# Transfer Denoising of Low-Rank Plus Sparse Matrices under Ambient and Rank Growth

arXiv: https://arxiv.org/abs/2601.21873 · HTML: https://mlsanity.com/paper/2601.21873/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 25 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 10 of 10)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [An Overview of Multi-Task Learning in Deep Neural Networks](https://mlsanity.com/paper/1706.05098/) (2017)
- [Spectral Methods for Data Science: A Statistical Perspective](https://mlsanity.com/paper/2012.08496/) (2020)
- [Bridging Convex and Nonconvex Optimization in Robust PCA: Noise, Outliers, and Missing Data](https://mlsanity.com/paper/2001.05484/) (2020)
- [Spectral State Compression of Markov Processes](https://mlsanity.com/paper/1802.02920/) (2018)
- [Transition Transfer Q-Learning for Composite Markov Decision Processes](https://mlsanity.com/paper/2502.00534/) (2025)
- [Structured Matrix Learning under Arbitrary Entrywise Dependence and Estimation of Markov Transition Kernel](https://mlsanity.com/paper/2401.02520/) (2024)

## Abstract (arXiv)

We study transfer learning for low-rank plus sparse matrix denoising when both ambient and latent dimensions grow. A data-rich source task provides subspace information for a higher-dimensional, data-scarce target with a small rank increment and localized sparse edits. We develop an anchored alternating-projection estimator that preserves transferred subspaces while learning target-specific coefficients, additional latent directions, and sparse modifications. We establish deterministic error bounds that separate target noise, representation growth, and source-estimation error, identifying improved rates through small structural increments and reduced noise within inherited subspaces. We further extend it to approximate anchoring quantifies robustness to subspace mismatch. We establish application-specific guarantees for Markov transition matrix estimation from single trajectories with dependent noise and for structured covariance estimation, with the latter analysis provided in the appendix. Experiments demonstrate consistent improvements over non-transfer baselines on synthetic data and an approximately 45% reduction in principal-angle error on a NYC taxi transition-estimation task with expanding state spaces.