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Learning causal structure poses a combinatorial search problem that typically involves evaluating structures with a score or independence test. The resulting search is costly, and designing suitable scores or tests that capture prior knowledge is difficult. In this work, we propose to amortize causal structure learning. Rather than searching over structures, we train a variational inference model to predict the causal structure from observational or interventional data. This allows us to bypass both the search over graphs and the hand-engineering of suitable score functions. Instead, our inference model acquires domain-specific inductive biases for causal discovery solely from data generated by a simulator. The architecture of our inference model emulates permutation invariances that are crucial for statistical efficiency in structure learning, which facilitates generalization to significantly larger problem instances than seen during training. On synthetic data and semisynthetic gene expression data, our models exhibit robust generalization capabilities when subject to substantial distribution shifts and significantly outperform existing algorithms, especially in the challenging genomics domain.
Author Information
Lars Lorch (ETH Zürich)
Scott Sussex (ETH Zurich)
Jonas Rothfuss (ETH Zurich)
Andreas Krause (ETH Zurich)
Bernhard Schölkopf (MPI for Intelligent Systems, Tübingen)
Bernhard Scholkopf received degrees in mathematics (London) and physics (Tubingen), and a doctorate in computer science from the Technical University Berlin. He has researched at AT&T Bell Labs, at GMD FIRST, Berlin, at the Australian National University, Canberra, and at Microsoft Research Cambridge (UK). In 2001, he was appointed scientific member of the Max Planck Society and director at the MPI for Biological Cybernetics; in 2010 he founded the Max Planck Institute for Intelligent Systems. For further information, see www.kyb.tuebingen.mpg.de/~bs.
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Edwin Bonilla · Thomas Dietterich · Theodoros Damoulas · Andreas Krause · Daniel Sheldon · Iadine Chades · J. Zico Kolter · Bistra Dilkina · Carla Gomes · Hugo P Simao -
2013 Workshop: Bayesian Optimization in Theory and Practice »
Matthew Hoffman · Jasper Snoek · Nando de Freitas · Michael A Osborne · Ryan Adams · Sebastien Bubeck · Philipp Hennig · Remi Munos · Andreas Krause -
2013 Workshop: Discrete Optimization in Machine Learning: Connecting Theory and Practice »
Stefanie Jegelka · Andreas Krause · Pradeep Ravikumar · Kazuo Murota · Jeffrey A Bilmes · Yisong Yue · Michael Jordan -
2013 Workshop: Modern Nonparametric Methods in Machine Learning »
Arthur Gretton · Mladen Kolar · Samory Kpotufe · John Lafferty · Han Liu · Bernhard Schölkopf · Alexander Smola · Rob Nowak · Mikhail Belkin · Lorenzo Rosasco · peter bickel · Yue Zhao -
2013 Workshop: NIPS 2013 Workshop on Causality: Large-scale Experiment Design and Inference of Causal Mechanisms »
Isabelle Guyon · Leon Bottou · Bernhard Schölkopf · Alexander Statnikov · Evelyne Viegas · james m robins -
2013 Poster: High-Dimensional Gaussian Process Bandits »
Josip Djolonga · Andreas Krause · Volkan Cevher -
2013 Poster: The Randomized Dependence Coefficient »
David Lopez-Paz · Philipp Hennig · Bernhard Schölkopf -
2013 Poster: Statistical analysis of coupled time series with Kernel Cross-Spectral Density operators. »
Michel Besserve · Nikos K Logothetis · Bernhard Schölkopf -
2013 Poster: Causal Inference on Time Series using Restricted Structural Equation Models »
Jonas Peters · Dominik Janzing · Bernhard Schölkopf -
2013 Poster: Distributed Submodular Maximization: Identifying Representative Elements in Massive Data »
Baharan Mirzasoleiman · Amin Karbasi · Rik Sarkar · Andreas Krause -
2012 Workshop: Discrete Optimization in Machine Learning (DISCML): Structure and Scalability »
Stefanie Jegelka · Andreas Krause · Jeffrey A Bilmes · Pradeep Ravikumar -
2012 Poster: Learning from Distributions via Support Measure Machines »
Krikamol Muandet · Kenji Fukumizu · Francesco Dinuzzo · Bernhard Schölkopf -
2012 Spotlight: Learning from Distributions via Support Measure Machines »
Krikamol Muandet · Kenji Fukumizu · Francesco Dinuzzo · Bernhard Schölkopf -
2012 Poster: Semi-Supervised Domain Adaptation with Non-Parametric Copulas »
David Lopez-Paz · José Miguel Hernández-Lobato · Bernhard Schölkopf -
2012 Spotlight: Semi-Supervised Domain Adaptation with Non-Parametric Copulas »
David Lopez-Paz · José Miguel Hernández-Lobato · Bernhard Schölkopf -
2012 Poster: The representer theorem for Hilbert spaces: a necessary and sufficient condition »
Francesco Dinuzzo · Bernhard Schölkopf -
2011 Workshop: Philosophy and Machine Learning »
Marcello Pelillo · Joachim M Buhmann · Tiberio Caetano · Bernhard Schölkopf · Larry Wasserman -
2011 Workshop: Discrete Optimization in Machine Learning (DISCML): Uncertainty, Generalization and Feedback »
Andreas Krause · Pradeep Ravikumar · Stefanie S Jegelka · Jeffrey A Bilmes -
2011 Workshop: Cosmology meets Machine Learning »
Michael Hirsch · Sarah Bridle · Bernhard Schölkopf · Phil Marshall · Stefan Harmeling · Mark Girolami -
2011 Oral: Scalable Training of Mixture Models via Coresets »
Dan Feldman · Matthew Faulkner · Andreas Krause -
2011 Poster: Scalable Training of Mixture Models via Coresets »
Dan Feldman · Matthew Faulkner · Andreas Krause -
2011 Invited Talk: From kernels to causal inference »
Bernhard Schölkopf -
2011 Poster: Contextual Gaussian Process Bandit Optimization »
Andreas Krause · Cheng Soon Ong -
2011 Poster: Crowdclustering »
Ryan G Gomes · Peter Welinder · Andreas Krause · Pietro Perona -
2011 Poster: Recovering Intrinsic Images with a Global Sparsity Prior on Reflectance »
Peter Gehler · Carsten Rother · Martin Kiefel · Lumin Zhang · Bernhard Schölkopf -
2011 Poster: Causal Discovery with Cyclic Additive Noise Models »
Joris M Mooij · Dominik Janzing · Tom Heskes · Bernhard Schölkopf -
2010 Workshop: Discrete Optimization in Machine Learning: Structures, Algorithms and Applications »
Andreas Krause · Pradeep Ravikumar · Jeffrey A Bilmes · Stefanie Jegelka -
2010 Spotlight: Switched Latent Force Models for Movement Segmentation »
Mauricio A Alvarez · Jan Peters · Bernhard Schölkopf · Neil D Lawrence -
2010 Poster: Space-Variant Single-Image Blind Deconvolution for Removing Camera Shake »
Stefan Harmeling · Michael Hirsch · Bernhard Schölkopf -
2010 Poster: Switched Latent Force Models for Movement Segmentation »
Mauricio A Alvarez · Jan Peters · Bernhard Schölkopf · Neil D Lawrence -
2010 Poster: Probabilistic latent variable models for distinguishing between cause and effect »
Joris M Mooij · Oliver Stegle · Dominik Janzing · Kun Zhang · Bernhard Schölkopf -
2010 Spotlight: Efficient Minimization of Decomposable Submodular Functions »
Peter G Stobbe · Andreas Krause -
2010 Poster: Discriminative Clustering by Regularized Information Maximization »
Ryan G Gomes · Andreas Krause · Pietro Perona -
2010 Poster: Efficient Minimization of Decomposable Submodular Functions »
Peter G Stobbe · Andreas Krause -
2010 Poster: Near-Optimal Bayesian Active Learning with Noisy Observations »
Daniel Golovin · Andreas Krause · Debajyoti Ray -
2009 Workshop: Connectivity Inference in Neuroimaging »
Karl Friston · Moritz Grosse-Wentrup · Uta Noppeney · Bernhard Schölkopf -
2009 Workshop: Discrete Optimization in Machine Learning: Submodularity, Polyhedra and Sparsity »
Andreas Krause · Pradeep Ravikumar · Jeffrey A Bilmes -
2009 Poster: Kernel Choice and Classifiability for RKHS Embeddings of Probability Distributions »
Bharath Sriperumbudur · Kenji Fukumizu · Arthur Gretton · Gert Lanckriet · Bernhard Schölkopf -
2009 Oral: Kernel Choice and Classifiability for RKHS Embeddings of Probability Distributions »
Bharath Sriperumbudur · Kenji Fukumizu · Arthur Gretton · Gert Lanckriet · Bernhard Schölkopf -
2009 Poster: Online Learning of Assignments »
Matthew Streeter · Daniel Golovin · Andreas Krause -
2009 Spotlight: Online Learning of Assignments »
Matthew Streeter · Daniel Golovin · Andreas Krause -
2008 Workshop: Causality: objectives and assessment »
Isabelle Guyon · Dominik Janzing · Bernhard Schölkopf -
2008 Mini Symposium: Computational Photography »
Bill Freeman · Bernhard Schölkopf -
2008 Poster: Characteristic Kernels on Groups and Semigroups »
Kenji Fukumizu · Bharath Sriperumbudur · Arthur Gretton · Bernhard Schölkopf -
2008 Oral: Characteristic Kernels on Groups and Semigroups »
Kenji Fukumizu · Bharath Sriperumbudur · Arthur Gretton · Bernhard Schölkopf -
2008 Poster: Nonlinear causal discovery with additive noise models »
Patrik O Hoyer · Dominik Janzing · Joris M Mooij · Jonas Peters · Bernhard Schölkopf -
2008 Poster: Effects of Stimulus Type and of Error-Correcting Code Design on BCI Speller Performance »
Jeremy Hill · Jason Farquhar · Suzanne Martens · Felix Bießmann · Bernhard Schölkopf -
2008 Poster: Bayesian Experimental Design of Magnetic Resonance Imaging Sequences »
Matthias Seeger · Hannes Nickisch · Rolf Pohmann · Bernhard Schölkopf -
2008 Spotlight: Nonlinear causal discovery with additive noise models »
Patrik O Hoyer · Dominik Janzing · Joris M Mooij · Jonas Peters · Bernhard Schölkopf -
2008 Spotlight: Bayesian Experimental Design of Magnetic Resonance Imaging Sequences »
Matthias Seeger · Hannes Nickisch · Rolf Pohmann · Bernhard Schölkopf -
2008 Spotlight: Effects of Stimulus Type and of Error-Correcting Code Design on BCI Speller Performance »
Jeremy Hill · Jason Farquhar · Suzanne Martens · Felix Bießmann · Bernhard Schölkopf -
2008 Poster: An empirical Analysis of Domain Adaptation Algorithms for Genomic Sequence Analysis »
Gabriele B Schweikert · Christian Widmer · Bernhard Schölkopf · Gunnar Rätsch -
2008 Poster: Diffeomorphic Dimensionality Reduction »
Christian Walder · Bernhard Schölkopf -
2007 Spotlight: Kernel Measures of Conditional Dependence »
Kenji Fukumizu · Arthur Gretton · Xiaohai Sun · Bernhard Schölkopf -
2007 Poster: An Analysis of Inference with the Universum »
Fabian H Sinz · Olivier Chapelle · Alekh Agarwal · Bernhard Schölkopf -
2007 Poster: Kernel Measures of Conditional Dependence »
Kenji Fukumizu · Arthur Gretton · Xiaohai Sun · Bernhard Schölkopf -
2007 Spotlight: An Analysis of Inference with the Universum »
Fabian H Sinz · Olivier Chapelle · Alekh Agarwal · Bernhard Schölkopf -
2007 Spotlight: Selecting Observations against Adversarial Objectives »
Andreas Krause · H. Brendan McMahan · Carlos Guestrin · Anupam Gupta -
2007 Spotlight: A Kernel Statistical Test of Independence »
Arthur Gretton · Kenji Fukumizu · Choon Hui Teo · Le Song · Bernhard Schölkopf · Alexander Smola -
2007 Poster: A Kernel Statistical Test of Independence »
Arthur Gretton · Kenji Fukumizu · Choon Hui Teo · Le Song · Bernhard Schölkopf · Alexander Smola -
2007 Poster: Selecting Observations against Adversarial Objectives »
Andreas Krause · H. Brendan McMahan · Carlos Guestrin · Anupam Gupta -
2006 Poster: Implicit Surfaces with Globally Regularised and Compactly Supported Basis Functions »
Christian Walder · Bernhard Schölkopf · Olivier Chapelle -
2006 Poster: Learning Dense 3D Correspondence »
Florian Steinke · Bernhard Schölkopf · Volker Blanz -
2006 Poster: A Local Learning Approach for Clustering »
Mingrui Wu · Bernhard Schölkopf -
2006 Poster: A Kernel Method for the Two-Sample-Problem »
Arthur Gretton · Karsten Borgwardt · Malte J Rasch · Bernhard Schölkopf · Alexander Smola -
2006 Poster: Correcting Sample Selection Bias by Unlabeled Data »
Jiayuan Huang · Alexander Smola · Arthur Gretton · Karsten Borgwardt · Bernhard Schölkopf -
2006 Spotlight: Correcting Sample Selection Bias by Unlabeled Data »
Jiayuan Huang · Alexander Smola · Arthur Gretton · Karsten Borgwardt · Bernhard Schölkopf -
2006 Talk: A Kernel Method for the Two-Sample-Problem »
Arthur Gretton · Karsten Borgwardt · Malte J Rasch · Bernhard Schölkopf · Alexander Smola -
2006 Poster: A Nonparametric Approach to Bottom-Up Visual Saliency »
Wolf Kienzle · Felix A Wichmann · Bernhard Schölkopf · Matthias Franz -
2006 Poster: Learning with Hypergraphs: Clustering, Classification, and Embedding »
Denny Zhou · Jiayuan Huang · Bernhard Schölkopf