Research

Here is an overview of my academic work. I have started my career as a pure mathematician working on operator algebras, representation theory, and probability theory. In recent years, my work has focused on causal inference and machine learning.

Research in Causal Inference

Publications

• Y. Aalaila, G. Großmann, S. Mukherjee, J. Wahl, and S. Vollmer, Chaotic and complex dynamics expose the limits of counterfactual reasoning. Scientific Reports 16 (1), 16978, 2026.
  
  
• N.-D. Reiter, J. Wahl, A. Gerhardus, and J. Runge, Causal Inference on Process Graphs: Causal Structure and Effect Identification. Bernoulli 32 (2), 1356-1382, 2026.
  
  
• C. Lohse and J. Wahl, Sortability of Time Series Data. Transactions on Machine Learning Research (TMLR), 2835-8856, 2025.
  
  
• P. Brouillard, C. Squires, J. Wahl, K. P. Kording, K. Sachs, A. Drouin, and D. Sridhar, The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications. Proceedings of the Fourth Conference on Causal Learning and Reasoning, PMLR 275:834-873, 2025.
  
  
• R. Herman, J. Wahl, U. Ninad, and J. Runge, Unitless Unrestricted Markov-Consistent SCM Generation: Better Benchmark Datasets for Causal Discovery. Proceedings of the Fourth Conference on Causal Learning and Reasoning, PMLR 275:1506-1531, 2025.
  
  
• J. Wahl and J. Runge, Separation-based distance measures for causal graphs. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:3412-3420, 2025.
  
  
• J. Wahl, U. Ninad, and J. Runge, Foundations of Causal Discovery on Groups of Variables, Journal of Causal Inference, 12 (1), p. 20230041, 2024.
  
  
• S. Bing, T. Hochsprung, J. Wahl, U. Ninad, and J. Runge, Invariance & Causal Representation Learning: Prospects and Limitations, Transactions on Machine Learning Research (TMLR), 2835-8856, 2024.
  
  
  
• S. Bing, U. Ninad*, J. Wahl*, and J. Runge, Identifying Linearly-Mixed Causal Representations from Multi-Node Interventions, Proceedings of the Third Conference on Causal Learning and Reasoning (CLeaR), PMLR 236:843-867, 2024. (*equal contribution)
  
  
• T. Hochsprung, J. Wahl*, A. Gerhardus*, U. Ninad*, and J. Runge, Increasing Effect Sizes of Pairwise Conditional Independence Tests between Random Vectors. Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, PMLR 216:879-889, 2023. (*equal contribution)
  
  
• J. Wahl*, U. Ninad*, and J. Runge, Vector causal inference between two groups of variables.  Proceedings of the AAAI Conference on Artificial Intelligence, 37(10), 12305-12312, 2023. (*equal contribution) 
  
  
• W. Günther, U. Ninad*, J. Wahl*, and J. Runge, Conditional Independence Testing with Heteroskedastic Data and Applications to Causal Discovery, Advances in Neural Information Processing Systems (NeurIPS) 35, 2022. (*equal contribution)
  

Accepted for publication

• S. Faltenbacher*, J. Wahl*, R. Herman, and J. Runge, How PC-based Methods Err: Towards Better Reporting of Assumption Violations and Small Sample Errors. Preprint: arXiv:2502.14719. Accepted for publication at Uncertainty in Artificial Intelligence (UAI) 2026 (*equal contribution).
  

Preprints

• C. Lohse, A. Dhir, A. Ba, B. Eck, M. Ruffini, and J. Wahl, PRIM: Meta-Learned Bayesian Root Cause Analysis. Preprint: arXiv:2605.08786, 2026.
  
  
• U. Ninad, J. Wahl*, A. Gerhardus*, and J. Runge, Causal discovery on vector-valued variables and consistency-guided aggregation. Preprint: arXiv:2505.10476, 2025. (*equal contribution)
  
  
• N.-D. Reiter, J. Wahl, G. C. Hegerl, and J. Runge, Asymptotic Uncertainty in the Estimation of Frequency Domain Causal Effects for Linear Processes. Preprint: arXiv:2406.18191, 2024.
  
  
• A. Gerhardus, J. Wahl, S. Faltenbacher, U. Ninad, and J. Runge, Projecting infinite time series graphs to finite marginal graphs using number theory. Preprint: arXiv:2310.05526, 2023.
  
  
• N.-D. Reiter, A. Gerhardus, J. Wahl, and J. Runge, Causal Inference on Process Graphs: The Structural Equation Process Representation. Preprint: arXiv:2305.11561, 2023.
  

Workshop contributions and other scientific writings

•  G. Grossmann, Y. Aalaila, D. A. Selby, S. Mukherjee, S. Vollmer, and J. Wahl, Rethinking Counterfactuals: Hidden Assumptions and Practical Pitfalls. Oral contribution to the 7th Workshop on Formal Reasoning about Causation, Responsibility, and Explanations in Science and Technology (CREST), 2026.
  
  
• C. Lohse, A. Selk, A. Ba, J. Wahl, M. Ruffini, Licence to Scale: A Microservice Simulation Environment for Benchmarking Agentic AI. Peer-reviewed contribution to NeurIPS (2025) Workshop on Scaling Environments for Agents (SEA).
  
  
• P. Brouillard, C. Squires, J. Wahl, K. P. Kording, K. Sachs, A. Drouin, and D. Sridhar, The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications. Peer-reviewed contribution to The Future of Machine Learning Data Practices and Repositories at ICLR 2025 (Spotlight).
  
  
• C. Lohse and J. Wahl, Sortability of Time Series Data. Peer-reviewed contribution to the Workshop Causal Inference for Time Series (CI4TS) at UAI 2024 (poster).
  
  
• M. Prasow-Émond, Y. Plancherel, P.J. Mason, M.D. Piggott, and J. Wahl, Impacts of Climate Change on Small Island Nations: A Data Science Framework using Remote Sensing and Observational Time Series, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-18919, 2024.
  
  
• S. Bing, J. Wahl*, U. Ninad*, and J. Runge, Invariance & Causal Representation Learning: Prospects and Limitations. Peer-reviewed contribution to NeurIPS 2023 Workshop on Causal Representation Learning.
  
  
• M. Langer, K. Baum, K. Hartmann, S. Hessel, T. Speith, and J. Wahl, Explainability auditing for intelligent systems: a rationale for multi-disciplinary perspectives. 2021 IEEE 29th International Requirements Engineering Conference Workshops (REW) (2021), 164-168.
  
  
• J. Wahl, Where are all the guns? Modeling firearm ownership in the United States. Patterns 3 (2022), no. 8, 100571.
  This is a review article on a paper using causal inference techniques to model firearm ownership.
  

Research in Pure Mathematics

Publications

• J. Wahl, Traces on Diagram Algebras II: Centralizer algebras of easy groups and new variations of the Young graph. Algebraic Combinatorics 5 (2022), no. 3, 413-436.
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• J. Wahl, Traces On Diagram Algebras I: Free Partition Quantum Groups, Random Lattice Paths And Random Walks On Trees. Journal of the London Mathematical Society 105 (2022), no. 4, 2324-2372.
  
  
• S. Vaes and J. Wahl, Bernoulli actions of type III_1 and L^2-cohomology, Geom. and Func. Anal. (GAFA) 28 (2018), 518–562.
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• Y. Arano, T. de Laat, and J. Wahl, The Fourier algebra of a rigid C*-tensor category, Publ. Res. Inst. Math. Sci. 54 (2018), no. 2, 393–410.​
  
  
• P. Tarrago and J. Wahl, Free wreath product quantum groups and standard invariants of subfactors, Advances in Mathematics 331 (2018), 1–57.
  
  
• Y. Arano, T. de Laat, and J. Wahl, Howe-Moore type theorems for quantum groups and C*-tensor categories, Compos. Math. 154 (2018), no. 2, 328–341.
  
  
• J. Wahl, A note on reduced and von Neumann algebraic free wreath products, Illinois J. Math. 59 (2015) no. 3, 801–817.

Under submission

• J. Wahl, The cut-off profile of a random walk on the irreducible representations of the symmetric group, 2026.
  
  
• M. A. Hahn, B. O’Callaghan, J. Wahl, Tropicalising hypergeometric tau-functions, Preprint: arXiv:2511.00463, 2025.
  

PhD thesis

• Nonsingular Bernoulli actions and quantum symmetries. Arenberg Doctoral School, KU Leuven, 2018.