Reduced-rank regression for the multivariate linear model

By Alan J. Izenman. 1975

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Citations in the corpus

Implicit Regularization of Discrete Gradient Dynamics in Deep Linear Neural Networks (2019, neutral): “The path followed by the two-layer formulation actually corresponds to successively solving the initial regression problem with a growing low rank constraint which is also know as reduced-rank regression [Izenman, 1975].”
ENVELOPE MODELS FOR PARSIMONIOUS AND EFFICIENT MULTIVARIATE LINEAR REGRESSION (2010, methodology): “This, in effect, combines envelope models with models for multivariate reduced rank regression (Anderson, 1951; Izenman, 1975; Davies and Tso, 1982; Bura and Cook, 2003).”
Multi-output learning via spectral filtering (2012, methodology): “In statistics we mention the Curds & Whey method of Breiman and Friedman (1997), Reduced Rank Regression (Izenman 1975), Filtered Canonical y-variate Regression (van der Merwe and Zidek 1980) and Partial Least Squares (Wold et al. 1984).”
On label dependence and loss minimization in multi-label classification (2012, methodology): “Several methods introduced for multivariate regression, like C&W (Breiman and Friedman 1997), reduced-rank regression (RRR) (Izenman 1975), and FICYREG (an der Merwe and Zidek 1980), can be seen as a realization of the scheme (25).”
Dimension reduction and coefficient estimation in multivariate linear regression (2007, methodology): “Many popular methods including canonical correlation (Hotelling, 1935, 1936), reduced rank (Anderson, 1951; Izenman, 1975; Reinsel and Velu, 1998), principal components (Massy, 1965), partial least squares (Wold, 1975) and joint continuum regression (Brooks and Stone, 1994) among others can all be…”
A survey on multi‐output regression (2015, methodology): “• When we assume a linear model with a non-full rank matrix of coeﬃcients 33,34 .”
Vector Field Learning via Spectral Filtering (2010, methodology): “In statistics we mention the Curds & Whey method [11], Reduced Rank Regression [12], Filtered Canonical y-variate Regression [13] and Partial Least Squares [14].”
Envelopes and reduced-rank regression (2015, methodology): “…of the two methods25 when appropriate and that has the potential to perform better than either of them.26 Reduced-rank regression (Anderson 1951; Izenman 1975; Reinsel and Velu 1998) arises27 frequently in multivariate statistical analysis, and has been applied widely across the applied28…”
A Model-Free Test for Reduced Rank in Multivariate Regression (2003, background): “Asymptotic distributions of estimators of B and asymptotic rank tests are available when ± is normally distributed (Anderson 1951; Izenman 1975;Reinsel and Velu 1998; Schmidli 1996).”
Convex multi-task feature learning (2008, background): “Other interesting approaches which may be pursued in the context of multi-task learning include multivariate linear models in statistics such as reduced rank regression [30], partial least squares [45] and canonical correlation analysis [29] (see also [16]).”
On Spectral Learning (2010, background): “This occurs, for example, in multi-task learning and problems closely related to it (Abernethy et al., 2009; Argyriou et al., 2007a,b; Cand̀es and Recht, 2008; Cavallanti et al., 2008; Izenman, 1975; Maurer, 2006a,a; Srebro et al., 2005; Yuan et al., 2007, etc.).”
Moment-based dimension reduction for multivariate response regression (2006, background): “Under normality of the error terms, the asymptotic distributions of estimators of the coefficient matrix and asymptotic rank tests are available (Anderson 1951; Izenman 1975; Reinsel and Velu 1998, Ch. 2; Schmidli 1995, Ch. 4).”