In this paper, our aim is to briefly survey and articulate the logical and philosophical foundations of using (first-order) logic to represent (probabilistic) knowledge in a non-technical fashion. Our motivation is three fold. First, for machine learning researchers unaware of why the research community cares about relational representations, this article can serve as a gentle introduction. Second, for logical experts who are newcomers to the learning area, such an article can help in navigating the differences between finite vs infinite, and subjective probabilities vs random-world semantics. Finally, for researchers from statistical relational learning and neuro-symbolic AI, who are usually embedded in finite worlds with subjective probabilities, appreciating what infinite domains and random-world semantics brings to the table is of utmost theoretical import.

Continuous Markov random fields are a general formalism to model joint probability distributions over events with continuous outcomes. We prove that marginal computation for constrained continuous MRFs is #P-hard in general and present a polynomial-time approximation scheme under mild assumptions on the structure of the random field. Moreover, we introduce a sampling algorithm to compute marginal distributions and develop novel techniques to increase its efficiency. Continuous MRFs are a general purpose probabilistic modeling tool and we demonstrate how they can be applied to statistical relational learning. On the problem of collective classification, we evaluate our algorithm and show that the standard deviation of marginals serves as a useful measure of confidence.

Continuous Markov random fields are a general formalism to model joint probability distributions over events with continuous outcomes. We prove that marginal computation for constrained continuous MRFs is #P-hard in general and present a polynomial-time approximation scheme under mild assumptions on the structure of the random field. Moreover, we introduce a sampling algorithm to compute marginal distributions and develop novel techniques to increase its efficiency. Continuous MRFs are a general purpose probabilistic modeling tool and we demonstrate how they can be applied to statistical relational learning. On the problem of collective classification, we evaluate our algorithm and show that the standard deviation of marginals serves as a useful measure of confidence.

Here is an excellent ILP reference, somewhat older but publicly available. The most recent issue of SIGKDD Explorations is a special issue devoted to multi-relational data mining.

Nowadays web users actively generate content on different social media platforms. The large number of users requiring personalized services creates a unique opportunity for researchers to explore user modelling. Substantial research has been done by utilizing user generated content to model users by applying different classification or regression techniques. These techniques are powerful types of machine learning approaches, however they only partially model social media users. In this work, we introduce a new statistical relational learning (SRL) framework suitable for this purpose, which we call PSL Q . PSL Q is the first SRL framework that supports reasoning with soft quantifiers, such as “most” and “a few”. Indeed, in models for social media it is common to assume that friends are influenced by each other’s behavior, beliefs, and preferences. Thus, having a trait only becomes probable once most or some of one’s friends have that trait. Expressing this dependency requires a soft quantifier, which can be modeled with PSL^Q. Our experimental results for link prediction in social trust networks demonstrate that the use of soft quantifiers not only allows for a natural and intuitive formulation of domain knowledge, but also improves the accuracy of inferred results.

Electronic health records (EHRs) are an emerging relational domain with large potential to improve clinical outcomes. We apply two statistical relational learning (SRL) algorithms to the task of predicting primary myocardial infarction. We show that one SRL algorithm, relational functional gradient boosting, outperforms propositional learners particularly in the medically-relevant high recall region. We observe that both SRL algorithms predict outcomes better than their propositional analogs and suggest how our methods can augment current epidemiological practices.