# Projectivity revisited

@inproceedings{Weitkamper2022ProjectivityR, title={Projectivity revisited}, author={Felix Weitkamper}, year={2022} }

The behaviour of statistical relational representations across diﬀerently sized domains has become a focal area of research from both a modelling and a complexity viewpoint. In 2018, Jaeger and Schulte suggested projectivity of a family of distributions as a key property, ensuring that marginal inference is independent of the domain size. However, Jaeger and Schulte assume that the domain is characterised only by its size. This contribution extends the notion of projectivity from families of…

## References

SHOWING 1-10 OF 24 REFERENCES

### A Complete Characterization of Projectivity for Statistical Relational Models

- MathematicsIJCAI
- 2020

A class of directed graphical latent variable models that precisely correspond to the class of projective relational models are introduced that shed new light onto the old open problem of how to apply Halpern et al.'s "random worlds approach" for probabilistic inference to general relational signatures.

### On Projectivity in Markov Logic Networks

- Computer ScienceArXiv
- 2022

This paper characterize the necessary and sufﬁcient conditions for a two-variable MLN to be projective, and isolates a special model in this class of MLNs, namely Relational Block Model (RBM), which is shown to be the best possible projective MLN in the two- variable fragment.

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

- EconomicsArXiv
- 2018

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.

### CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS.

- Computer Science, MathematicsAnnals of statistics
- 2013

It is shown that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM's expressive power.

### Population Size Extrapolation in Relational Probabilistic Modelling

- Computer ScienceSUM
- 2014

The dependence on population is analyzed for relational undirected models in particular Markov logic networks and relational directed models for relational logistic regression and how probabilities for real data sets depend on the population size is shown.

### Markov Logic in Infinite Domains

- Mathematics, Computer ScienceUAI
- 2007

This paper shows that a Markov logic network (MLN) admits a Gibbs measure as long as each ground atom has a finite number of neighbors, and relates the problem of satisfiability in first-order logic to the properties of MLN measures.

### A Statistical Learning Method for Logic Programs with Distribution Semantics

- Computer ScienceICLP
- 1995

The distribution semantics is a straightforward generalization of the traditional least model semantics and can capture semantics of diverse information processing systems ranging from Bayesian networks to Hidden Markov models to Boltzmann machines in a single framework with mathematical rigor.

### Stochastic Planning and Lifted Inference

- Computer ScienceStatistical Relational Artificial Intelligence
- 2010

Stochastic planning should be used as a core problem domain for relational probabilistic models providing problems of interest that are challenging for current approaches and significant scope for extending their capabilities.

### Markov logic networks

- Computer ScienceMachine Learning
- 2006

Experiments with a real-world database and knowledge base in a university domain illustrate the promise of this approach to combining first-order logic and probabilistic graphical models in a single representation.

### Reasoning About Infinite Random Structures with Relational Bayesian Networks

- Computer ScienceKR
- 1998

This paper extends the semantics of relational Bayesian networks, so that they also define probability distributions over countably infinite structures, and shows that probabilistic queries about these distributions are decidable.