Statistics for High-Dimensional Data: Methods, Theory and Applications, Peter Buhlman and Sara van de Geer著, Springer, 2011年6月, 558pp., 価格 114,99〓, ISBN 978-3642201912

By 松井秀俊. 2014

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Subfields: Artificial Intelligence, Statistics and Probability, Statistical Learning Theory

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Citations in the corpus

Fused Lasso Additive Model (2014, neutral): “Proofs are in the Appendix.”
Sparse Partially Linear Additive Models (2014, background): “5.1 SYNTHETIC PROBLEM To illustrate the use of SPLAM, we generate N = 2000 points from the model y = 2 sin(2x1)+ x22 + exp(−x3)+ x4 − 3x5 + 2.5x6 + 10x7 + 2x8 − 7x9 + 5x10 + , where ∼ N (0, 1).”
Variance-based Regularization with Convex Objectives (2016, background): “Example 2 (High-dimensional problems): In high dimensional problems, the Euclidean scaling of Example 1 may be problematic, so that using l1-constraints is preferred [16].”
Gradient Sparsification for Communication-Efficient Distributed Optimization (2017, positive): “The notion of (ρ, s)-approximately sparsity is inspired by the restricted eigenvalue condition used in high-dimensional statistics [5].”
CAM: Causal Additive Models, high-dimensional order search and penalized regression (2013, background): “n, a group compatibility condition (for the basis vectors), and a beta-min condition about the minimal size of the ℓ2-norm of the coeﬃcients for the basis functions of the active variables in Aj; see [4], Chapter 5.6, Theorem 8.2. The sparsity and group compatibility condition ensure identiﬁability ”
Minimax Optimal Procedures for Locally Private Estimation (2016, background): “Recently, there has been substantial interest in high-dimensional problems in which the dimension d is larger than the sample size n , but a low-dimensional latent structure makes inference possible (Bühlmann and van de Geer 2011; Negahban et al. 2012).”
Causal Transfer in Machine Learning (2015, methodology): “A ’+’ next to a subset S corresponds to the method for MTL described in the last paragraph of Section 2.2 linear models with 1 penalization, variable screening is a well studied problem, see e.g. compatibility and β min conditions [B¨uhlmann and van de Geer, 2011, Chapter 2.5].”
Sparse coding for multitask and transfer learning (2012, neutral): “cal results guarantee a good performance of this method under the assumption that the vector corresponding to the underlying predictor is sparse, or at least has a very small ℓ1-norm, see for example [11, 12, 31] and references therein. In this work, we consider the case where the predictors are lin”
On asymptotically optimal confidence regions and tests for high-dimensional models (2013, methodology): “d estimation of a high-dimensional parameter [6, 11, 12, 24, 33, 34, 47, 51] or variable selection [17, 30, 49, 53]. Other references and exposition to a broad class of models can be found in [18] or [10]. Very little work has been done for constructing conﬁdence intervals, statistical testing and a”
The Right Complexity Measure in Locally Private Estimation: It is not the Fisher Information (2018, neutral): “This contrasts the non-private case, where non-asymptotic rates of log are possible [7, 41].”
Simultaneous Inference for High-Dimensional Linear Models (2016, positive): “The statistical properties of these procedures have been extensively studied in the literature; see B¨uhlmann and van de Geer (2011).”
Online Decision Making with High-Dimensional Covariates (2020, background): “In particular, only a small number of a patient’s genetic biomarkers or past diagnoses (corresponding to certain pre-existing conditions) may be relevant to the success of a specific treatment.”