# Learning High-dimensional Gaussian Graphical Models under Total Positivity without Adjustment of Tuning Parameters

arXiv: https://arxiv.org/abs/1906.05159 · HTML: https://mlsanity.com/paper/1906.05159/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2019.

## Built on by (most cited first, 9 of 9)

- [Fast Projected Newton-like Method for Precision Matrix Estimation under Total Positivity](https://mlsanity.com/paper/2112.01939/) (2021)
- [Sparse Graph Learning Under Laplacian-Related Constraints](https://mlsanity.com/paper/2111.08161/) (2021)
- [Adaptive Estimation of Graphical Models under Total Positivity](https://mlsanity.com/paper/2210.15471/) (2022)
- [Online Inference for Mixture Model of Streaming Graph Signals with Non-White Excitation](https://mlsanity.com/paper/2207.14019/) (2022)
- [Learning Gaussian Graphical Models under Total Positivity via Spectral Graph Sparsification](https://mlsanity.com/paper/2605.17154/) (2026)
- [A note on incorrect inferences in non-binary qualitative probabilistic networks](https://mlsanity.com/paper/2208.09344/) (2022)
- [Inconsistency of cross-validation for structure learning in Gaussian graphical models](https://mlsanity.com/paper/2312.17047/) (2023)
- [False Discovery Rate Control via Frequentist-assisted Horseshoe](https://mlsanity.com/paper/2502.05460/) (2025)
- [Spectral Sparsification of Laplacian-Constrained Gaussian and H"usler-Reiss Graphical Models](https://mlsanity.com/paper/2606.16681/) (2026)

## Abstract (arXiv)

We consider the problem of estimating an undirected Gaussian graphical model when the underlying distribution is multivariate totally positive of order 2 (MTP2), a strong form of positive dependence. Such distributions are relevant for example for portfolio selection, since assets are usually positively dependent. A large body of methods have been proposed for learning undirected graphical models without the MTP2 constraint. A major limitation of these methods is that their structure recovery guarantees in the high-dimensional setting usually require a particular choice of a tuning parameter, which is unknown a priori in real world applications. We here propose a new method to estimate the underlying undirected graphical model under MTP2 and show that it is provably consistent in structure recovery without adjusting the tuning parameters. This is achieved by a constraint-based estimator that infers the structure of the underlying graphical model by testing the signs of the empirical partial correlation coefficients. We evaluate the performance of our estimator in simulations and on financial data.