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Sebastian Weichwald.

Google Scholar / Github / Twitter

I am interested in the foundations of causal inference and its potential to provide novel insights in applications such as neuroimaging. We were the first to provide a comprehensive set of causal interpretation rules for encoding and decoding models in neuroimaging studies (NeuroImage paper, explainer video (5 min)).

I am a PhD student at the Max Planck Institute for Intelligent Systems and associate fellow of the Max Planck ETH Center for Learning Systems, supervised by Bernhard Schölkopf and Joachim M. Buhmann. I obtained my MSc in Computational Statistics and Machine Learning from University College London, funded by the German National Academic Foundation (Studienstiftung) and the German Academic Exchange Service (DAAD), and my BSc in Mathematics from the University of Tübingen.

Questions? Comments? Want to work with me? Just shoot me an email .


Nov 2018.
We are happy to announce that Nicolas Boumal and Bamdev Mishra (both core developers of manopt) are joining the pymanopt team as maintainers. This will improve integration of new methods as well as maintenance level, and will also help to slowly grow the python userbase transitioning away from non-open non-free matlab.
On another positive note, it appears that FAIR may be using our toolbox...pssst ;-)...which resulted in this pull request by Leon Bottou from Facebook AI Research that could bring PyTorch support to pymanopt in the very near future.
Oct 2018.
Aaron Bahde successfully completed his essay rotation with me on "Different Notions of Causality employed in fMRI Analysis" as part of his master's studies in Neural Information Processing – Congratulations!
Jul 2018.
Information leak in NIPS 2018 review process / CMT platform, potentially compromising anonymity of submitters — after I had informed the NIPS chairs and CMT responsibles they acted timely and adequately to fix the issue 👍Comments? ⤳ this twitter thread
Jun 2018.
New manuscript and code is out: groupICA: Independent component analysis for grouped data. Check out the project website for an audible example of the "America's Got Talent Duet Problem" as well as a video demonstrating the increased stability of groupICA over pooledICA when applied to EEG data.
May 2017.
I am happy to confirm the speakers for the causality workshop in July that I am organising. We will have Frederick Eberhardt (Caltech) presenting work on micro and macro causal variables, Caroline Uhler (MIT) on causality in genomics, as well as talks on causality and fairness, group invariance principles for causal inference, and the detection of confounding via typicality principles.
Mar 2017.
I got awarded a CLS exchange fellowship to fund my 6 months research stay at ETH Zurich. I am looking forward to a collaboration with the cardiology section of the University Hospital Zurich as well as TAing for the machine learning lecture at ETH where we organise practical machine learning challenges for ~400 students.




groupICA: Independent component analysis for grouped data

N Pfister*, S Weichwald*, P Bühlmann, B Schölkopf; *Equal contribution

groupICA extends the ordinary ICA model to incorporate group-wise structure in data and provides a justified alternative to the use of ICA on data blindly pooled across groups (e.g. subjects). We explain its causal interpretation and motivation, provide an efficient estimation procedure, prove identifiability under mild assumptions, and demonstrate applicability to EEG data.

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

Mortality prediction for patients with acute coronary syndrome

paper writing in progress

In a collaboration with the University Heart Center Zurich and the ETH Zurich we are developing robust models for predicting 1-year mortality after acute coronary syndromes. Our approach is robust, interpretable, only uses objective measurements as input instead of subjective assessments by clinicians, and improves performance upon state-of-the-art.

Peer-reviewed articles.


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.

doi / pdf

MERLiN: Mixture Effect Recovery in Linear Networks

S Weichwald, M Grosse-Wentrup, A Gretton
IEEE Journal of Selected Topics in Signal Processing, 10(7):12541266, 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.

arXiv / code / doi / pdf

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

J Townsend, N Koep, S Weichwald
Journal of Machine Learning Research, 17(137):15, 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.)

arXiv / code / documentation / jmlr / pdf

Causal interpretation rules for encoding and decoding models in neuroimaging

S Weichwald, T Meyer, O Özdenizci, B Schölkopf, T Ball, M Grosse-Wentrup
NeuroImage, 110:4859, 2015

We provide a set of rules which causal statements are warranted and which ones are not supported by empirical evidence. Especially, 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.

arXiv / doi / explainer video (5 min)
pdf / slides / tutorial video (35 min)

Peer-reviewed conference papers.


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.

arXiv / pdf

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).

arXiv / pdf

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.

arXiv / code / doi / pdf / slides

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.

arXiv / doi / pdf

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
(best student paper award)

In this work it is shown that index finger positions can be differentiated from non-invasive EEG recordings in healthy human subjects. Among the different spectral features investigated, high β-power (20–30 Hz) over contralateral sensorimotor cortex carried most information about finger position.

arXiv / doi / pdf



The right tool for the right question — beyond the encoding versus decoding dichotomy

S Weichwald, M Grosse-Wentrup

2017. In this commentary, we construct two simple and analytically tractable examples to provide further intuition about the problems with interpreting encoding and decoding models. We argue that if we want to understand how the brain generates cognition, we need to move beyond the encoding versus decoding dichotomy and instead discuss and develop tools that are specifically tailored to our endeavour.

arXiv / pdf

A note on the expected minimum error probability in equientropic channels

S Weichwald, T Fomina, B Schölkopf, M Grosse-Wentrup

2017. In this note, we characterise the quality of a code (i. e. a given encoding routine) by an upper bound on the expected minimum error probability that can be achieved when using this code. We show that for equientropic channels this upper bound is minimal for codes with maximal marginal entropy.

arXiv / pdf

What is Cantor's continuum problem?

S Weichwald

2013. 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.


Langton's Ant (MATLAB-Simulation)

S Weichwald

2011. A few small scripts which allow to simulate the ant's behaviour within different two-dimensional grids with different kinds of borders. The ant is represented by a little red triangle which allows to indicate the current direction. One can follow the ant move by move, step by step or in fast-forward mode.


Appeal for open access, preprints and accepted manuscripts.

In my opinion research results should be accessible to everyone. If not publishing open access, authors should consider posting preprints or accepted manuscripts on arXiv or their personal website. The SHERPA/RoMEO database makes it easy to check a journal's/publisher's policy and decide on posting a preprint or author accepted manuscript.


Jun 2017.
Our paper Causal Consistency of Structural Equation Models has been accepted for an oral presentation at UAI 2017.
May 2017.
I will be giving a causality tutorial at PRNI 2017. (slides)
Nov 2016.
I am now associate PhD Fellow of the Max Planck ETH Center for Learning Systems.
Aug 2016.
Our paper MERLiN: Mixture Effect Recovery in Linear Networks got published in the IEEE Journal of Selected Topics in Signal Processing.
Jun 2016.
Attending OHBM 2016 – exciting! Thanks to Russell Poldrack, Martin Lindquist, and Christoph Herrmann for making our symposium "What Neuroimaging Can Tell Us? From Correlation to Causation and Cognitive Ontologies" a success! (The slides for my talk can be found here.)
Mar 2016.
Our symposium "What Neuroimaging Can Tell Us? From Correlation to Causation and Cognitive Ontologies" has been accepted for the OHBM 2016 Annual Meeting. I feel honoured to be organising this together with Moritz and to be part of the speakers line-up together with Russell Poldrack, Martin Lindquist, and Christoph Herrmann.
Mar 2016.
We have released an early version of Pymanopt: A Python Toolbox for Manifold Optimization using Automatic Differentiation. This example demonstrates how to infer the parameters of a Mixture of Gaussian (MoG) model using manifold optimisation instead of expectation maximisation (EM).
Jan 2016.
Moritz's OHBM 2015 educational talk Causal Interpretation Rules for Encoding and Decoding Models in Neuroimaging is online.
Dec 2015.
New manuscript and code is out: MERLiN: Mixture Effect Recovery in Linear Networks.
Aug 2015.
Completed my master's at UCL with a thesis on causal effect recovery from linear mixtures. It's time for holidays in the United States!
Besides an exciting road trip I am also looking forward to interesting intermezzi: I will present our recent work at the Poldrack Lab (Stanford University, September), the LIINC group (Columbia University, October), and will visit Martin Lindquist (Johns Hopkins University, October).
Jun 2015.
A new explainer video (5 min) describing our work is online.
I will present our recent work at this year's UAI Workshop "Advances in Causal Inference" (Amsterdam, July).
May 2015.
Moritz will present our recent work at this year's PRNI workshop (Stanford University, June).
I have been invited for talks at the FMRIB Analysis Group (University of Oxford, July) and the LIINC group (Columbia University, October). Furthermore, I will be visiting Martin Lindquist (Johns Hopkins University, October).
– Looking forward to meeting inspiring people and having interesting discussions!
Nov 2014.
A golden oldie worth a reread: Data Set Selection by Doudou LaLoudouana and Mambobo Bonouliqui Tarare.
Aug 2014.
Let's have a drink, let's have a Kernel!
Feb 2014.
An interesting article: Scientific method: Statistical errors : Nature News & Comment.
Jan 2014.
Videos and slides of MLSS 2013 Tübingen can now be downloaded.
Oct 2013.
An interesting article: Unreliable research: Trouble at the lab | The Economist.
Imprint & Credits