Related papers: On Projectivity in Markov Logic Networks

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…

Combining logic and probability has been a long stand- ing goal of AI research. Markov Logic Networks (MLNs) achieve this by attaching weights to formulas in first-order logic, and can be seen as templates for constructing features for…

Markov networks are popular models for discrete multivariate systems where the dependence structure of the variables is specified by an undirected graph. To allow for more expressive dependence structures, several generalizations of Markov…

A Markov logic network (MLN) $\mathbb{M}$ determines a probability distribution $\mathbb{P}_n^\mathbb{M}$ on the set $\mathbf{W}_n$ of structures, or ``possible worlds'', with domain $\{1, \ldots, n\}$. We study the properties of such…

We introduce neural Markov logic networks (NMLNs), a statistical relational learning system that borrows ideas from Markov logic. Like Markov logic networks (MLNs), NMLNs are an exponential-family model for modelling distributions over…

A generative probabilistic model for relational data consists of a family of probability distributions for relational structures over domains of different sizes. In most existing statistical relational learning (SRL) frameworks, these…

Undirected graphical models known as Markov networks are popular for a wide variety of applications ranging from statistical physics to computational biology. Traditionally, learning of the network structure has been done under the…

Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is…

Knowledge graph reasoning, which aims at predicting the missing facts through reasoning with the observed facts, is critical to many applications. Such a problem has been widely explored by traditional logic rule-based approaches and recent…

LPMLN is a probabilistic extension of answer set programs with the weight scheme derived from that of Markov Logic. Previous work has shown how inference in LPMLN can be achieved. In this paper, we present the concept of weight learning in…

Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first…

Graphical models are a rich language for describing high-dimensional distributions in terms of their dependence structure. While there are algorithms with provable guarantees for learning undirected graphical models in a variety of…

Markov Logic Networks (MLNs) are well-suited for expressing statistics such as "with high probability a smoker knows another smoker" but not for expressing statements such as "there is a smoker who knows most other smokers", which is…

A pseudo independent (PI) model is a probabilistic domain model (PDM) where proper subsets of a set of collectively dependent variables display marginal independence. PI models cannot be learned correctly by many algorithms that rely on a…

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…

Learning the structure of Markov random fields (MRFs) plays an important role in multivariate analysis. The importance has been increasing with the recent rise of statistical relational models since the MRF serves as a building block of…

We consider deep multivariate models for heterogeneous collections of random variables. In the context of computer vision, such collections may e.g. consist of images, segmentations, image attributes, and latent variables. When developing…

Markov Logic Networks (MLNs), which elegantly combine logic rules and probabilistic graphical models, can be used to address many knowledge graph problems. However, inference in MLN is computationally intensive, making the industrial-scale…

We consider Markov logic networks and relational logistic regression as two fundamental representation formalisms in statistical relational artificial intelligence that use weighted formulas in their specification. However, Markov logic…

What can large language models learn? By definition, language models (LM) are distributions over strings. Therefore, an intuitive way of addressing the above question is to formalize it as a matter of learnability of classes of…