Higher Order Reduced Rank Regression

• URL: http://arxiv.org/abs/2503.06528v1
• Date: Sun, 09 Mar 2025 09:21:38 GMT
• Title: Higher Order Reduced Rank Regression
• Authors: Leia Greenberg, Haim Avron,
• Abstract summary: Reduced Rank Regression (RRR) is a widely used method for multi-response regression.<n>This paper introduces Higher Order Reduced Rank Regression (HORRR)<n>HORRR is capable of capturing nonlinear interactions in multi-response regression.
• Score: 7.002470330184841
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Reduced Rank Regression (RRR) is a widely used method for multi-response regression. However, RRR assumes a linear relationship between features and responses. While linear models are useful and often provide a good approximation, many real-world problems involve more complex relationships that cannot be adequately captured by simple linear interactions. One way to model such relationships is via multilinear transformations. This paper introduces Higher Order Reduced Rank Regression (HORRR), an extension of RRR that leverages multi-linear transformations, and as such is capable of capturing nonlinear interactions in multi-response regression. HORRR employs tensor representations for the coefficients and a Tucker decomposition to impose multilinear rank constraints as regularization akin to the rank constraints in RRR. Encoding these constraints as a manifold allows us to use Riemannian optimization to solve this HORRR problems. We theoretically and empirically analyze the use of Riemannian optimization for solving HORRR problems.

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