# Low-rank MMSE filters, Kronecker-product representation, and regularization: a new perspective

arXiv: https://arxiv.org/abs/2512.14932 · HTML: https://mlsanity.com/paper/2512.14932/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 16 Dec 2025.

## Builds on (most cited first, 6 of 6)

- [Generalized Low Rank Models](https://mlsanity.com/paper/1410.0342/) (2014)
- [Tucker Tensor Regression and Neuroimaging Analysis](https://mlsanity.com/paper/1304.5637/) (2013)
- [Bayesian Tensor Regression](https://mlsanity.com/paper/1509.06490/) (2015)
- [Nuclear Norm Regularization for Deep Learning](https://mlsanity.com/paper/2405.14544/) (2024)
- [Tensor Regression](https://mlsanity.com/paper/2308.11419/) (2023)
- [Automatic Regularization for Linear MMSE Filters](https://mlsanity.com/paper/2312.06560/) (2023)

## Abstract (arXiv)

In this work, we propose a method to efficiently find the regularization parameter for low-rank MMSE filters based on a Kronecker-product representation. We show that the regularization parameter is surprisingly linked to the problem of rank selection and, thus, properly choosing it, is crucial for low-rank settings. The proposed method is validated through simulations, showing significant gains over commonly used methods.