# Evaluating structure learning algorithms with a balanced scoring function

arXiv: https://arxiv.org/abs/1905.12666 · HTML: https://mlsanity.com/paper/1905.12666/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2019.

## Built on by (most cited first, 10 of 10)

- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [Assumption violations in causal discovery and the robustness of score matching](https://mlsanity.com/paper/2310.13387/) (2023)
- [Adjustment Identification Distance: A gadjid for Causal Structure Learning](https://mlsanity.com/paper/2402.08616/) (2024)
- [Can Large Language Models Help Experimental Design for Causal Discovery?](https://mlsanity.com/paper/2503.01139/) (2025)
- [Effective and efficient structure learning with pruning and model averaging strategies](https://mlsanity.com/paper/2112.00398/) (2021)
- [Stable Structure Learning with HC-Stable and Tabu-Stable Algorithms](https://mlsanity.com/paper/2504.01740/) (2025)
- [Dynamic Expert-Guided Model Averaging for Causal Discovery](https://mlsanity.com/paper/2601.16715/) (2026)
- [Hybrid Bayesian network discovery with latent variables by scoring multiple interventions](https://mlsanity.com/paper/2112.10574/) (2021)
- [Investigating the validity of structure learning algorithms in identifying risk factors for intervention in patients with diabetes](https://mlsanity.com/paper/2403.14327/) (2024)
- [Time series causal discovery with variable lags](https://mlsanity.com/paper/2605.04081/) (2026)

## Abstract (arXiv)

Several structure learning algorithms have been proposed towards discovering causal or Bayesian Network (BN) graphs. The validity of these algorithms tends to be evaluated by assessing the relationship between the learnt and the ground truth graph. However, there is no agreed scoring metric to determine this relationship. Moreover, this paper shows that some of the commonly used metrics tend to be biased in favour of graphs that minimise edges. While graphs that are less complex are desirable, some of the metrics favour underfitted graphs, thereby encouraging limited propagation of evidence. This paper proposes the Balanced Scoring Function (BSF) that eliminates this bias by adjusting the reward function based on the difficulty of discovering an edge, or no edge, proportional to their occurrence rate in the ground truth graph. The BSF score can be used in conjunction with other traditional metrics to provide an alternative and unbiased assessment about the capability of a structure learning algorithm in discovering causal or BN graphs.