Domain-Liftability of Relational Marginal Polytopes

Complex Markov Logic Networks: Expressivity and Liftability

We study expressivity of Markov logic networks (MLNs). We introduce complex MLNs, which use complex-valued weights, and we show that, unlike standard MLNs with real-valued weights, complex MLNs are fully expressive. We then observe that discrete Fourier transform can be computed using weighted first order model counting (WFOMC) with complex weights and use this observation to design an algorithm for computing relational marginal polytopes which needs substantially less calls to a WFOMC oracle than a recent algorithm.

Characterizing Polarization in Social Networks using the Signed Relational Latent Distance Model

Graph representation learning has become a prominent tool for the characterization and understanding of the structure of networks in general and social networks in particular. Typically, these representation learning approaches embed the networks into a low-dimensional space in which the role of each individual can be characterized in terms of their latent position. A major current concern in social networks is the emergence of polarization and filter bubbles promoting a mindset of "us-versus-them" that may be defined by extreme positions believed to ultimately lead to political violence and t…

The Complexity of Bayesian Networks Specified by Propositional and Relational Languages

We examine the complexity of inference in Bayesian networks specified by logical languages. We consider representations that range from fragments of propositional logic to function-free first-order logic with equality; in doing so we cover a variety of plate models and of probabilistic relational models. We study the complexity of inferences when network, query and domain are the input (the inferential and the combined complexity), when the network is fixed and query and domain are the input (the query/data complexity), and when the network and query are fixed and the domain is the input (the …

Relational Marginal Problems: Theory and Estimation

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 t…

一阶逻辑二变量片段中的精确采样

On Exact Sampling in the Two-Variable Fragment of First-Order Logic

本文证明一阶逻辑二变量片段（FO²）在采样下具有域可提升性，即存在多项式时间采样算法，并扩展至计数约束情形，方法构造性，可应用于组合结构均匀生成及统计关系模型采样。

超越一阶逻辑的提升推理

Lifted Inference beyond First-Order Logic

本研究扩展了C^2逻辑片段的域可提升性，使其能处理有向无环图、连通图、树和森林等现实数据属性，并提出“通过分裂计数”的新方法论，为概率推理和组合结构计数提供通用框架。