: Least-Squares vs. Ridge Estimation. 19 25 1.8 Notes and References. 34 2 Incorporating Prior Information. Regularization for Increasing the Numerical Stability*. Outlook. Linear Regression. ;. 1 2 5 10 13 18 37 38 41 45 48 53 63 71 77 2.1 2.2 Overview. 2.3 Post-Processing Methods. 2.4 2.5 2.6 2.7 2.8 Hôlder Inequality*. . . 3 Graphical
Models. 81 3.1 Overview. 82 3.2 3.3 Gaussian Graphical Models. 85 87 3.4 3.5 3.6 Neighborhood Selection. 91 Exercises. 95 R Lab: Estimating a Gene-Gene Coactivation Network. 98 3.7 Notes and References. 1°7 4 Tuning-Parameter Calibration. 1θ9 4.1 Overview. 4.2 4.3 4.4 Bounds on the Lasso's Effective Noise. HO 113 HO 1շ1 4.5 Exercises. 127 Sparsity-Inducing Prior Functions. Optimality Conditions*.
Exercises. R Lab: Overfitting. Notes and References. —· Maximum Regularized Likelihood Estimation. Cross-Validation. . . Adaptive Validation.
XIV Contents 46 R Lab: Cross-Validation. 4.7 Notes and References. 5 Inference. 5.1 5.2 One-Step Estimators. Confidence Intervals. 5.3 5.4 5.5 Exercises. R Lab: Confidence Intervals in Low and High Dimensions. 157 Notes and References. 166 6 Theory I: Prediction. 169 6.1 6.2 6.3 6.4 Overview. Basic Inequalities. Prediction Guarantees. Prediction Guarantees for Sparse and Weakly Correlated
Models. 170 175 182 192 6.5 6.6 Exercises. 204 Notes and References. 208 7 Theory 11: Estimation and Support Recovery. 211 7.1 7.2 7.3 7.4 7.5 7.6 Overview. Estimation Guarantees in tL·Ioss. Estimation Guarantees in Հ-Խտտ. Support Recovery Guarantees. Exercises. Notes and References. 212 213 218 231 235 237 A Supplementary Information. 239 Solutions. 240 A.l A.2 A.3 A.4 A.5 A.6 A.7 Solutions for ► Chap. 1 . Solutions
for ► Chap. 2. Solutions for ► Chap. 3. Solutions for ► Chap. 4. Solutions for ► Chap. 5. Solutions for ► Chap. 6. Solutions for ► Chap. 7. . 240 257 271 2g5 2gg 295 300 В Mathematical Background. 3θ9 B.1 B.2 Analysis. 3og Matrix Algebra . 131 135 139 140 146 153 Bibliography. . „„ Index. . . 345 |
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| id | DE-604.BV047642767 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:48:01Z |
| indexdate | 2024-10-09T12:01:14Z |
| institution | BVB |
| isbn | 9783030737917 9783030737948 |
| issn | 2197-4136 |
| language | English |
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| physical | XIV, 355 Seiten Diagramme |
| publishDate | 2022 |
| publishDateSearch | 2022 |
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| publisher | Springer |
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| spelling | Lederer, Johannes 1984- Verfasser (DE-588)1055925775 aut Fundamentals of high-dimensional statistics with exercises and R labs Johannes Lederer Cham Springer [2022] © 2022 XIV, 355 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics Statistical Theory and Methods Big Data Data Structures and Information Theory Artificial Intelligence Statistics and Computing/Statistics Programs Machine Learning Statistics Big data Data structures (Computer science) Artificial intelligence Machine learning Erscheint auch als Online-Ausgabe 978-3-030-73792-4 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033026971&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lederer, Johannes 1984- Fundamentals of high-dimensional statistics with exercises and R labs Statistical Theory and Methods Big Data Data Structures and Information Theory Artificial Intelligence Statistics and Computing/Statistics Programs Machine Learning Statistics Big data Data structures (Computer science) Artificial intelligence Machine learning |
| title | Fundamentals of high-dimensional statistics with exercises and R labs |
| title_auth | Fundamentals of high-dimensional statistics with exercises and R labs |
| title_exact_search | Fundamentals of high-dimensional statistics with exercises and R labs |
| title_exact_search_txtP | Fundamentals of high-dimensional statistics with exercises and R labs |
| title_full | Fundamentals of high-dimensional statistics with exercises and R labs Johannes Lederer |
| title_fullStr | Fundamentals of high-dimensional statistics with exercises and R labs Johannes Lederer |
| title_full_unstemmed | Fundamentals of high-dimensional statistics with exercises and R labs Johannes Lederer |
| title_short | Fundamentals of high-dimensional statistics |
| title_sort | fundamentals of high dimensional statistics with exercises and r labs |
| title_sub | with exercises and R labs |
| topic | Statistical Theory and Methods Big Data Data Structures and Information Theory Artificial Intelligence Statistics and Computing/Statistics Programs Machine Learning Statistics Big data Data structures (Computer science) Artificial intelligence Machine learning |
| topic_facet | Statistical Theory and Methods Big Data Data Structures and Information Theory Artificial Intelligence Statistics and Computing/Statistics Programs Machine Learning Statistics Big data Data structures (Computer science) Artificial intelligence Machine learning |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033026971&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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