Generalise your usual linear regression to multilinear regression. Useful tool: tensor decompositions. Tensorly I think is the main implementation of note.
Anandkumar, Anima, Rong Ge, Daniel Hsu, Sham M. Kakade, and Matus Telgarsky. 2015. “Tensor Decompositions for Learning Latent Variable Models (A Survey for ALT).” In Algorithmic Learning Theory, edited by Kamalika Chaudhuri, Claudio Gentile, and Sandra Zilles, 19–38. Lecture Notes in Computer Science. Springer International Publishing.
Anandkumar, Animashree, Rong Ge, Daniel Hsu, Sham M. Kakade, and Matus Telgarsky. 2014. “Tensor Decompositions for Learning Latent Variable Models.” The Journal of Machine Learning Research 15 (1): 2773–2832.
Bi, Xuan, Xiwei Tang, Yubai Yuan, Yanqing Zhang, and Annie Qu. 2021. “Tensors in Statistics.” Annual Review of Statistics and Its Application 8 (1): 345–68.
Cui, Tiangang, and Sergey Dolgov. 2022. “Deep Composition of Tensor-Trains Using Squared Inverse Rosenblatt Transports.” Foundations of Computational Mathematics 22 (6): 1863–1922.
Kossaifi, Jean, Yannis Panagakis, Anima Anandkumar, and Maja Pantic. 2019. “TensorLy: Tensor Learning in Python.” Journal of Machine Learning Research 20 (26): 1–6.
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