Nils Dycke, Matej Zečević, Ilia Kuznetsov, Beatrix Suess, Kristian Kersting, Iryna Gurevych. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2025.

Structure learning is a crucial task in science, especially in fields such as medicine and biology, where the wrong identification of (in)dependencies among random variables can have significant implications. The primary objective of structure learning is to learn a Directed Acyclic Graph (DAG) that represents the underlying probability distribution of the data. Many prominent DAG learners rely on least square losses or log-likelihood losses for optimization. It is well-known from regression models that least square losses are heavily influenced by the scale of the variables. Recently it has been demonstrated that the scale of data also affects performance of structure learning algorithms, though with a strong focus on linear 2-node systems and simulated data. Moving beyond these results, we provide conditions under which square-based losses are minimal for wrong DAGs in $d$-dimensional cases. Furthermore, we also show that scale can impair performance of structure learners if relations among variables are non-linear for both square based and log-likelihood based losses. We confirm our theoretical findings through extensive experiments on synthetic and real-world data.

Causal inference in hybrid domains, characterized by a mixture of discrete and continuous variables, presents a formidable challenge. We take a step towards this direction and propose Characteristic Interventional Sum-Product Network ($\chi$SPN) that is capable of estimating interventional distributions in presence of random variables drawn from mixed distributions. $\chi$SPN uses characteristic functions in the leaves of an interventional SPN (iSPN) thereby providing a unified view for discrete and continuous random variables through the Fourier{–}Stieltjes transform of the probability measures. A neural network is used to estimate the parameters of the learned iSPN using the intervened data. Our experiments on 3 synthetic heterogeneous datasets suggest that $\chi$SPN can effectively capture the interventional distributions for both discrete and continuous variables while being expressive and causally adequate. We also show that $\chi$SPN generalize to multiple interventions while being trained only on a single intervention data.

Abstract The recent years have been marked by extended research on adversarial attacks, especially on deep neural networks. With this work we intend on posing and investigating the question of whether the phenomenon might be more general in nature, that is, adversarial-style attacks outside classical classification tasks. Specifically, we investigate optimization problems as they constitute a fundamental part of modern AI research. To this end, we consider the base class of optimizers namely Linear Programs (LPs). On our initial attempt of a naïve mapping between the formalism of adversarial examples and LPs, we quickly identify the key ingredients missing for making sense of a reasonable notion of adversarial examples for LPs. Intriguingly, the formalism of Pearl’s notion to causality allows for the right description of adversarial like examples for LPs. Characteristically, we show the direct influence of the Structural Causal Model (SCM) onto the subsequent LP optimization, which ultimately exposes a notion of confounding in LPs (inherited by said SCM) that allows for adversarial-style attacks. We provide both the general proof formally alongside existential proofs of such intriguing LP-parameterizations based on SCM for three combinatorial problems, namely Linear Assignment, Shortest Path and a real world problem of energy systems.

Structural causal models (SCMs) are a powerful tool for understanding the complex causal relationships that underlie many real-world systems. As these systems grow in size, the number of variables and complexity of interactions between them does, too. Thus, becoming convoluted and difficult to analyze. This is particularly true in the context of machine learning and artificial intelligence, where an ever increasing amount of data demands for new methods to simplify and compress large scale SCM. While methods for marginalizing and abstracting SCM already exist today, they may destroy the causality of the marginalized model. To alleviate this, we introduce the concept of consolidating causal mechanisms to transform large-scale SCM while preserving consistent interventional behaviour. We show consolidation is a powerful method for simplifying SCM, discuss reduction of computational complexity and give a perspective on generalizing abilities of consolidated SCM.

While probabilistic models are an important tool for studying causality, doing so suffers from the intractability of inference. As a step towards tractable causal models, we consider the problem of learning interventional distributions using sum-product networks (SPNs) that are over-parameterized by gate functions, e.g., neural networks. Providing an arbitrarily intervened causal graph as input, effectively subsuming Pearl's do-operator, the gate function predicts the parameters of the SPN. The resulting interventional SPNs are motivated and illustrated by a structural causal model themed around personal health. Our empirical evaluation against competing methods from both generative and causal modelling demonstrates that interventional SPNs indeed are both expressive and causally adequate.