publications
Research papers and preprints by Felix Schur on causal inference, reinforcement learning, bandit algorithms, time series, and statistical machine learning.
2026
- Who Caused Y? Learning Causal Parents Using Independent Risk MinimizationFelix Schur, Sorawit Saengkyongam, and Jonas PetersIn Advances in Neural Information Processing Systems (NeurIPS), 2026
We study identifiability and estimation of the direct causes, that is, the parents, of a designated target Y in a structural causal model using only observational data. Our main assumption is an additive-noise model for Y: the value of Y equals some function of its parents plus noise that is independent of those parents. We allow for general functional relationships and hidden confounding among all other variables. We prove that under a "no-backward" additive-noise condition the true parent set, PA(Y), is identified from the observational distribution by a simple population principle: among all candidate variable sets that make the regression residual of Y independent of the regressors, choose the one with the smallest residual variance, and—if several tie—the smallest set. To justify the "no-backward" condition, we propose a novel identifiability scheme based on identifiability witnesses: we prove that in finite-dimensional analytic model classes, for which we have an identifiability witness (that is, a single identifiable model), residual independence for sets containing descendants of Y holds only on Lebesgue-null exceptional parameter sets. This scheme is strong enough to recover known identifiability results. For finite data, we propose Independent Risk Minimization (IndRM), which offers a simple, local, and non-interventional route to isolating the direct causes of Y in multivariate systems, avoiding global model assumptions and full-graph search.
@inproceedings{schur2026whocausedy, title = {Who Caused {Y}? Learning Causal Parents Using Independent Risk Minimization}, author = {Schur, Felix and Saengkyongam, Sorawit and Peters, Jonas}, booktitle = {Advances in Neural Information Processing Systems (NeurIPS)}, year = {2026}, url = {https://openreview.net/forum?id=kvVc2NQe9H}, } - Many Experiments, Few Repetitions, Unpaired Data, and Sparse Effects: Is Causal Inference Possible?Felix Schur, Niklas Pfister, Peng Ding, and 2 more authorsIn Proceedings of the 43rd International Conference on Machine Learning (ICML), 2026
In many applications, practical constraints prevent measuring covariates and outcomes on the same units, resulting in unpaired data. We study the problem of estimating causal effects under hidden confounding in the following unpaired data setting: we observe some covariates X and an outcome Y under different experimental conditions (environments) but do not observe them jointly—we either observe X or Y. Under appropriate regularity conditions, the problem can be cast as an instrumental variable (IV) regression with the environment acting as a (possibly high-dimensional) instrument. When there are many environments but only a few observations per environment, standard two-sample IV estimators fail to be consistent. We propose a GMM-type estimator based on cross-fold sample splitting of the instrument–covariate sample that also applies in standard IV settings. We prove that it is consistent as the number of environments grows but the sample size per environment remains constant. We further extend the method to sparse causal effects via L1-regularized estimation and post-selection refitting.
@inproceedings{schur2026manyexperiments, title = {Many Experiments, Few Repetitions, Unpaired Data, and Sparse Effects: Is Causal Inference Possible?}, author = {Schur, Felix and Pfister, Niklas and Ding, Peng and Mukherjee, Sach and Peters, Jonas}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning (ICML)}, volume = {306}, series = {Proceedings of Machine Learning Research}, pages = {108536--108572}, publisher = {PMLR}, year = {2026}, archiveprefix = {arXiv}, primaryclass = {stat.ML}, url = {https://proceedings.mlr.press/v306/schur26a.html}, } - The Price of Knowledge: Optimal Algorithms for Costly BanditsFelix Schur, Jesus Lago, and Tanner FiezIn Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence (UAI), 2026
We study stochastic bandits in which observing a reward is optional but incurs an action-dependent cost. This setting captures applications where feedback acquisition (e.g., human evaluation or randomized testing) is expensive, and the learner must trade off exploration, exploitation, and observation cost. We formulate regret to include both reward loss and the cumulative cost of requested observations. Our first result is structural: for minimizing regret, it is without loss of generality to consider two-phase policies that first request observations during an exploration phase and then commit to a single action without further observations. Building on this reduction, we introduce two cost-sensitive complexity measures that extend maximum information gain: a cost-adjusted information gain for minimax analysis, and a cost- and gap-adjusted information gain for instance-dependent analysis. Using these quantities, we develop two Gaussian-process-based algorithms, C3-GP and GP-C-LUCB, and derive regret upper bounds for correlated-action settings with heterogeneous (i.e., action-dependent) observation costs. In the finite independent-action setting, we further prove matching lower and upper bounds (up to constants/logarithmic factors), yielding a tight characterization of both minimax and instance-dependent regret in terms of the proposed cost-aware complexity measures.
@inproceedings{schur2026priceofknowledge, title = {The Price of Knowledge: Optimal Algorithms for Costly Bandits}, author = {Schur, Felix and Lago, Jesus and Fiez, Tanner}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence (UAI)}, volume = {337}, series = {Proceedings of Machine Learning Research}, pages = {6064--6090}, publisher = {PMLR}, year = {2026}, url = {https://proceedings.mlr.press/v337/schur26a.html}, } - Action-Free Offline RL via Demonstrator DiversityFelix SchurIn ICML Workshop on Demos (DEMO), 2026
A central bottleneck in transitioning from offline representation learning to online decision-making is the "action gap": passive datasets (e.g., online videos) often lack the action labels required to ground latent representations in environment dynamics. We propose to bridge this gap by exploiting demonstrator diversity. Even when actions are unobserved, systematic variation in transitions across demonstrators can help disentangle latent action choice from environment stochasticity. We formalize this as a statewise column-stochastic non-negative matrix factorization (NMF) problem, where demonstrator-specific policies act as mixtures over shared latent transition kernels. Under "sufficiently scattered" policy diversity and rank conditions, we prove that latent actions and dynamics are identifiable up to a permutation. We extend these results to continuous observation spaces via a Gram-determinant minimum-volume criterion and prove that spatial continuity ensures a globally consistent action labeling. Our framework shows how heterogeneity in passive data can substitute for missing action labels, leaving limited interaction to resolve only the final action-label alignment.
@inproceedings{schur2026latentactions, title = {Action-Free Offline {RL} via Demonstrator Diversity}, author = {Schur, Felix}, booktitle = {ICML Workshop on Demos (DEMO)}, year = {2026}, archiveprefix = {arXiv}, primaryclass = {cs.LG}, url = {https://icml.cc/virtual/2026/83703}, } - Prediction-Intervention Games and Invariant SetsLinus Kühne, Felix Schur, and Jonas PetersIn Advances in Neural Information Processing Systems (NeurIPS), 2026
We consider the following two-player game: using observational data, the leader chooses a prediction function for a response variable Y from given covariates. The follower then reacts with an intervention on some covariates in the underlying structural causal model to maximize their own objective. The leader knows the intervention targets, but may have limited knowledge of the follower’s objective. We call this setup a prediction-intervention game, a special case of a Stackelberg game. Finding an optimal strategy for the leader is generally difficult. To avoid severe performance loss, the leader may base their prediction on the causal parents of Y, or more generally on an invariant subset of covariates. We prove that predictors based on the stable blanket, a specific invariant subset, weakly dominate those based on the causal parents in the game for two common classes of follower objectives. We further upper bound the leader’s post-intervention risk by a worst-case risk over allowed interventions and strengthen existing distribution generalization results to analyze this bound: we give sufficient conditions under which stable-blanket predictors are worst-case optimal, and show by examples that these conditions cannot in general be dropped. Finally, we discuss practical strategies when the causal graph is unknown and test them on simulated and real-world data.
@inproceedings{kuehne2026predictionintervention, title = {Prediction-Intervention Games and Invariant Sets}, author = {Kühne, Linus and Schur, Felix and Peters, Jonas}, booktitle = {Advances in Neural Information Processing Systems (NeurIPS)}, year = {2026}, archiveprefix = {arXiv}, primaryclass = {stat.ML}, url = {https://openreview.net/forum?id=XRaoy63niz}, } - DecoR: Deconfounding Time Series with Robust RegressionFelix Schur, Pio Blieske, and Jonas PetersJournal of the Royal Statistical Society Series B: Statistical Methodology, 2026
Causal inference on time series data is a challenging problem, especially in the presence of unobserved confounders. In this work, we focus on estimating the causal effect of a multivariate time series on a univariate time series when a third (possibly multivariate) time series confounds the relationship but remains unobserved. By assuming spectral sparsity of the confounder, we show how this problem can be framed as an adversarial outlier problem in the frequency domain. We introduce Deconfounding by Robust regression (DecoR), a novel approach that estimates the causal effect using robust linear regression in the frequency domain. We consider two robust regression techniques and provide improved bounds on their estimation errors. Applying these results to DecoR, we prove, under suitable assumptions, upper bounds for the estimation error of DecoR that imply consistency. We demonstrate DecoR’s effectiveness through experiments on both synthetic and real-world data from Earth system science. The simulation experiments furthermore suggest that DecoR is robust with respect to model misspecification.
@article{schur2026decor, title = {DecoR: Deconfounding Time Series with Robust Regression}, author = {Schur, Felix and Blieske, Pio and Peters, Jonas}, journal = {Journal of the Royal Statistical Society Series B: Statistical Methodology}, volume = {88}, number = {3}, pages = {799--818}, year = {2026}, doi = {10.1093/jrsssb/qkaf067}, }
2025
- Transferring Causal Effects using ProxiesManuel Iglesias-Alonso, Felix Schur, Julius Kügelgen, and 1 more authorIn Advances in Neural Information Processing Systems (NeurIPS), 2025
We consider the problem of estimating a causal effect in a multi-domain setting. The causal effect of interest is confounded by an unobserved confounder and can change between the different domains. We assume that we have access to a proxy of the hidden confounder and that all variables are discrete or categorical. We propose methodology to estimate the causal effect in the target domain, where we assume to observe only the proxy variable. Under these conditions, we prove identifiability (even when treatment and response variables are continuous). We introduce two estimation techniques, prove consistency, and derive confidence intervals. The theoretical results are supported by simulation studies and a real-world example studying the causal effect of website rankings on consumer choices.
@inproceedings{iglesias2025transferring, title = {Transferring Causal Effects using Proxies}, author = {Iglesias-Alonso, Manuel and Schur, Felix and von Kügelgen, Julius and Peters, Jonas}, booktitle = {Advances in Neural Information Processing Systems (NeurIPS)}, year = {2025}, archiveprefix = {arXiv}, primaryclass = {stat.ML}, }
2024
- Identifying Elasticities in Autocorrelated Time Series Using Causal GraphsSilvana Tiedemann, Jorge Sanchez Canales, Felix Schur, and 4 more authors2024
The price elasticity of demand can be estimated from observational data using instrumental variables (IV). However, naive IV estimators may be inconsistent in settings with autocorrelated time series. We argue that causal time graphs can simplify IV identification and help select consistent estimators. To do so, we propose to first model the equilibrium condition by an unobserved confounder, deriving a directed acyclic graph (DAG) while maintaining the assumption of a simultaneous determination of prices and quantities. We then exploit recent advances in graphical inference to derive valid IV estimators, including estimators that achieve consistency by simultaneously estimating nuisance effects. We further argue that observing significant differences between the estimates of presumably valid estimators can help to reject false model assumptions, thereby improving our understanding of underlying economic dynamics. We apply this approach to the German electricity market, estimating the price elasticity of demand on simulated and real-world data. The findings underscore the importance of accounting for structural autocorrelation in IV-based analysis.
@misc{tiedemann2024identifyingelasticities, title = {Identifying Elasticities in Autocorrelated Time Series Using Causal Graphs}, author = {Tiedemann, Silvana and Sanchez Canales, Jorge and Schur, Felix and Sgarlato, Raffaele and Hirth, Lion and Ruhnau, Oliver and Peters, Jonas}, year = {2024}, archiveprefix = {arXiv}, primaryclass = {econ.EM}, }
2023
- Lifelong Bandit Optimization: No Prior and No RegretFelix Schur, Parnian Kassraie, Jonas Rothfuss, and 1 more authorIn Proceedings of the 39th Conference on Uncertainty in Artificial Intelligence (UAI), Aug 2023
Machine learning algorithms are often repeatedly applied to problems with similar structure over and over again. We focus on solving a sequence of bandit optimization tasks and develop LIBO, an algorithm which adapts to the environment by learning from past experience and becomes more sample-efficient in the process. We assume a kernelized structure where the kernel is unknown but shared across all tasks. LIBO sequentially meta-learns a kernel that approximates the true kernel and solves the incoming tasks with the latest kernel estimate. Our algorithm can be paired with any kernelized or linear bandit algorithm and guarantees oracle optimal performance, meaning that as more tasks are solved, the regret of LIBO on each task converges to the regret of the bandit algorithm with oracle knowledge of the true kernel. Naturally, if paired with a sublinear bandit algorithm, LIBO yields a sublinear lifelong regret. We also show that direct access to the data from each task is not necessary for attaining sublinear regret. We propose F-LIBO, which solves the lifelong problem in a federated manner.
@inproceedings{schur23a, title = {Lifelong Bandit Optimization: No Prior and No Regret}, author = {Schur, Felix and Kassraie, Parnian and Rothfuss, Jonas and Krause, Andreas}, booktitle = {Proceedings of the 39th Conference on Uncertainty in Artificial Intelligence (UAI)}, pages = {1847--1857}, year = {2023}, month = aug, publisher = {PMLR}, archiveprefix = {arXiv}, primaryclass = {cs.LG}, }