Multivariate multiple linear regression with a constraint that the coefficient matrix should be of low rank.

Reduced rank regression (RRR) is multivariate multiple linear regression with a constraint that the coefficient matrix should be of low rank. It allows to investigate how one multivariate dataset $X$ can predict another multivariate dataset $Y$, by performing a dimensionality reduction in both $X$ and $Y$ at the same time. It is closely related to canonical correlation analysis (CCA).

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