# On the Sample Complexity of Graphical Model Selection for Non-Stationary Processes

arXiv: https://arxiv.org/abs/1701.04724 · HTML: https://mlsanity.com/paper/1701.04724/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2017.

## Built on by (most cited first, 3 of 3)

- [On Sparse High-Dimensional Graphical Model Learning For Dependent Time Series](https://mlsanity.com/paper/2111.07897/) (2021)
- [Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Access](https://mlsanity.com/paper/2505.18344/) (2025)
- [Multivariate Time Series Data Imputation via Distributionally Robust Regularization](https://mlsanity.com/paper/2602.00844/) (2026)

## Abstract (arXiv)

We characterize the sample size required for accurate graphical model selection from non-stationary samples. The observed data is modeled as a vector-valued zero-mean Gaussian random process whose samples are uncorrelated but have different covariance matrices. This model contains as special cases the standard setting of i.i.d. samples as well as the case of samples forming a stationary or underspread (non-stationary) processes. More generally, our model applies to any process model for which an efficient decorrelation can be obtained. By analyzing a particular model selection method, we derive a sufficient condition on the required sample size for accurate graphical model selection based on non-stationary data.