# Learning Continuous Exponential Families Beyond Gaussian

arXiv: https://arxiv.org/abs/2102.09198 · HTML: https://mlsanity.com/paper/2102.09198/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 50 references that are in the map.
- First posted on arXiv 18 Feb 2021.

## Builds on (most cited first, 13 of 13)

- [JuMP: A Modeling Language for Mathematical Optimization](https://mlsanity.com/paper/1508.01982/) (2015)
- [Interaction Screening: Efficient and Sample-Optimal Learning of Ising Models](https://mlsanity.com/paper/1605.07252/) (2016)
- [Learning Graphical Models Using Multiplicative Weights](https://mlsanity.com/paper/1706.06274/) (2017)
- [On Graphical Models via Univariate Exponential Family Distributions](https://mlsanity.com/paper/1301.4183/) (2013)
- [Optimal structure and parameter learning of Ising models](https://mlsanity.com/paper/1612.05024/) (2016)
- [Efficient Learning of Discrete Graphical Models](https://mlsanity.com/paper/1902.00600/) (2019)
- [Learning Some Popular Gaussian Graphical Models without Condition Number Bounds](https://mlsanity.com/paper/1905.01282/) (2019)
- [Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting](https://mlsanity.com/paper/1711.00950/) (2017)
- [On Learning Continuous Pairwise Markov Random Fields](https://mlsanity.com/paper/2010.15031/) (2020)
- [Learning Ising Models with Independent Failures](https://mlsanity.com/paper/1902.04728/) (2019)
- [On Semiparametric Exponential Family Graphical Models](https://mlsanity.com/paper/1412.8697/) (2014)
- [Learning of Discrete Graphical Models with Neural Networks](https://mlsanity.com/paper/2006.11937/) (2020)
- [Vector-Space Markov Random Fields via Exponential Families](https://mlsanity.com/paper/1505.05117/) (2015)

## Built on by (most cited first, 6 of 6)

- [Provable benefits of score matching](https://mlsanity.com/paper/2306.01993/) (2023)
- [A Computationally Efficient Method for Learning Exponential Family Distributions](https://mlsanity.com/paper/2110.15397/) (2021)
- [Codiscovering graphical structure and functional relationships within data: A Gaussian Process framework for connecting the dots](https://mlsanity.com/paper/2311.17007/) (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)

## Abstract (arXiv)

We address the problem of learning of continuous exponential family distributions with unbounded support. While a lot of progress has been made on learning of Gaussian graphical models, we still lack scalable algorithms for reconstructing general continuous exponential families modeling higher-order moments of the data beyond the mean and the covariance. Here, we introduce a computationally efficient method for learning continuous graphical models based on the Interaction Screening approach. Through a series of numerical experiments, we show that our estimator maintains similar requirements in terms of accuracy and sample complexity scalings compared to alternative approaches such as maximization of conditional likelihood, while considerably improving upon the algorithm's run-time.