# Understanding Domain-Size Generalization in Markov Logic Networks

arXiv: https://arxiv.org/abs/2403.15933 · HTML: https://mlsanity.com/paper/2403.15933/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 31 references that are in the map.
- First posted on arXiv 23 Mar 2024.

## Builds on (most cited first, 9 of 9)

- [An asymptotic analysis of probabilistic logic programming, with implications for expressing projective families of distributions](https://mlsanity.com/paper/2102.08777/) (2021)
- [Inference, Learning, and Population Size: Projectivity for SRL Models](https://mlsanity.com/paper/1807.00564/) (2018)
- [A Complete Characterization of Projectivity for Statistical Relational Models](https://mlsanity.com/paper/2004.10984/) (2020)
- [Relational Marginal Problems: Theory and Estimation](https://mlsanity.com/paper/1709.05825/) (2017)
- [On Projectivity in Markov Logic Networks](https://mlsanity.com/paper/2204.04009/) (2022)
- [Scaling the weight parameters in Markov logic networks and relational logistic regression models](https://mlsanity.com/paper/2103.15140/) (2021)
- [Probabilities of the Third Type: Statistical Relational Learning and Reasoning with Relative Frequencies](https://mlsanity.com/paper/2202.10367/) (2022)
- [Exponential-Family Models of Random Graphs: Inference in Finite-, Super-, and Infinite Population Scenarios](https://mlsanity.com/paper/1707.04800/) (2017)
- [Projectivity revisited](https://mlsanity.com/paper/2207.00625/) (2022)

## Abstract (arXiv)

We study the generalization behavior of Markov Logic Networks (MLNs) across relational structures of different sizes. Multiple works have noticed that MLNs learned on a given domain generalize poorly across domains of different sizes. This behavior emerges from a lack of internal consistency within an MLN when used across different domain sizes. In this paper, we quantify this inconsistency and bound it in terms of the variance of the MLN parameters. The parameter variance also bounds the KL divergence between an MLN's marginal distributions taken from different domain sizes. We use these bounds to show that maximizing the data log-likelihood while simultaneously minimizing the parameter variance corresponds to two natural notions of generalization across domain sizes. Our theoretical results apply to Exponential Random Graphs and other Markov network based relational models. Finally, we observe that solutions known to decrease the variance of the MLN parameters, like regularization and Domain-Size Aware MLNs, increase the internal consistency of the MLNs. We empirically verify our results on four different datasets, with different methods to control parameter variance, showing that controlling parameter variance leads to better generalization.