Sliced Inverse Regression for Dimension Reduction

By Ker-Chau Li. 1991

Subfields: Statistics and Probability, Representation & Self-Supervised Learning

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Supervised Dimensionality Reduction via Distance Correlation Maximization (2016, methodology): “…14.19 13.64 12.94 12.12 11.73 LAD [Cook and Forzani, 2009] 17.70 17.62 17.34 17.15 16.89 SAVE [Shao et al., 2009] 19.32 18.74 18.62 17.76 17.21 SIR [Li, 1991] 21.53 21.23 20.97 20.77 20.64 [Suzuki and Sugiyama, 2013] 14.38 13.14 12.86 12.73 12.69 gKDR [Fukumizu and Leng, 2014] 13.65 12.86 12.67…”
Domain Generalization via Invariant Feature Representation (2013, methodology): “To avoid slicing the output space explicitly (Li 1991, Wu 2008), we exploit its kernel structure when estimating the covariance of the inverse regressor.”
Sufficient Forecasting Using Factor Models (2015, methodology): “In practice, H has little influence on the estimated directions, whichwas first pointed out in Li (1991) and can be seen from (2.8).”
Kernel dimension reduction in regression (2009, methodology): “As suggested in a seminal paper by Li [23], it is of great interest to develop procedures for estimating this subspace, quite apart from any interest in the conditional distribution P (Y | X) or the conditional mean E(Y | X).”
Breaking the Curse of Dimensionality with Convex Neural Networks (2014, background): “A variety of algorithms exist for this problem (Li, 1991; Fukumizu et al., 2004; Dalalyan et al., 2008).”
Joint covariate selection and joint subspace selection for multiple classification problems (2010, background): “There has been a large literature on sufficient dimension reduction (e.g., Chiaromonte and Cook 2002; Fukumizu et al. 2008; Li 1991), but the focus has been on univariate response variables.”
Distributed optimization of deeply nested systems (2012, methodology): “obtain nonlinear networks is widely applied beyond RBF networks, for example with support vector machines (Scho¨lkopf and Smola, 2001), kernel PCA (Sch¨olkopf et al., 1998), slice inverse regression (Li, 1991) and others. We wish to capitalize on this attractive property to train deep autoencoders c”
On a Projective Resampling Method for Dimension Reduction With Multivariate Responses (2008, background): “…include ordinary least squares (OLS; Li and Duan 1989), principal Hessian directions (PHD; Li 1992), SIR, sliced average variance estimator (SAVE; Cook and Weisberg 1991; Cook and Critchley 2000), kernel inverse regression (Zhu and Fang 1996; Ferre and Yao 2005), structure adaptive estimator…”
Direct estimation of the index coefficient in a single-index model (2001, methodology): “Another direct method of index coefficient estimation, called “sliced inverse regression” has been proposed in Li and Duan (1989), Duan and Li (1991) and Li (1991).”
Moment-based dimension reduction for multivariate response regression (2006, methodology): “In general, the extension of existing dimension reduction methods such as SIR (Sliced inverse regression, Li 1991) and SAVE (Cook and Weisberg 1991) for univariate response regressions to their multivariate analogs is conceptually straightforward.”
A Consistent Estimator of the Expected Gradient Outerproduct (2014, background): “[7]), and many of them incorporating the estimation of derivate functionals of the unknown f .”
Statistical Methods with Varying Coefficient Models. (2008, methodology): “…many methods have been * The work is supported by the NSF grants DMS-0532370 and NIH grant R01-GM072611. proposed to reduce dimension, which includes the projection pursuit (Huber, 1985), the sliced inverse regression (Li, 1991), the single index models (Härdle and Stoker, 1990) and others.”
ldr: An R Software Package for Likelihood-Based Su?cient Dimension Reduction (2014, methodology): “Numerous suﬃcient dimension reduction methods have been proposed in the statistics literature since the seminal paper of Li (1991) on sliced inverse regression (SIR).”
Empirical likelihood confidence regions in a partially linear single‐index model (2006, methodology): “With more general frameworks, sliced inverse regression (see Li (1991)) and the approach that was proposed by Carroll et al. (1997) are two promising tools in this area.”
Dimension reduction for nonelliptically distributed predictors (2009, methodology): “Dimension reduction for regression [Li (1991, 1992), Cook and Weisberg (1991), Cook (1994, 1996)] is aimed at finding a lower dimensional vector of linear combinations of the predictors, which retains as much as possible the information in the relationship between the response and the original…”
Partial least squares: a versatile tool for the analysis of high-dimensional genomic data (2006, unknown): “other supervised dimension approaches such as su cient dimension reduction [ 2 , 3, 4], it”
Defection Detection: Measuring and Understanding the Predictive Accuracy of Customer Churn Models (2006, methodology): “The variable selection problem can be approached with methods of data reduction that minimize the loss of information on the dependent variable (Cook and Lee 1999; Li 1991).”