# Greedy structure learning from data that contain systematic missing values

arXiv: https://arxiv.org/abs/2107.04184 · HTML: https://mlsanity.com/paper/2107.04184/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 37 references that are in the map.
- First posted on arXiv 9 Jul 2021.

## Builds on (most cited first, 8 of 8)

- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Graphical Models for Processing Missing Data](https://mlsanity.com/paper/1801.03583/) (2018)
- [Causal Discovery in the Presence of Missing Data](https://mlsanity.com/paper/1807.04010/) (2018)
- [Large-scale empirical validation of Bayesian Network structure learning algorithms with noisy data](https://mlsanity.com/paper/2005.09020/) (2020)
- [Fast Causal Inference with Non-Random Missingness by Test-Wise Deletion](https://mlsanity.com/paper/1705.09031/) (2017)
- [Anomaly Detection in the Presence of Missing Values](https://mlsanity.com/paper/1809.01605/) (2018)
- [Hard and Soft EM in Bayesian Network Learning from Incomplete Data](https://mlsanity.com/paper/2012.05269/) (2020)
- [Learning Bayesian Networks from Incomplete Data with the Node-Average Likelihood](https://mlsanity.com/paper/2004.14441/) (2020)

## Built on by (most cited first, 13 of 13)

- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [bnRep: A repository of Bayesian networks from the academic literature](https://mlsanity.com/paper/2409.19158/) (2024)
- [Open problems in causal structure learning: A case study of COVID-19 in the UK](https://mlsanity.com/paper/2305.03859/) (2023)
- [Identification of Causal Structure in the Presence of Missing Data with Additive Noise Model](https://mlsanity.com/paper/2312.12206/) (2023)
- [The Impact of Missing Data on Causal Discovery: A Multicentric Clinical Study](https://mlsanity.com/paper/2305.10050/) (2023)
- [Causal Discovery on Higher-Order Interactions](https://mlsanity.com/paper/2511.14206/) (2025)
- [Dynamic Expert-Guided Model Averaging for Causal Discovery](https://mlsanity.com/paper/2601.16715/) (2026)
- [Data Imputation by Pursuing Better Classification: A Supervised Kernel-Based Method](https://mlsanity.com/paper/2405.07800/) (2024)
- [Recursive Equations For Imputation Of Missing Not At Random Data With Sparse Pattern Support](https://mlsanity.com/paper/2507.16107/) (2025)
- [KG-SoftMAP: Soft Knowledge-Graph Priors for Bayesian Network Structure Learning from Sparse Discrete Data](https://mlsanity.com/paper/2606.10358/) (2026)
- [Towards a Transportable Causal Network Model Based on Observational Healthcare Data](https://mlsanity.com/paper/2311.08427/) (2023)
- [LUME-DBN: Full Bayesian Learning of DBNs from Incomplete data in Intensive Care](https://mlsanity.com/paper/2511.04333/) (2025)
- [Integrated Imputation-Classification for Supervised Learning with Missing Data](https://mlsanity.com/paper/2610.04273/) (2026)

## Abstract (arXiv)

Learning from data that contain missing values represents a common phenomenon in many domains. Relatively few Bayesian Network structure learning algorithms account for missing data, and those that do tend to rely on standard approaches that assume missing data are missing at random, such as the Expectation-Maximisation algorithm. Because missing data are often systematic, there is a need for more pragmatic methods that can effectively deal with data sets containing missing values not missing at random. The absence of approaches that deal with systematic missing data impedes the application of BN structure learning methods to real-world problems where missingness are not random. This paper describes three variants of greedy search structure learning that utilise pairwise deletion and inverse probability weighting to maximally leverage the observed data and to limit potential bias caused by missing values. The first two of the variants can be viewed as sub-versions of the third and best performing variant, but are important in their own in illustrating the successive improvements in learning accuracy. The empirical investigations show that the proposed approach outperforms the commonly used and state-of-the-art Structural EM algorithm, both in terms of learning accuracy and efficiency, as well as both when data are missing at random and not at random.