# Inference, Learning, and Population Size: Projectivity for SRL Models

arXiv: https://arxiv.org/abs/1807.00564 · HTML: https://mlsanity.com/paper/1807.00564/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2018.

## Built on by (most cited first, 7 of 7)

- [An asymptotic analysis of probabilistic logic programming, with implications for expressing projective families of distributions](https://mlsanity.com/paper/2102.08777/) (2021)
- [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)
- [Projectivity revisited](https://mlsanity.com/paper/2207.00625/) (2022)
- [The generalised distribution semantics and projective families of distributions](https://mlsanity.com/paper/2211.06751/) (2022)
- [Understanding Domain-Size Generalization in Markov Logic Networks](https://mlsanity.com/paper/2403.15933/) (2024)

## Abstract (arXiv)

A subtle difference between propositional and relational data is that in many relational models, marginal probabilities depend on the population or domain size. This paper connects the dependence on population size to the classic notion of projectivity from statistical theory: Projectivity implies that relational predictions are robust with respect to changes in domain size. We discuss projectivity for a number of common SRL systems, and identify syntactic fragments that are guaranteed to yield projective models. The syntactic conditions are restrictive, which suggests that projectivity is difficult to achieve in SRL, and care must be taken when working with different domain sizes.