# Relational Marginal Problems: Theory and Estimation

arXiv: https://arxiv.org/abs/1709.05825 · HTML: https://mlsanity.com/paper/1709.05825/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2017.

## Built on by (most cited first, 5 of 5)

- [Micro and Macro Level Graph Modeling for Graph Variational Auto-Encoders](https://mlsanity.com/paper/2210.16844/) (2022)
- [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)
- [Polynomial-Time Relational Probabilistic Inference in Open Universes](https://mlsanity.com/paper/2505.04115/) (2025)
- [Understanding Domain-Size Generalization in Markov Logic Networks](https://mlsanity.com/paper/2403.15933/) (2024)

## Abstract (arXiv)

In the propositional setting, the marginal problem is to find a (maximum-entropy) distribution that has some given marginals. We study this problem in a relational setting and make the following contributions. First, we compare two different notions of relational marginals. Second, we show a duality between the resulting relational marginal problems and the maximum likelihood estimation of the parameters of relational models, which generalizes a well-known duality from the propositional setting. Third, by exploiting the relational marginal formulation, we present a statistically sound method to learn the parameters of relational models that will be applied in settings where the number of constants differs between the training and test data. Furthermore, based on a relational generalization of marginal polytopes, we characterize cases where the standard estimators based on feature's number of true groundings needs to be adjusted and we quantitatively characterize the consequences of these adjustments. Fourth, we prove bounds on expected errors of the estimated parameters, which allows us to lower-bound, among other things, the effective sample size of relational training data.