# Differentiable and Transportable Structure Learning

arXiv: https://arxiv.org/abs/2206.06354 · HTML: https://mlsanity.com/paper/2206.06354/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 94 references that are in the map.
- First posted on arXiv 13 Jun 2022.

## Builds on (most cited first, 27 of 27)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Sim-to-Real Transfer of Robotic Control with Dynamics Randomization](https://mlsanity.com/paper/1710.06537/) (2017)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [DECAF: Generating Fair Synthetic Data Using Causally-Aware Generative Networks](https://mlsanity.com/paper/2110.12884/) (2021)
- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks](https://mlsanity.com/paper/2010.09133/) (2020)
- [Machine Learning Methods Economists Should Know About](https://mlsanity.com/paper/1903.10075/) (2019)
- [Learning Gaussian Networks](https://mlsanity.com/paper/1302.6808/) (2013)
- [Differentiable Causal Discovery Under Unmeasured Confounding](https://mlsanity.com/paper/2010.06978/) (2020)
- [DAGs with No Curl: An Efficient DAG Structure Learning Approach](https://mlsanity.com/paper/2106.07197/) (2021)
- [MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanisms](https://mlsanity.com/paper/2111.03187/) (2021)
- [Unsuitability of NOTEARS for Causal Graph Discovery](https://mlsanity.com/paper/2104.05441/) (2021)
- [Strong Completeness and Faithfulness in Bayesian Networks](https://mlsanity.com/paper/1302.4973/) (2013)
- [CASTLE: Regularization via Auxiliary Causal Graph Discovery](https://mlsanity.com/paper/2009.13180/) (2020)
- [On the Convergence of Continuous Constrained Optimization for Structure Learning](https://mlsanity.com/paper/2011.11150/) (2020)
- [Towards Federated Bayesian Network Structure Learning with Continuous Optimization](https://mlsanity.com/paper/2110.09356/) (2021)
- [On the Logic of Causal Models](https://mlsanity.com/paper/1304.2355/) (2013)
- [Multi-task Learning of Order-Consistent Causal Graphs](https://mlsanity.com/paper/2111.02545/) (2021)
- [Perfect Tree-Like Markovian Distributions](https://mlsanity.com/paper/1301.3834/) (2013)

## Abstract (arXiv)

Directed acyclic graphs (DAGs) encode a lot of information about a particular distribution in their structure. However, compute required to infer these structures is typically super-exponential in the number of variables, as inference requires a sweep of a combinatorially large space of potential structures. That is, until recent advances made it possible to search this space using a differentiable metric, drastically reducing search time. While this technique -- named NOTEARS -- is widely considered a seminal work in DAG-discovery, it concedes an important property in favour of differentiability: transportability. To be transportable, the structures discovered on one dataset must apply to another dataset from the same domain. We introduce D-Struct which recovers transportability in the discovered structures through a novel architecture and loss function while remaining fully differentiable. Because D-Struct remains differentiable, our method can be easily adopted in existing differentiable architectures, as was previously done with NOTEARS. In our experiments, we empirically validate D-Struct with respect to edge accuracy and structural Hamming distance in a variety of settings.