High-Dimensional Data Analysis 高维数据分析
作者: 蔡天文 沈晓桐
出版时间:2010-10-08
出版社:高等教育出版社
- 高等教育出版社
- 9787040298512
- 1
- 253474
- 精装
- 16开
- 2010-10-08
- 300
- 307
- 理学
- 统计学
Over the last few years, significant developments have been taking place in high-dimensional data analysis, driven primarily by a wide range of applications in many fields such as genomics and signal processing. in particular, substantial advances have been made in the areas of feature selection, covariance estimation,classification and regression. this book intends to examine important issues arising from high-dimensional data analysis to explore key ideas for statistical inference and prediction.
It is structured around topics on multiple hypothesis testing, feature selection, regression, classification, dimension reduction, as well as applications in survival analysis and biomedical research.
The book will appeal to graduate students and new researchers interested in the plethora of opportunities available in highdimensional data analysis.
Front Matter
Part I High-Dimensional Classication
Chapter 1 High-Dimensional Classication
Jianqing Fan, Yingying Fan and Yichao Wu
1 Introduction
2 Elements of classications
3 Impact of dimensionality on classication
4 Distance-based classication Rules
5 Feature selection by independence rule
6 Loss-based classication
7 Feature selection in loss-based classication
8 Multi-category classication
References
Chapter 2 Flexible Large Margin Classiers
Yufeng Liu and Yichao Wu
1 Background on classication
2 The support vector machine: the margin formulation and
the SV interpretation
3 Regularization framework
4 Some extensions of the SVM: Bounded constraint machine
and the balancing SVM
5 Multicategory classiers
6 Probability estimation
7 Conclusions and discussions
References
Part II Large-Scale Multiple Testing
Chapter 3 A Compound Decision-Theoretic Approach to Large-Scale Multiple Testing
T. Tony Cai and Wenguang Sun
1 Introduction
2 FDR controlling procedures based on p-values
3 Oracle and adaptive compound decision rules for FDR control
4 Simultaneous testing of grouped hypotheses
5 Large-scale multiple testing under dependence
6 Open problems
References
Part III Model Building with Variable Selection
Chapter 4 Model Building with Variable Selection
Ming Yuan
1 Introduction
2 Why variable selection
3 Classical approaches
4 Bayesian and stochastic search
5 Regularization
6 Towards more interpretable models
7 Further readings
References
Chapter 5 Bayesian Variable Selection in Regressionwith Networked Predictors
Feng Tai, Wei Pan and Xiaotong Shen
1 Introduction
2 Statistical models
3 Estimation
4 Results
5 Discussion
References
Part IV High-Dimensional Statistics in Genomics
Chapter 6 High-Dimensional Statistics in Genomics
Hongzhe Li
1 Introduction
2 Identication of active transcription factors using
time-course gene expression data
3 Methods for analysis of genomic data with a graphical structure
4 Statistical methods in eQTL studies
5 Discussion and future direction
References
Chapter 7 An Overview on Joint Modeling of Censored Survival Time and Longitudinal Data
Runze Li and Jian-Jian Ren
1 Introduction
2 Survival data with longitudinal covariates
3 Joint modeling with right censored data
4 Joint modeling with interval censored data
5 Further studies
References
Part V Analysis of Survival and Longitudinal Data
Chapter 8 Survival Analysis with High-Dimensional Covariates
Bin Nan
1 Introduction
2 Regularized Cox regression
3 Hierarchically penalized Cox regression with grouped variables
4 Regularized methods for the accelerated failure time model
5 Tuning parameter selection and a concluding remark
References
Part VI Sucient Dimension Reduction in Regression
Chapter 9 Sucient Dimension Reduction in Regression
Xiangrong Yin
1 Introduction
2 Sucient dimension reduction in regression
3 Sucient variable selection (SVS)
4 SDR for correlated data and large-p-small-n
5 Further discussion
References
Chapter 10 Combining Statistical Procedures
Lihua Chen and Yuhong Yang
1 Introduction
2 Combining for adaptation
3 Combining procedures for improvement
4 Concluding remarks
References
Subject Index
Author Index
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