Currently, I am a group leader for the causality group at the MPI Tuebingen.

My work focuses mainly on causal inference: we try to learn causal structures either from purely observational data or from a combination of observational and interventional data. We therefore develop both theory and methodology. Our work relates to areas like high-dimensional statistics, computational statistics or graphical models. It's an exciting research area with lots of open questions!

Before joining Tuebingen, I was a postdoc (Marie Curie fellowship) at the Seminar für Statistik, ETH Zurich (CH). During my PhD and Postdoc I have been working with Dominik Janzing and Bernhard Schölkopf at the MPI for Intelligent Systems, Tübingen (GER), and later with Peter Bühlmann and Nicolai Meinshausen at ETH Zurich. I have spent three months with Leon Bottou at Microsoft Research (WA, USA) in 2011 and two months with Martin Wainwright at UC Berkeley (CA, USA) in 2013. In 2014, I have been working with Peter Spirtes at CMU (Pittsburgh, USA) for two months. I studied Mathematics in Heidelberg (GER) and in Cambridge (UK).

- In June, I have been elected as a member of the Junge Akademie.
- In August, I will join the statistics group in the Department of Mathematical Sciences at the University of Copenhagen as an associate professor.
- Aug 22nd - 26th, I will teach at a summer course on machine learning at the Technical University of Denmark in Copenhagen.
- Niklas successfully finished his master thesis (congratulations!), which resulted in this arxiv paper.
- Our paper on invariant prediction got accepted as a discussion paper at JRSS, Series B.

1. **Consider the following problem**: we are given data from gene A (or B) and a phenotype. Clearly, both variables are correlated. What is the best prediction for the phenotype given we are deleting gene A (or B), such that its activity becomes zero?

2. **Causality matters**: Intuitively, the optimal prediction should depend on the underlying causal structure:

But then, if we do not accept any form of causal notion, we cannot distinguish between these two cases and our best prediction must be: "I do not know."!

3. **Causal Model**: If we want to be able to describe the above situation properly, we need a so-called causal model that (1) models observational data and (2) interventional data (e.g., the distribution that arises after the gene deletion) and that (3) outputs a graph. Functional Causal Models (also called Structural Equation Models) are one class of such models, see the figure on the right. If you are interested in more details, see the script below, for example.

4. **Examples of questions that are studied in this field:** How can one compute intervention distributions from the graph and the observational distribution efficiently? What if some of the variables are unobserved? What are nice graphical representations? Under which assumptions can we reconstruct the causal model from the observational distribution ("causal discovery")? What if we are also given data from some of the intervention distributions? Does causal knowledge help in more "classical" tasks in machine learning and statistics?

I have written a script on causality that I am more than happy to receive feedback on. Please note that it is still missing some sections. It can be downloaded here.

- Mar 2016: Workshop on Computationally and Statistically Efficient Inference

for Complex Large-scale Data, Oberwolfach - Nov 2015: Workshop on "Exploring the earth system data cube", Jena
- Oct 2015: Tutorial at GCPR, Aachen
- Sep 2015: DMV - Minisymposium Statistics on Complex Structures, Hamburg
- Jul 2015: ISI - World Statistics Congress, Rio de Janeiro
- Mar 2015: Workshop on Big Data in Health Policy, Toronto
- Mar 2015: Causation from Correlation?, Die Junge Akademie, Ohlstadt
- Dec 2014: ERCIM, Working Group CMStatistics, Pisa
- Jul 2014: IMS Annual Meeting, Sydney
- Jun 2014: Workshop on Simplicity and Causal Discovery, Pittsburgh
- Dec 2013: NIPS Workshop on Causality, Lake Tahoe
- Sep 2012: Networks: Processes and Causality, Menorca
- Sep 2010: International Symposium on Quantum Thermodynamics, Stuttgart
- Oct 2009: Machine Learning approaches to statistical dep. and causality, Schloss Dagstuhl

- Feb 2016: Department of Statistics, University of Oxford, Oxford
- Jan 2015: University of St. Andrews, St Andrews
- Jan 2015: Statslab, University of Cambridge, Cambridge
- Jan 2015: Microsoft Research, Cambridge
- Jan 2015: UCL Seminar Series, London
- Jan 2015: WIAS, Berlin
- Jul 2014: UCLA, Los Angeles
- Jul 2014: Caltech, Pasadena
- Mar 2014: University of Regensburg, Regensburg
- Jan 2014: University of Amsterdam, Amsterdam
- Jan 2014: University of Nijmegen, Nijmegen
- Nov 2013: UC Berkeley, Berkeley
- Dec 2012: IST Austria, Vienna
- Nov 2012: MPI for Dynamics and Self-Organization, Goettingen
- Jun 2012: Teleconference Causality
- Jun 2011: Seminar for Statistics, ETH Zurich, Zurich
- Jun 2010: MPI for Biogeochemistry, Jena
- Mar 2009: Teleconference Causality

- Jul 2015, Workshop on Advances in Causal Inference at UAI 2015, Amsterdam, The Netherlands (co-organizer)
- Apr 2015, Workshop on Networks: Processes and Causality at DALI 2015, La Palma.
- Jul 2014, Workshop on Causal Inference: Learning and Prediction at UAI 2014, Quebec, Canada (co-organzier)

- ACM Transactions on Intelligent Systems and Technology
- Annals of Statistics
- Bernoulli Journal
- Biometrika
- IEEE Transactions of Pattern Analysis and Machine Intelligence
- IEEE Information Theory
- Journal of American Statistical Association
- Journal of Causal Infernece
- Journal of Machine Learning Research
- Neurocomputing
- NeuroImage
- Statistics and Computing

- AISTATS 2015
- ICML (2012, 2013, 2014)
- ICONIP 2011
- IEEE Int. Workshop on ML for Signal Proc. (2012)
- NIPS (2011, 2015)
- COLT 2015
- UAI (2012, 2013, 2014, 2015, 2016)

- Seminar: Learning Blackjack, ETH Zurich, spring semester 2016
- Lecture: Intelligente Systeme I - Empirische Inferenz (with M. Hirsch), University of Tuebingen, summer semester 2015
- Lecture: Causality (with M. Maathuis and N. Meinshausen), ETH Zurich, spring semester 2015
- Seminar: Functional Data Analysis (with H. R. Kuensch), ETH Zurich, spring semester 2014
- Seminar: Causal Inference from Observational Data, ETH Zurich, spring semester 2013

- Master Theses: Radu Tanase, David Buerge, Niklas Pfister (all ETH Zurich)
- Interns: Fabian Gieringer, Ivan Ustyuzhaninov, Jan Gleixner

- Course on Causality, Machine Learning Summer School Cádiz, Spain, May, 2016
- Course on Causality (with B. Schoelkopf), Machine Learning Summer School Tuebingen, Germany, summer 2015

- Kausalitaet, Exoplaneten und Black Jack: wie man aus Daten lernt, Sommerakademie 2015
- Akademieleitung, Deutsche SchülerAkademie 2013, 2014
- Wahrscheinlichkeiten als Sprache, Deutsche SchülerAkademie 2012
- Woher kommt der Strom?, Deutsche SchülerAkademie 2011
- It's Magic, Deutsche SchülerAkademie 2010
- Huete, Naegel, Schuhkartons, Deutsche SchülerAkademie 2009

- Foundations of Mathematical Statistics, ETH Zurich, autumn semester 2012
- Computational Statistics, ETH Zurich, spring semester 2012
- Introduction to Statistics, University of Heidelberg, summer semester 2006
- Analysis II, University of Heidelberg, winter semester 2005
- Analysis I, University of Heidelberg, summer semester 2005

- R-code for
**Half-Sibling Regression**(only simulations on iid data). - R-code for
**SID**can be downloaded from CRAN, package name: "SID". Paper: J. Peters, P. Bühlmann: "Structural Intervention Distance (SID) for Evaluating Causal Graphs", Neural Computation, 2015. - R-code for
**CAM**can be downloaded from CRAN, package name: "CAM". Paper: P. Bühlmann, J. Peters, J. Ernest: CAM: Causal Additive Models, high-dimensional Order Search and Penalized Regression, Annals of Statistics, 2014. - R-code for
**Timino**. Paper: J. Peters, D. Janzing, B. Schölkopf: Causal Inference on Time Series using Structural Equation Models, Advances in Neural Information Processing Systems 26, 2014. - R-code for
**ANMs**. Paper: J. Peters, J. Mooij, D. Janzing, B. Schölkopf: Causal Discovery with Continuous Additive Noise Models, JMLR, 2014. - Matlab-code for
**Cause-Effect-Pairs**(same paper). - R-code for
**Invariant Prediction**can be downloaded from CRAN, package name: "InvariantCausalPrediction". Paper: J. Peters, P. Bühlmann, N. Meinshausen: Causal inference using invariant prediction: identification and confidence intervals, arXiv:1501.01332.

- N. Pfister, P. Bühlmann, B. Schölkopf,
**J. Peters**: Kernel-based Tests for Joint Independence, http://arxiv.org/abs/1603.00285 - M. Rojas-Carulla, B. Schölkopf, R. Turner,
**J. Peters**: Causal Transfer in Machine Learning, http://arxiv.org/abs/1507.05333

- S. Bauer, B. Schölkopf,
**J. Peters**: The Arrow of Time in Multivariate Time Series, arXiv:1603.00784, ICML, 2043–2051, 2016. - N. Meinshausen, A. Hauser, J. Mooij, P. Versteeg,
**J. Peters**, P. Bühlmann: Causal inference from gene perturbationexperiments: methods, software and validation, Proceedings of the National Academy of Sciences 113 (27) 7361-7368, 2016. - B. Schölkopf, D. Hogg, D. Wang, D. Foreman-Mackey, D. Janzing, C.-J. Simon-Gabriel,
**J. Peters**: Modeling Confounding by Half-Sibling Regression, Proceedings of the National Academy of Sciences 113 (27) 7391-7398, 2016. - J. Mooij,
**J. Peters**, D. Janzing, J. Zscheischler, B. Schölkopf: Distinguishing cause from effect using observational data: methods and benchmarks, arXiv:1412.3773, JMLR 17:1-102, 2016. **J. Peters**, P. Bühlmann, N. Meinshausen: Causal inference using invariant prediction: identification and confidence intervals, arXiv:1501.01332, accepted at Journal of the Royal Statistical Society, Series B (with discussion).- S. Sippel, J. Zscheischler, M. Heimann, F. Otto,
**J. Peters**, M. Mahecha: Quantifying changes in climate variability and extremes: pitfalls and their overcoming, accepted in Geophysical Research Letters 42:9990-9998, 2015. - D. Rothenhäusler, C. Heinze,
**J. Peters**, N. Meinshausen: backShift: Learning causal cyclic graphs from unknown shift interventions, Advances in Neural Information Processing Systems 28 (NIPS 2015), 1513-1521, 2015. - B. Schölkopf, D. Hogg, D. Wang, D. Foreman-Mackey, D. Janzing, C-J. Simon-Gabriel,
**J. Peters**: Removing systematic errors for exoplanet search via latent causes, 32nd International Conference on Machine Learning (ICML 2015), 2218-2226, 2015. - B. Schölkopf, K. Muandet, K. Fukumizu, S. Harmeling,
**J. Peters**: Computing Functions of Random Variables via Reproducing Kernel Hilbert Space Representations, Statistics and Computing 25:755-766, 2015. **J. Peters**, P. Bühlmann: Structural Intervention Distance (SID) for Evaluating Causal Graphs, Neural Computation 27:771-799, 2015. bibtex**J. Peters**: On the Intersection Property of Conditional Independence and its Application to Causal Discovery, Journal of Causal Inference 3:97-108, 2015. bibtex- P. Bühlmann,
**J. Peters**, J. Ernest: CAM: Causal Additive Models, high-dimensional Order Search and Penalized Regression, Annals of Statistics 42:2526-2556, 2014. bibtex **J. Peters**, J. Mooij, D. Janzing, B. Schölkopf: Causal Discovery with Continuous Additive Noise Models, JMLR 15:2009-2053, 2014. bibtex**J. Peters**, D. Janzing, B. Schölkopf: Causal Inference on Time Series using Restricted Structural Equation Models, Advances in Neural Information Processing Systems 26 (NIPS 2013), 154-162, 2014. bibtex**J. Peters**, P. Bühlmann: Identifiability of Gaussian Structural Equation Models with Equal Error Variances, Biometrika, 101(1):219-228, 2014. bibtex- L. Bottou,
**J. Peters**, J. Quiñonero-Candela, D. X. Charles, D. M. Chickering, E. Portugaly, D. Ray, P. Simard, E. Snelson: Counterfactual Reasoning and Learning Systems, JMLR 14:3207-3260, 2013. bibtex - E. Sgouritsa, D. Janzing,
**J.****Peters**, B. Schölkopf: Identifying Finite Mixtures of Nonparametric Product Distributions and Causal Inference of Confounders*,*29th Conference on Uncertainty in Artificial Intelligence (UAI 2013), 556-565, 2013. bibtex - B. Schölkopf, D. Janzing,
**J. Peters**, E.Sgouritsa, K.Zhang, J. M. Mooij: On causal and anticausal learning*,*29th International Conference on Machine Learning (ICML 2012), 1255-1262, 2012. bibtex **J. Peters**, J. M. Mooij, D. Janzing, B. Schölkopf: Identifiability of Causal Graphs using Functional Models, 27th Conference on Uncertainty in Artificial Intelligence (UAI 2011), AUAI Press, USA, 589-598, 2011. bibtex- D. Janzing, E. Sgouritsa, O. Stegle,
**J. Peters**, B. Schölkopf: Detecting low-complexity unobserved causes, 27th Conference on Uncertainty in Artificial Intelligence (UAI 2011), AUAI Press, USA, 383-391, 2011. bibtex - K. Zhang,
**J. Peters**, D. Janzing, B. Schölkopf: Kernel-based Cond. Independence Test and Application in Causal Discovery, 27th Conference on Uncertainty in Artificial Intelligence (UAI 2011), AUAI Press, USA, 804-813. bibtex **J. Peters**, D. Janzing, B. Schölkopf: Causal Inference on Discrete Data using Additive Noise Models, IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 33:2436-2450, 2011. bibtex**J. Peters**, D. Janzing, B. Schölkopf: Identifying Cause and Effect on Discrete Data using Additive Noise Models, JMLR Workshop and Conference Proceedings Volume 9: 13th International Conference on Artificial Intelligence and Statistics (AISTATS 2010), MIT Press, Cambridge, MA, USA, 597-604, 2010. (conference version of TPAMI 2011) bibtex- D. Janzing,
**J. Peters**, J. M. Mooij, B. Schölkopf: Identifying Confounders Using Additive Noise Models, 25th Conference on Uncertainty in Artificial Intelligence (UAI 2009), AUAI Press, USA, 249-257, 2009. bibtex - J. M. Mooij, D. Janzing,
**J. Peters**, B. Schölkopf: Regression by Dependence Minimization and its Application to Causal Inference in Additive Noise Models, 26th International Conference on Machine Learning (ICML 2009), ACM Press, New York, NY, USA, 745-752, 2009. bibtex **J. Peters**, D. Janzing, A. Gretton, B. Schölkopf: Detecting the Direction of Causal Time Series, 26th International Conference on Machine Learning (ICML 2009), ACM Press, New York, NY, USA, 801-808, 2009. bibtex- P. Hoyer, D. Janzing, J. M. Mooij,
**J. Peters**, B. Schölkopf: Nonlinear Causal Discovery with Additive Noise Models, Advances in Neural Information Processing Systems 21 (NIPS 2008), Curran, Red Hook, NY, USA, 689-696, 2009. bibtex

- PhD Thesis: Restricted Structural Equation Models for Causal Inference, ETH Zurich, 2012. This version includes minor corrections which can be downloaded separately: Errata. bibtex
- Diploma Thesis: Asymmetries of Time Series under Inverting their Direction, University of Heidelberg, 2008. bibtex

- B. Schölkopf, D. Janzing,
**J. Peters**, E. Sgouritsa, K. Zhang, J. Mooij: Semi-supervised learning in causal and anticausal settings In: Empirical Inference, (Ed) B. Schölkopf, Z. Luo, and V. Vovk, Springer-Verlag, 129-141, 2013. **J. Peters**, D. Janzing, A. Gretton, B. Schölkopf: Kernel Methods for Detecting the Direction of Time Series, GfKl 2008, 32nd Annual Conference of the German Classification Society, Springer, Berlin, Germany, 57-66, 2008. bibtex

A current version of my CV (Jan 2016) can be downloaded here.

30 results
(BibTeX)

**The Arrow of Time in Multivariate Time Serie**
*Proceedings of the 33rd International Conference on Machine Learning*, 48, pages: 2043-2051, JMLR Workshop and Conference Proceedings, (Editors: Balcan, M. F. and Weinberger, K. Q.), JMLR, ICML, 2016 (conference)

**Distinguishing cause from effect using observational data: methods and benchmarks**
*Journal of Machine Learning Research*, 17(32):1-102, 2016 (article)

**Modeling Confounding by Half-Sibling Regression**
*Proceedings of the National Academy of Science*, 113(27):7391-7398, 2016 (article)

**Quantifying changes in climate variability and extremes: Pitfalls and their overcoming**
*Geophysical Research Letters*, 42(22):9990-9998, November 2015 (article)

**BACKSHIFT: Learning causal cyclic graphs from unknown shift interventions**
*Advances in Neural Information Processing Systems 28*, pages: 1513-1521, (Editors: C. Cortes, N.D. Lawrence, D.D. Lee, M. Sugiyama and R. Garnett), Curran Associates, Inc., 29th Annual Conference on Neural Information Processing Systems (NIPS), 2015 (conference)

**Causal inference using invariant prediction: identification and confidence intervals**
*Journal of the Royal Statistical Society, Series B*, 2015, (with discussion) (article) Accepted

**Removing systematic errors for exoplanet search via latent causes**
In *Proceedings of The 32nd International Conference on Machine Learning*, 37, pages: 2218–2226, JMLR Workshop and Conference Proceedings, (Editors: Bach, F. and Blei, D.), JMLR, ICML, 2015 (inproceedings)

**On the Intersection Property of Conditional Independence and its Application to Causal Discovery**
*Journal of Causal Inference*, 3(1):97-108, 2015 (article)

**Structural Intervention Distance (SID) for Evaluating Causal Graphs**
*Neural Computation *, 27(3):771-799, 2015 (article)

**Computing Functions of Random Variables via Reproducing Kernel Hilbert Space Representations**
*Statistics and Computing *, 25(4):755-766, 2015 (article)

**CAM: Causal Additive Models, high-dimensional order search and penalized regression**
*Annals of Statistics*, 42(6):2526-2556, 2014 (article)

**Identifiability of Gaussian Structural Equation Models with Equal Error Variances**
*Biometrika*, 101(1):219-228, 2014 (article)

**Causal Discovery with Continuous Additive Noise Models **
*Journal of Machine Learning Research*, 15, pages: 2009-2053, 2014 (article)

**Counterfactual Reasoning and Learning Systems: The Example of Computational Advertising**
*Journal of Machine Learning Research*, 14, pages: 3207-3260, 2013 (article)

**Semi-supervised learning in causal and anticausal settings**
In *Empirical Inference*, pages: 129-141, 13, Festschrift in Honor of Vladimir Vapnik, (Editors: Schölkopf, B., Luo, Z. and Vovk, V.), Springer, 2013 (inbook)

**Identifying Finite Mixtures of Nonparametric Product Distributions and Causal Inference of Confounders **
In *Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence (UAI)*, pages: 556-565, (Editors: A Nicholson and P Smyth), AUAI Press Corvallis, Oregon, USA, UAI, 2013 (inproceedings)

**Causal Inference on Time Series using Restricted Structural Equation Models**
In *Advances in Neural Information Processing Systems 26*, pages: 154-162, (Editors: C.J.C. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K.Q. Weinberger), 27th Annual Conference on Neural Information Processing Systems (NIPS), 2013 (inproceedings)

**Restricted structural equation models for causal inference**
ETH Zurich, Switzerland, 2012 (phdthesis)

**On Causal and Anticausal Learning**
In *Proceedings of the 29th International Conference on Machine Learning*, pages: 1255-1262, (Editors: J Langford and J Pineau), Omnipress, New York, NY, USA, ICML, 2012 (inproceedings)

**Detecting low-complexity unobserved causes**
In pages: 383-391, (Editors: FG Cozman and A Pfeffer), AUAI Press, Corvallis, OR, USA, 27th Conference on Uncertainty in Artificial Intelligence (UAI), July 2011 (inproceedings)