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Moritz Willig

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6 papers

2 author rows

TMLR Journal 2025 Journal Article

Structural Causal Circuits: Probabilistic Circuits Climbing All Rungs of Pearl's Ladder of Causation

Florian Peter Busch
Moritz Willig
Matej Zečević
Kristian Kersting
Devendra Singh Dhami

The complexity and vastness of our world can require large models with numerous variables. Unfortunately, coming up with a model that is both accurate and able to provide predictions in a reasonable amount of time can prove difficult. One possibility to help overcome such problems is sum-product networks (SPNs), probabilistic models with the ability to tractably perform inference in linear time. In this paper, we extend SPNs' capabilities to the field of causality and introduce the family of structural causal circuits (SCCs), a type of SPNs capable of answering causal questions. Starting from conventional SPNs, we ``climb the ladder of causation'' and show how SCCs can represent not only observational but also interventional and counterfactual problems. We demonstrate successful application in different settings, ranging from simple binary variables to physics-based simulations.

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ICLR Conference 2025 Conference Paper

Systems with Switching Causal Relations: A Meta-Causal Perspective

Moritz Willig
Tim Nelson Tobiasch
Florian Peter Busch
Jonas Seng
Devendra Singh Dhami
Kristian Kersting

Most work on causality in machine learning assumes that causal relationships are driven by a constant underlying process. However, the flexibility of agents' actions or tipping points in the environmental process can change the qualitative dynamics of the system. As a result, new causal relationships may emerge, while existing ones change or disappear, resulting in an altered causal graph. To analyze these qualitative changes on the causal graph, we propose the concept of meta-causal states, which groups classical causal models into clusters based on equivalent qualitative behavior and consolidates specific mechanism parameterizations. We demonstrate how meta-causal states can be inferred from observed agent behavior, and discuss potential methods for disentangling these states from unlabeled data. Finally, we direct our analysis towards the application of a dynamical system, showing that meta-causal states can also emerge from inherent system dynamics, and thus constitute more than a context-dependent framework in which mechanisms emerge only as a result of external factors.

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NeurIPS Conference 2025 Conference Paper

When Causal Dynamics Matter: Adapting Causal Strategies through Meta-Aware Interventions

Moritz Willig
Tim Woydt
Devendra Singh Dhami
Kristian Kersting

Many causal inference frameworks rely on a staticity assumption, where repeated interventions are expected to yield consistent outcomes, often summarized by metrics like the Average Treatment Effect (ATE). This assumption, however, frequently fails in dynamic environments where interventions can alter the system's underlying causal structure, rendering traditional `static' ATE insufficient or misleading. Recent works on meta-causal models (MCM) offer a promising avenue by enabling qualitative reasoning over evolving relationships. In this work, we propose a specific class of MCM with desirable properties for explicitly modeling and predicting intervention outcomes under meta-causal dynamics, together with a first method for meta-causal analysis. Through expository examples in high-impact domains of medical treatment and judicial decision-making, we highlight the severe consequences that arise when system dynamics are neglected and demonstrate the successful application of meta-causal strategies to navigate these challenges.

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UAI Conference 2024 Conference Paper

χSPN: Characteristic Interventional Sum-Product Networks for Causal Inference in Hybrid Domains

Harsh Poonia
Moritz Willig
Zhongjie Yu 0001
Matej Zecevic
Kristian Kersting
Devendra Singh Dhami

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 Ch aracteristic I nterventional 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.

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TMLR Journal 2023 Journal Article

Causal Parrots: Large Language Models May Talk Causality But Are Not Causal

Matej Zečević
Moritz Willig
Devendra Singh Dhami
Kristian Kersting

Some argue scale is all what is needed to achieve AI, covering even causal models. We make it clear that large language models (LLMs) cannot be causal and give reason onto why sometimes we might feel otherwise. To this end, we define and exemplify a new subgroup of Structural Causal Model (SCM) that we call meta SCM which encode causal facts about other SCM within their variables. We conjecture that in the cases where LLM succeed in doing causal inference, underlying was a respective meta SCM that exposed correlations between causal facts in natural language on whose data the LLM was ultimately trained. If our hypothesis holds true, then this would imply that LLMs are like parrots in that they simply recite the causal knowledge embedded in the data. Our empirical analysis provides favoring evidence that current LLMs are even weak `causal parrots.'

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NeurIPS Conference 2023 Conference Paper

Do Not Marginalize Mechanisms, Rather Consolidate!

Moritz Willig
Matej Zečević
Devendra Dhami
Kristian Kersting

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.

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