# Learning Large Causal Structures from Inverse Covariance Matrix via Sparse Matrix Decomposition

arXiv: https://arxiv.org/abs/2211.14221 · HTML: https://mlsanity.com/paper/2211.14221/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 50 references that are in the map.
- First posted on arXiv 25 Nov 2022.

## Builds on (most cited first, 19 of 19)

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Counterfactual Generative Networks](https://mlsanity.com/paper/2101.06046/) (2021)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery](https://mlsanity.com/paper/2112.02761/) (2021)
- [On Causal Discovery with Equal Variance Assumption](https://mlsanity.com/paper/1807.03419/) (2018)
- [Learning linear structural equation models in polynomial time and sample complexity](https://mlsanity.com/paper/1707.04673/) (2017)
- [Large-Scale Differentiable Causal Discovery of Factor Graphs](https://mlsanity.com/paper/2206.07824/) (2022)
- [Reliable Causal Discovery with Improved Exact Search and Weaker Assumptions](https://mlsanity.com/paper/2201.05666/) (2022)
- [Optimal estimation of Gaussian DAG models](https://mlsanity.com/paper/2201.10548/) (2022)
- [Learning DAGs without imposing acyclicity](https://mlsanity.com/paper/2006.03005/) (2020)
- [A Polynomial-Time Algorithm for Deciding Markov Equivalence of Directed Cyclic Graphical Models](https://mlsanity.com/paper/1302.3600/) (2013)
- [Efficient Permutation Discovery in Causal DAGs](https://mlsanity.com/paper/2011.03610/) (2020)
- [From graphs to DAGs: a low-complexity model and a scalable algorithm](https://mlsanity.com/paper/2204.04644/) (2022)

## Built on by (most cited first, 1 of 1)

- [QWO: Speeding Up Permutation-Based Causal Discovery in LiGAMs](https://mlsanity.com/paper/2410.23155/) (2024)

## Abstract (arXiv)

Learning causal structures from observational data is a fundamental problem facing important computational challenges when the number of variables is large. In the context of linear structural equation models (SEMs), this paper focuses on learning causal structures from the inverse covariance matrix. The proposed method, called ICID for Independence-preserving Decomposition from Inverse Covariance matrix, is based on continuous optimization of a matrix decomposition model that preserves the nonzero patterns of the inverse covariance matrix. Through theoretical and empirical evidences, we show that ICID efficiently identifies the sought directed acyclic graph (DAG) assuming the knowledge of noise variances. Moreover, ICID is shown empirically to be robust under bounded misspecification of noise variances in the case where the noise variances are non-equal. The proposed method enjoys a low complexity, as reflected by its time efficiency in the experiments, and also enables a novel regularization scheme that yields highly accurate solutions on the Simulated fMRI data (Smith et al., 2011) in comparison with state-of-the-art algorithms.