Tensor regression

2020-11-19 — 2020-11-19

Wherein the extension of linear regression to multilinear forms is presented, and the use of tensor decompositions for parameter reduction and the Tensorly library as a practical implementation are noted.

algebra

Hilbert space

Generalize your usual linear regression to multilinear regression. Useful tool: tensor decompositions. Tensorly is the main implementation of note.

1 Incoming

Tiangang Cui

2 References

Anandkumar, Animashree, Ge, Hsu, et al. 2014. “Tensor Decompositions for Learning Latent Variable Models.” The Journal of Machine Learning Research.

Anandkumar, Anima, Ge, Hsu, et al. 2015. “Tensor Decompositions for Learning Latent Variable Models (A Survey for ALT).” In Algorithmic Learning Theory. Lecture Notes in Computer Science.

Bi, Tang, Yuan, et al. 2021. “Tensors in Statistics.” Annual Review of Statistics and Its Application.

Cui, and Dolgov. 2022. “Deep Composition of Tensor-Trains Using Squared Inverse Rosenblatt Transports.” Foundations of Computational Mathematics.

Kossaifi, Panagakis, Anandkumar, et al. 2019. “TensorLy: Tensor Learning in Python.” Journal of Machine Learning Research.