# Transfer Learning for High-dimensional Reduced Rank Time Series Models

arXiv: https://arxiv.org/abs/2504.15691 · HTML: https://mlsanity.com/paper/2504.15691/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 33 references that are in the map.
- First posted on arXiv 22 Apr 2025.

## Builds on (most cited first, 14 of 14)

- [Provable Meta-Learning of Linear Representations](https://mlsanity.com/paper/2002.11684/) (2020)
- [A Survey on Negative Transfer](https://mlsanity.com/paper/2009.00909/) (2020)
- [Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality](https://mlsanity.com/paper/2006.10593/) (2020)
- [Confidence Intervals and Hypothesis Testing for High-Dimensional Regression](https://mlsanity.com/paper/1306.3171/) (2013)
- [Transfer Learning under High-dimensional Generalized Linear Models](https://mlsanity.com/paper/2105.14328/) (2021)
- [Transfer Learning for Nonparametric Classification: Minimax Rate and Adaptive Classifier](https://mlsanity.com/paper/1906.02903/) (2019)
- [Regularized estimation in sparse high-dimensional time series models](https://mlsanity.com/paper/1311.4175/) (2013)
- [Transfer Learning in Large-scale Gaussian Graphical Models with False Discovery Rate Control](https://mlsanity.com/paper/2010.11037/) (2020)
- [Learning from Similar Linear Representations: Adaptivity, Minimaxity, and Robustness](https://mlsanity.com/paper/2303.17765/) (2023)
- [Fast Rates by Transferring from Auxiliary Hypotheses](https://mlsanity.com/paper/1412.1619/) (2014)
- [Online Debiasing for Adaptively Collected High-dimensional Data with Applications to Time Series Analysis](https://mlsanity.com/paper/1911.01040/) (2019)
- [Estimating Structured Vector Autoregressive Model](https://mlsanity.com/paper/1602.06606/) (2016)
- [Smoothness Adaptive Hypothesis Transfer Learning](https://mlsanity.com/paper/2402.14966/) (2024)
- [Hypothesis Transfer Learning with Surrogate Classification Losses: Generalization Bounds through Algorithmic Stability](https://mlsanity.com/paper/2305.19694/) (2023)

## Abstract (arXiv)

The objective of transfer learning is to enhance estimation and inference in a target data by leveraging knowledge gained from additional sources. Recent studies have explored transfer learning for independent observations in complex, high-dimensional models assuming sparsity, yet research on time series models remains limited. Our focus is on transfer learning for sequences of observations with temporal dependencies and a more intricate model parameter structure. Specifically, we investigate the vector autoregressive model (VAR), a widely recognized model for time series data, where the transition matrix can be deconstructed into a combination of a sparse matrix and a low-rank one. We propose a new transfer learning algorithm tailored for estimating high-dimensional VAR models characterized by low-rank and sparse structures. Additionally, we present a novel approach for selecting informative observations from auxiliary datasets. Theoretical guarantees are established, encompassing model parameter consistency, informative set selection, and the asymptotic distribution of estimators under mild conditions. The latter facilitates the construction of entry-wise confidence intervals for model parameters. Finally, we demonstrate the empirical efficacy of our methodologies through both simulated and real-world datasets.