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Beware of the Simulated DAG! Varsortability in Additive Noise Models

AG Reisach, C Seiler, S Weichwald

In additive noise models (ANMs), the ordering of variables by marginal variances may be indicative of the causal order. We introduce varsortability as a measure of this agreement between orderings. Since varsortability is high in simulated ANMs, we advocate reporting varsortability when benchmarking.

pdf / arXiv / bib



Compositional Abstraction Error and a Category of Causal Models

AF Rischel, S Weichwald
accepted at Uncertainty in Artificial Intelligence (UAI), 2021

We argue that compositionality is a desideratum for causal model transformations and the associated errors. We introduce a category of finite interventional causal models and, leveraging theory of enriched categories, prove that our framework enjoys the desired compositionality properties.

pdf / arXiv / bib

Improving 1-year mortality prediction in ACS patients using machine learning

S Weichwald, A Candreva*, R Burkholz*, R Klingenberg, L Räber, D Heg, R Manka, B Gencer, F Mach, D Nanchen, N Rodondi, S Windecker, R Laaksonen, SL Hazen, Av Eckardstein, F Ruschitzka, TF Lüscher, JM Buhmann, CM Matter; *Equal contribution
European Heart Journal: Acute Cardiovascular Care (accepted)

We discuss a model development procedure for small imbalanced data.

pdf / doi / free access

Causality in cognitive neuroscience: concepts, challenges, and distributional robustness

S Weichwald, J Peters
Journal of Cognitive Neuroscience, 33(2):226–247, 2021

We outline why we believe that distributional robustness and model generalisability can be useful for guiding causality research in cognitive neuroscience. In particular, it can help with respect to the scarcity of targeted interventional data and the difficulty of defining the right variables. We provide an accessible introduction to causality and review selected causal discovery approaches and their underlying ideas, assumptions, and problems.

pdf / doi / arXiv / bib

Causal structure learning from time series: Large regression coefficients may predict causal links better in practice than small p-values

S Weichwald, ME Jakobsen, PB Mogensen, L Petersen, N Thams, G Varando
Proceedings of the NeurIPS 2019 Competition and Demonstration Track, Proceedings of Machine Learning Research, 123:27−36, 2020

We describe the algorithms for causal structure learning from time series data that won the NeurIPS competition »Causality 4 Climate« 2019. We examine why large regression coefficients may predict causal links better in practice than small p-values and thus why normalising the data may sometimes hinder causal structure learning. The algorithms are available at tidybench.

pdf / arXiv / tidybench / bib

Robustifying Independent Component Analysis by Adjusting for Group-Wise Stationary Noise

N Pfister*, S Weichwald*, P Bühlmann, B Schölkopf; *Equal contribution
Journal of Machine Learning Research, 20(147):1−50, 2019

Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise this notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs.

pdf / JMLR / arXiv / Python/R/matlab / audible example / EEG example video / bib

Causal Consistency of Structural Equation Models

PK Rubenstein*, S Weichwald*, S Bongers, JM Mooij, D Janzing, M Grosse-Wentrup, B Schölkopf; *Equal contribution
Uncertainty in Artificial Intelligence (UAI), 2017

Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise this notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs.

pdf / arXiv / bib

Absence of EEG correlates of self-referential processing depth in ALS

T Fomina, S Weichwald, M Synofzik, J Just, L Schöls, B Schölkopf, M Grosse-Wentrup
PLoS ONE, 12(6):e0180136, 2017

We find that electroencephalography (EEG) correlates of self-referential thinking are present in healthy individuals, but not in those with ALS. In particular, thinking about themselves or others significantly modulates the bandpower in the medial prefrontal cortex in healthy individuals, but not in ALS patients.

pdf / doi / bib

Personalized Brain-Computer Interface Models for Motor Rehabilitation

A Mastakouri, S Weichwald, O Özdenizci, T Meyer, B Schölkopf, M Grosse-Wentrup
IEEE International Conference on Systems, Man, and Cybernetics (SMC 2017), 2017

We propose to fuse two currently separate research lines on novel therapies for stroke rehabilitation: brain-computer interface (BCI) training and transcranial electrical stimulation (TES).

pdf / doi / arXiv / bib

MERLiN: Mixture Effect Recovery in Linear Networks

S Weichwald, M Grosse-Wentrup, A Gretton
IEEE Journal of Selected Topics in Signal Processing, 10(7):1254–1266, 2016

MERLiN is a causal inference algorithm that can recover from an observed linear mixture a causal variable that is an effect of another given variable. MERLiN implements a novel idea on how to (re-)construct causal variables and is robust against hidden confounding.

pdf / doi / arXiv / code / bib

Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation

J Townsend, N Koep, S Weichwald
Journal of Machine Learning Research, 17(137):1–5, 2016

Pymanopt lowers the barriers to users wishing to use state of the art manifold optimization techniques, by using automated differentiation for calculating derivative information, saving users time and saving them from potential calculation and implementation errors.
(Example: manifold optimisation for inferring parameters of a MoG model.)

pdf / JLMR / arXiv / code / documentation / bib

Recovery of non-linear cause-effect relationships from linearly mixed neuroimaging data

S Weichwald, A Gretton, B Schölkopf, M Grosse-Wentrup
International Workshop on Pattern Recognition in Neuroimaging (PRNI), 2016

This paper proposes an extension of the MERLiN algorithm to identify non-linear cause-effect relationships between linearly mixed neuroimaging data.

pdf / doi / arXiv / code / slides / bib

Causal interpretation rules for encoding and decoding models in neuroimaging

S Weichwald, T Meyer, O Özdenizci, B Schölkopf, T Ball, M Grosse-Wentrup
NeuroImage, 110:48–59, 2015

We provide a set of rules which causal statements are warranted and which ones are not supported by empirical evidence. Only encoding models in the stimulus-based setting support unambiguous causal interpretations. By combining encoding and decoding models, however, we obtain insights into causal relations beyond those that are implied by each individual model type.

pdf / doi / arXiv / explainer / slides / bib

Causal and anti-causal learning in pattern recognition for neuroimaging

S Weichwald, B Schölkopf, T Ball, M Grosse-Wentrup
International Workshop on Pattern Recognition in Neuroimaging (PRNI), 2014

In this paper, we argue that it is not sufficient to distinguish between encoding- and decoding models: The interpretation of such models depends on whether they are employed in a stimulus- or response-based setting.

pdf / doi / arXiv / bib

Decoding index finger position from EEG using random forests

S Weichwald, T Meyer, B Schölkopf, T Ball, M Grosse-Wentrup
International Workshop on Cognitive Information Processing (CIP), 2014

We show that index finger positions can be differentiated from non-invasive EEG recordings in healthy human subjects. High β-power (20–30 Hz) over contralateral sensorimotor cortex carried most information about finger position.
This work won the best student paper award.

pdf / doi / arXiv / bib



Pragmatism and Variable Transformations in Causal Modelling

S Weichwald
ETH Zurich, 2019

The statistical treatment of causal modelling lays out methodology that, under well specified assumptions, enables us to infer cause-effect relationships from observational data. The adoption and fruitful utilisation of such methods remains limited, however, despite the statistical foundations and numerous theoretical advances. In this thesis, we present contributions towards closing the gap between statistical causal modelling and its successful application.

pdf / doi / bib



What is Cantor’s continuum problem?

S Weichwald

This seminar paper reviews Kurt Gödel’s article »What is Cantor’s continuum problem?«. As this paper aims to be almost self-contained, short recaps, rough explanations and selective examples are provided where appropriate.



Confounding-robust Independent Component Analysis.
Python / R / matlab / documentation
Python toolbox for optimisation on manifolds with support for automatic differentiation.
Part of the manopt family.
code / documentation
MERLiN non- & linear.
Mixture Effect Recovery in Linear Networks.
TIme series DiscoverY BENCHmark implementation of our competition-winning algorithms.


Imprint & Credits