# On Learning Continuous Pairwise Markov Random Fields

arXiv: https://arxiv.org/abs/2010.15031 · HTML: https://mlsanity.com/paper/2010.15031/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2020.

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

- [A Computationally Efficient Method for Learning Exponential Family Distributions](https://mlsanity.com/paper/2110.15397/) (2021)
- [On counterfactual inference with unobserved confounding](https://mlsanity.com/paper/2211.08209/) (2022)
- [Chow-Liu++: Optimal Prediction-Centric Learning of Tree Ising Models](https://mlsanity.com/paper/2106.03969/) (2021)
- [Learning Continuous Exponential Families Beyond Gaussian](https://mlsanity.com/paper/2102.09198/) (2021)
- [Attention: Marginal Probability is All You Need?](https://mlsanity.com/paper/2304.04556/) (2023)
- [On Computationally Efficient Learning of Exponential Family Distributions](https://mlsanity.com/paper/2309.06413/) (2023)
- [A Unified View on Learning Unnormalized Distributions via Noise-Contrastive Estimation](https://mlsanity.com/paper/2409.18209/) (2024)
- [Finite Sample Bounds for Learning with Score Matching](https://mlsanity.com/paper/2605.14168/) (2026)
- [Causal Inference for Sequential Settings under Interference and Latent Confounding](https://mlsanity.com/paper/2607.14940/) (2026)

## Abstract (arXiv)

We consider learning a sparse pairwise Markov Random Field (MRF) with continuous-valued variables from i.i.d samples. We adapt the algorithm of Vuffray et al. (2019) to this setting and provide finite-sample analysis revealing sample complexity scaling logarithmically with the number of variables, as in the discrete and Gaussian settings. Our approach is applicable to a large class of pairwise MRFs with continuous variables and also has desirable asymptotic properties, including consistency and normality under mild conditions. Further, we establish that the population version of the optimization criterion employed in Vuffray et al. (2019) can be interpreted as local maximum likelihood estimation (MLE). As part of our analysis, we introduce a robust variation of sparse linear regression a` la Lasso, which may be of interest in its own right.