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The theory of identifiable representation learning aims to build general-purpose methods that extract high-level latent (causal) factors from low-level sensory data. Most existing works focus on identifiable representation learning with observational data, relying on distributional assumptions on latent (causal) factors. However, in practice, we often also have access to interventional data for representation learning, e.g. from robotic manipulation experiments in robotics, from genetic perturbation experiments in genomics, or from electrical stimulation experiments in neuroscience. How can we leverage interventional data to help identify high-level latents? To this end, we explore the role of interventional data for identifiable representation learning in this work. We study the identifiability of latent causal factors with and without interventional data, under minimal distributional assumptions on latents. We prove that, if the true latent maps to the observed high-dimensional data via a polynomial function, then representation learning via minimizing standard reconstruction loss (used in autoencoders) can identify the true latents up to affine transformation. If we further have access to interventional data generated by hard $do$ interventions on some latents, then we can identify these intervened latents up to permutation, shift and scaling.
Author Information
Kartik Ahuja (Mila)
Yixin Wang (University of Michigan)
Divyat Mahajan (Microsoft Research)
I am a Research Fellow at Microsoft Research Lab India, where I work with Amit Sharma on Machine Learning and Causal Inference. Prior to joining MSR, I completed my undergraduate double major program in Mathematics and Computer Science from the Indian Institute of Technology, Kanpur. Interests: Machine Learning | Causal Inference | Explainability, Generalization and Robustness in Deep Learning
Yoshua Bengio (Mila / U. Montreal)
Yoshua Bengio is Full Professor in the computer science and operations research department at U. Montreal, scientific director and founder of Mila and of IVADO, Turing Award 2018 recipient, Canada Research Chair in Statistical Learning Algorithms, as well as a Canada AI CIFAR Chair. He pioneered deep learning and has been getting the most citations per day in 2018 among all computer scientists, worldwide. He is an officer of the Order of Canada, member of the Royal Society of Canada, was awarded the Killam Prize, the Marie-Victorin Prize and the Radio-Canada Scientist of the year in 2017, and he is a member of the NeurIPS advisory board and co-founder of the ICLR conference, as well as program director of the CIFAR program on Learning in Machines and Brains. His goal is to contribute to uncover the principles giving rise to intelligence through learning, as well as favour the development of AI for the benefit of all.
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2017 Poster: DPSCREEN: Dynamic Personalized Screening »
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2017 Poster: Variational Walkback: Learning a Transition Operator as a Stochastic Recurrent Net »
Anirudh Goyal · Nan Rosemary Ke · Surya Ganguli · Yoshua Bengio -
2017 Demonstration: A Deep Reinforcement Learning Chatbot »
Iulian Vlad Serban · Chinnadhurai Sankar · Mathieu Germain · Saizheng Zhang · Zhouhan Lin · Sandeep Subramanian · Taesup Kim · Michael Pieper · Sarath Chandar · Nan Rosemary Ke · Sai Rajeswar Mudumba · Alexandre de Brébisson · Jose Sotelo · Dendi A Suhubdy · Vincent Michalski · Joelle Pineau · Yoshua Bengio -
2017 Poster: GibbsNet: Iterative Adversarial Inference for Deep Graphical Models »
Alex Lamb · R Devon Hjelm · Yaroslav Ganin · Joseph Paul Cohen · Aaron Courville · Yoshua Bengio -
2017 Poster: Plan, Attend, Generate: Planning for Sequence-to-Sequence Models »
Caglar Gulcehre · Francis Dutil · Adam Trischler · Yoshua Bengio -
2017 Poster: Z-Forcing: Training Stochastic Recurrent Networks »
Anirudh Goyal · Alessandro Sordoni · Marc-Alexandre Côté · Nan Rosemary Ke · Yoshua Bengio -
2016 : Yoshua Bengio – Credit assignment: beyond backpropagation »
Yoshua Bengio -
2016 : From Brains to Bits and Back Again »
Yoshua Bengio · Terrence Sejnowski · Christos H Papadimitriou · Jakob H Macke · Demis Hassabis · Alyson Fletcher · Andreas Tolias · Jascha Sohl-Dickstein · Konrad P Koerding -
2016 : Yoshua Bengio : Toward Biologically Plausible Deep Learning »
Yoshua Bengio -
2016 : Panel on "Explainable AI" (Yoshua Bengio, Alessio Lomuscio, Gary Marcus, Stephen Muggleton, Michael Witbrock) »
Yoshua Bengio · Alessio Lomuscio · Gary Marcus · Stephen H Muggleton · Michael Witbrock -
2016 : Yoshua Bengio: From Training Low Precision Neural Nets to Training Analog Continuous-Time Machines »
Yoshua Bengio -
2016 Symposium: Deep Learning Symposium »
Yoshua Bengio · Yann LeCun · Navdeep Jaitly · Roger Grosse -
2016 Poster: Architectural Complexity Measures of Recurrent Neural Networks »
Saizheng Zhang · Yuhuai Wu · Tong Che · Zhouhan Lin · Roland Memisevic · Russ Salakhutdinov · Yoshua Bengio -
2016 Poster: Professor Forcing: A New Algorithm for Training Recurrent Networks »
Alex M Lamb · Anirudh Goyal · Ying Zhang · Saizheng Zhang · Aaron Courville · Yoshua Bengio -
2016 Poster: On Multiplicative Integration with Recurrent Neural Networks »
Yuhuai Wu · Saizheng Zhang · Ying Zhang · Yoshua Bengio · Russ Salakhutdinov -
2016 Poster: Binarized Neural Networks »
Itay Hubara · Matthieu Courbariaux · Daniel Soudry · Ran El-Yaniv · Yoshua Bengio -
2015 : RL for DL »
Yoshua Bengio -
2015 : Learning Representations for Unsupervised and Transfer Learning »
Yoshua Bengio -
2015 Symposium: Deep Learning Symposium »
Yoshua Bengio · Marc'Aurelio Ranzato · Honglak Lee · Max Welling · Andrew Y Ng -
2015 Poster: Attention-Based Models for Speech Recognition »
Jan K Chorowski · Dzmitry Bahdanau · Dmitriy Serdyuk · Kyunghyun Cho · Yoshua Bengio -
2015 Poster: Equilibrated adaptive learning rates for non-convex optimization »
Yann Dauphin · Harm de Vries · Yoshua Bengio -
2015 Spotlight: Equilibrated adaptive learning rates for non-convex optimization »
Yann Dauphin · Harm de Vries · Yoshua Bengio -
2015 Spotlight: Attention-Based Models for Speech Recognition »
Jan K Chorowski · Dzmitry Bahdanau · Dmitriy Serdyuk · Kyunghyun Cho · Yoshua Bengio -
2015 Poster: A Recurrent Latent Variable Model for Sequential Data »
Junyoung Chung · Kyle Kastner · Laurent Dinh · Kratarth Goel · Aaron Courville · Yoshua Bengio -
2015 Poster: BinaryConnect: Training Deep Neural Networks with binary weights during propagations »
Matthieu Courbariaux · Yoshua Bengio · Jean-Pierre David -
2015 Tutorial: Deep Learning »
Geoffrey E Hinton · Yoshua Bengio · Yann LeCun -
2014 Workshop: Second Workshop on Transfer and Multi-Task Learning: Theory meets Practice »
Urun Dogan · Tatiana Tommasi · Yoshua Bengio · Francesco Orabona · Marius Kloft · Andres Munoz · Gunnar Rätsch · Hal Daumé III · Mehryar Mohri · Xuezhi Wang · Daniel Hernández-lobato · Song Liu · Thomas Unterthiner · Pascal Germain · Vinay P Namboodiri · Michael Goetz · Christopher Berlind · Sigurd Spieckermann · Marta Soare · Yujia Li · Vitaly Kuznetsov · Wenzhao Lian · Daniele Calandriello · Emilie Morvant -
2014 Workshop: Deep Learning and Representation Learning »
Andrew Y Ng · Yoshua Bengio · Adam Coates · Roland Memisevic · Sharanyan Chetlur · Geoffrey E Hinton · Shamim Nemati · Bryan Catanzaro · Surya Ganguli · Herbert Jaeger · Phil Blunsom · Leon Bottou · Volodymyr Mnih · Chen-Yu Lee · Rich M Schwartz -
2014 Workshop: OPT2014: Optimization for Machine Learning »
Zaid Harchaoui · Suvrit Sra · Alekh Agarwal · Martin Jaggi · Miro Dudik · Aaditya Ramdas · Jean Lasserre · Yoshua Bengio · Amir Beck -
2014 Poster: How transferable are features in deep neural networks? »
Jason Yosinski · Jeff Clune · Yoshua Bengio · Hod Lipson -
2014 Poster: Identifying and attacking the saddle point problem in high-dimensional non-convex optimization »
Yann N Dauphin · Razvan Pascanu · Caglar Gulcehre · Kyunghyun Cho · Surya Ganguli · Yoshua Bengio -
2014 Poster: Generative Adversarial Nets »
Ian Goodfellow · Jean Pouget-Abadie · Mehdi Mirza · Bing Xu · David Warde-Farley · Sherjil Ozair · Aaron Courville · Yoshua Bengio -
2014 Poster: On the Number of Linear Regions of Deep Neural Networks »
Guido F Montufar · Razvan Pascanu · Kyunghyun Cho · Yoshua Bengio -
2014 Demonstration: Neural Machine Translation »
Bart van Merriënboer · Kyunghyun Cho · Dzmitry Bahdanau · Yoshua Bengio -
2014 Oral: How transferable are features in deep neural networks? »
Jason Yosinski · Jeff Clune · Yoshua Bengio · Hod Lipson -
2014 Poster: Iterative Neural Autoregressive Distribution Estimator NADE-k »
Tapani Raiko · Yao Li · Kyunghyun Cho · Yoshua Bengio -
2013 Workshop: Deep Learning »
Yoshua Bengio · Hugo Larochelle · Russ Salakhutdinov · Tomas Mikolov · Matthew D Zeiler · David Mcallester · Nando de Freitas · Josh Tenenbaum · Jian Zhou · Volodymyr Mnih -
2013 Workshop: Output Representation Learning »
Yuhong Guo · Dale Schuurmans · Richard Zemel · Samy Bengio · Yoshua Bengio · Li Deng · Dan Roth · Kilian Q Weinberger · Jason Weston · Kihyuk Sohn · Florent Perronnin · Gabriel Synnaeve · Pablo R Strasser · julien audiffren · Carlo Ciliberto · Dan Goldwasser -
2013 Poster: Multi-Prediction Deep Boltzmann Machines »
Ian Goodfellow · Mehdi Mirza · Aaron Courville · Yoshua Bengio -
2013 Poster: Generalized Denoising Auto-Encoders as Generative Models »
Yoshua Bengio · Li Yao · Guillaume Alain · Pascal Vincent -
2013 Poster: Stochastic Ratio Matching of RBMs for Sparse High-Dimensional Inputs »
Yann Dauphin · Yoshua Bengio -
2012 Workshop: Deep Learning and Unsupervised Feature Learning »
Yoshua Bengio · James Bergstra · Quoc V. Le -
2011 Workshop: Big Learning: Algorithms, Systems, and Tools for Learning at Scale »
Joseph E Gonzalez · Sameer Singh · Graham Taylor · James Bergstra · Alice Zheng · Misha Bilenko · Yucheng Low · Yoshua Bengio · Michael Franklin · Carlos Guestrin · Andrew McCallum · Alexander Smola · Michael Jordan · Sugato Basu -
2011 Workshop: Deep Learning and Unsupervised Feature Learning »
Yoshua Bengio · Adam Coates · Yann LeCun · Nicolas Le Roux · Andrew Y Ng -
2011 Oral: The Manifold Tangent Classifier »
Salah Rifai · Yann N Dauphin · Pascal Vincent · Yoshua Bengio · Xavier Muller -
2011 Poster: Shallow vs. Deep Sum-Product Networks »
Olivier Delalleau · Yoshua Bengio -
2011 Poster: The Manifold Tangent Classifier »
Salah Rifai · Yann N Dauphin · Pascal Vincent · Yoshua Bengio · Xavier Muller -
2011 Poster: Algorithms for Hyper-Parameter Optimization »
James Bergstra · Rémi Bardenet · Yoshua Bengio · Balázs Kégl -
2011 Poster: On Tracking The Partition Function »
Guillaume Desjardins · Aaron Courville · Yoshua Bengio -
2010 Workshop: Deep Learning and Unsupervised Feature Learning »
Honglak Lee · Marc'Aurelio Ranzato · Yoshua Bengio · Geoffrey E Hinton · Yann LeCun · Andrew Y Ng -
2009 Poster: Slow, Decorrelated Features for Pretraining Complex Cell-like Networks »
James Bergstra · Yoshua Bengio -
2009 Poster: An Infinite Factor Model Hierarchy Via a Noisy-Or Mechanism »
Aaron Courville · Douglas Eck · Yoshua Bengio -
2009 Session: Debate on Future Publication Models for the NIPS Community »
Yoshua Bengio -
2007 Poster: Augmented Functional Time Series Representation and Forecasting with Gaussian Processes »
Nicolas Chapados · Yoshua Bengio -
2007 Poster: Learning the 2-D Topology of Images »
Nicolas Le Roux · Yoshua Bengio · Pascal Lamblin · Marc Joliveau · Balázs Kégl -
2007 Spotlight: Augmented Functional Time Series Representation and Forecasting with Gaussian Processes »
Nicolas Chapados · Yoshua Bengio -
2007 Poster: Topmoumoute Online Natural Gradient Algorithm »
Nicolas Le Roux · Pierre-Antoine Manzagol · Yoshua Bengio -
2006 Poster: Greedy Layer-Wise Training of Deep Networks »
Yoshua Bengio · Pascal Lamblin · Dan Popovici · Hugo Larochelle -
2006 Talk: Greedy Layer-Wise Training of Deep Networks »
Yoshua Bengio · Pascal Lamblin · Dan Popovici · Hugo Larochelle