- 高维数据统计学(方法理论和应用)(英文版)
- - 作者：(瑞士)布尔曼//吉尔
  - 出版社：世界图书出版公司
  - ISBN：9787519211677
  - 出版日期：2016/05/01
  - 页数：556
- 售价：38

内容大纲
Peter Bühlmann在ETHZ是高维统计、因果推断方面的知名专家。布尔曼、吉尔所著的《高维数据统计学(方法理论和应用)(英文版)》统计学的前沿之作。这本书所针对的高维数据，是理论研究的热点，在实际中也有着广泛的应用。这本书重点阐述了Lasso和其他L1方法的变体，也有boosting等内容。
作者介绍
目录
1  Introduction
  1.1  The framework
  1.2  The possibilities and challenges
  1.3  About the book
    1.3.1  Organization of the book
  1.4  Some examples
    1.4.1  Prediction and biomarker discovery in genomics
2  Lasso for linear models
  2.1  Organization of the chapter
  2.2  Introduction and preliminaries
    2.2.1  The Lasso estimator
  2.3  Orthonormal design
  2.4  Prediction
    2.4.1  Practical aspects about the Lasso for prediction
    2.4.2  Some results from asymptotic theory
  2.5  Variable screening and -norms
    2.5.1  Tuning parameter selection for variable screening
    2.5.2  Motif regression for DNA binding sites
  2.6  Variable selection
    2.6.1  Neighborhood stability and irrepresentable condition
  2.7  Key properties and corresponding assumptions: a summary
  2.8  The adaptive Lasso: a two-stage procedure
    2.8.1  An illustration: simulated data and motif regression
    2.8.2  Orthonormal design
    2.8.3  The adaptive Lasso: variable selection under weak conditions
    2.8.4  Computation
    2.8.5  Multi-step adaptive Lasso
    2.8.6  Non-convex penalty functions
  2.9  Thresholding the Lasso
  2.10  The relaxed Lasso
  2.11  Degrees of freedom of the Lasso
  2.12  Path-following algorithms
    2.12.1  Coordinatewise optimization and shooting algorithms
  2.13  Elastic net: an extension
  Problems
3  Generalized linear models and the Lasso
  3.1  Organization of the chapter
  3.2  Introduction and preliminaries
    3.2.1  The Lasso estimator: penalizing the negative log-likelihood.
  3.3  Important examples of generalized linear models
    3.3.1  Binary response variable and logistic regression
    3.3.2  Poisson regression
    3.3.3  Multi-category response variable and multinomial distribution
  Problems
4  The group Lasso
  4.1  Organization of the chapter
  4.2  Introduction and preliminaries
    4.2.1  The group Lasso penalty
  4.3  Factor variables as covariates
    4.3.1  Prediction of splice sites in DNA sequences

  4.4  Properties of the group Lasso for generalized linear models
  4.5  The generalized group Lasso penalty
    4.5.1  Groupwise prediction penalty and parametrization invariance
  4.6  The adaptive group Lasso
    4.7  Algorithms for the group Lasso
    4.7.1  Block coordinate descent
    4.7.2  Block coordinate gradient descent
  Problems
5  Additive models and many smooth univariate functions
  5.1  Organization of the chapter
  5.2  Introduction and preliminaries
    5.2.1  Penalized maximum likelihood for additive models
  5.3  The sparsity-smoothness penalty
    5.3.1  Orthogonal basis and diagonal smoothing matrices
    5.3.2  Natural cubic splines and Sobolev spaces
    5.3.3  Computation
  5.4  A sparsity-smoothness penalty of group Lasso type
    5.4.1  Computational algorithm
    5.4.2  Alternative approaches
  5.5  Numerical examples
    5.5.1  Simulated example
……
6  Theory for the lasso
7  Variable selection with the lasso
8  Theory for -penalty procedures
9  Non-convex loss functions and -regularization
10  Stable solutions
11  P-values for linear models and beyond
12  Boosting and greedy algorithms
14  Probability and moment inequalities
Author index
Index
References

内容大纲

作者介绍

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