What's Here?

This page provides links to computer programs that implement the envelope methods described in this book. Links to some new methods are also given. The first section addresses envelope methodology, the second is on general algorithms for manifold optimization and the final section covers computing for sufficient dimension reduction. Last updated 13 January 2020.

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Envelope Computing

envlp

• envlp is a Matlab toolbox for fitting envelopes in multivariate linear regression. Based on Ross Lippert's sg_min toolbox for optimizing over Stiefel and Grassmann manifolds, it covers many methods, including response, partial, predictor, inner, scaled and heteroscedastic envelopes, along with associated inference methods. (Cook, Su and Yang, 2015)

Renvlp

• Renvlp is an R package by Minji Lee and Zhihua Su for fitting many types of envelopes. Except for inner envelopes, it has all of the capabilities of envlp plus many more, including weighted envelopes, envelopes in logistic and Poisson regression, simultaneous envelopes, groupwise envelopes and scaled predictor envelopes. It has also many inference tools plus a routine for fitting that does not presume a model.

• Renvlp is based on targeted routines rather than on a general purpose method for Grassmann fitting. In consequence it is less prone to get caught in local minima. Renvlp and envlp can give slightly different answers because they are based on different computing engines.

Matrix Envelopes

• MatrixEnv is an R package for fitting matrix envelopes in matrix-valued linear regression. This link takes you to Shanshan Ding's page where zip files with the code can be downloaded. This methodology was developed by Ding and Cook (2017).

Simultaneous, Reduced Rank and Tensor Envelopes

• Matlab packages for these three envelope types are maintained by Xin (Henry) Zhang at his homepage. He also has Matlab code for fitting the 1D algorithm, and the ECD and ECS algorithms.

• Henry Zhang and his students have also created an R pagkage TRES for envelope estimation with special emphasis on tensor envelope methods. The package also includes generic envelope estimation and an implementation of the model-free dimension selection method developed by Zhang and Mai (2018).

Spatial Envelopes

Rekabdarkolaee, Wang, Naji and Fluentes introduced spatial envelopes for the study of spatial data while allowing for dependencies across space. R code for their spatial envelope method, which is to appear in Statistica Sinica, is available here.

Sparse Envelopes, Envelope-based Sparse Partial Least Squares

• spenvlp is an R package that implements sparse envelopes, envelope-based partial least squares and envelope-based sparse partial least squares. It was provided by Zhihua Su and written by Guangyu Zhu. The package implements recent results by Zhu and Su that are to appear in the Annals of Statistics. A preprint is available in the Future Papers section of the Annals' webpage.

Functional Envelopes

Zhang, Wang and Wu (2018) developed functional envelopes for sufficient dimension reduction, including regressions involving functional or longitudinal data. A basic MatLab toolbox, PACE written by Chong Wang, was provided by Henry Zhang. Background on the functional analysis part of the code, including references and examples, is available here.

Bayesian Envelopes

Khare, Pal and Su (2017) developed a Bayesian version of envelopes for the multivariate linear model. A manifold-based R package, BENV, written by Subhadip Pal is available to implement their methodology. A faster non-manifold version is under development by Saptarshi Chakarborty et al.

Envelope Quantile Regression

Ding, Su, Zhu and Wang (2019) extended envelope methodology to quantile regression. An R package, envqr, that implements envelope quantile regression was written by Guangyu Zhu, and furnished by Shanshan Ding. Their paper, Envelope Quantile Regression, is available as a Forthcoming Paper from Statistica Sinica.

Clustering with Envelopes

Wang, Zhang, and Mai (2020) developed envelope-based mixture models for improved clustering by projecting onto low-dimensional latent spaces. Their approach also provides foundations for envelope methods in unsupervised and semi-supervised settings. An R package for their method, called CLEMM, is available from GitHub.

Nonlinearlty and Heteroscedasticity

Envelopes were recently extended to multi-response regression models with nonlinearity and heteroscedasticity by Zhang, Li and Shao (2020). Their development makes use of the martingale difference divergence matrix (Lee and Shao, 2018) and it introduces the concept of the Central Mean Envelope. A preprint of their paper, which is to appear in Biometrika, and a MatLab toolbox which implements their method are available from Zhang's webpage

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Manifold Optimization

Riemannian Manifold Optimization

• ManifoldOptim is an R interface to the ROPTLIB library for Riemannian Manifold Optimization. Illustrations of using this environment to fit envelopes are given in an associated paper by Martin, Raim, Huang and Adragni (2016).

Grassmann Manifold Optimization

• GrassmannOptim is an R package for Grassmann manifold optimization developed by Adragni, Cook and Wu, (2012)

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Computing for Sufficient Dimension Reduction

dr

• dr is an R package by Sandy Weisberg that implements basic SDR methodology like SIR, SAVE, pHd applied to the responses or residuals, and IRE. (Weisberg, 2002)

LDR

• LDR is a MatLab toolbox for likelihood-based sufficient dimension reduction (Cook, Forzani, Tomassi, 2011). It includes routines for computing principal components, principal fitted components (PFC) along with various extensions, covariance reductions (CORE) and likelihood aquired directions (LAD).

ldr

• Written by Kofi Adragni and Andrew Raim, ldr is an R counterpart of LDR. It provides R implementations of PFC and its extensions, CORE and LAD. It also implements a variable screening procedure based on PFC. (Adragni and Raim, 2014)

Matrix-valued Predictors and Tensor Sliced Inverse Regression

• Dfpfc is an R package that performs dimension folding PCA and PCF for regressions with matrix-valued predictors (Ding and Cook 2014).

  TensorSIR is an R package that implements sliced inverse regression for tensor-valued data (Ding and Cook, 2015).

High-dimensional Principal Fitted Components and Abundant Regression

• Abundant is an R package written by Adam Rothman for fitting high-dimensional PFCs and abundant regressions.

Sufficient Dimension Reduction: Methods and applications with R

This 2018 book by Bing Li contains descriptions of many SDR methods, along with corresponding R-code.