Timezone: »
Nonlinear independent component analysis (ICA) aims to recover the underlying independent latent sources from their observable nonlinear mixtures. How to make the nonlinear ICA model identifiable up to certain trivial indeterminacies is a long-standing problem in unsupervised learning. Recent breakthroughs reformulate the standard independence assumption of sources as conditional independence given some auxiliary variables (e.g., class labels and/or domain/time indexes) as weak supervision or inductive bias. However, nonlinear ICA with unconditional priors cannot benefit from such developments. We explore an alternative path and consider only assumptions on the mixing process, such as Structural Sparsity. We show that under specific instantiations of such constraints, the independent latent sources can be identified from their nonlinear mixtures up to a permutation and a component-wise transformation, thus achieving nontrivial identifiability of nonlinear ICA without auxiliary variables. We provide estimation methods and validate the theoretical results experimentally. The results on image data suggest that our conditions may hold in a number of practical data generating processes.
Author Information
Yujia Zheng (Carnegie Mellon University)
Ignavier Ng (Carnegie Mellon University)
Kun Zhang (CMU & MBZUAI)
More from the Same Authors
-
2022 : Tier Balancing: Towards Dynamic Fairness over Underlying Causal Factors »
Zeyu Tang · Yatong Chen · Yang Liu · Kun Zhang -
2022 : Scalable Causal Discovery with Score Matching »
Francesco Montagna · Nicoletta Noceti · Lorenzo Rosasco · Kun Zhang · Francesco Locatello -
2023 Poster: On the Identifiability of Sparse ICA without Assuming Non-Gaussianity »
Ignavier Ng · Yujia Zheng · Xinshuai Dong · Kun Zhang -
2023 Poster: Generalizing Nonlinear ICA Beyond Structural Sparsity »
Yujia Zheng · Kun Zhang -
2023 Poster: Counterfactual Generation with Identifiability Guarantee »
hanqi yan · Lingjing Kong · Lin Gui · Yuejie Chi · Eric Xing · Yulan He · Kun Zhang -
2023 Poster: Temporally Disentangled Representation Learning under Unknown Nonstationarity »
Xiangchen Song · Weiran Yao · Yewen Fan · Xinshuai Dong · Guangyi Chen · Juan Carlos Niebles · Eric Xing · Kun Zhang -
2023 Poster: Identification of Nonlinear Latent Hierarchical Models »
Lingjing Kong · Biwei Huang · Feng Xie · Eric Xing · Yuejie Chi · Kun Zhang -
2023 Poster: Subspace Identification for Multi-Source Domain Adaptation »
Zijian Li · Ruichu Cai · Guangyi Chen · Boyang Sun · Zhifeng Hao · Kun Zhang -
2023 Poster: Learning World Models with Identifiable Factorization »
Yuren Liu · Biwei Huang · Zhengmao Zhu · Honglong Tian · Mingming Gong · Yang Yu · Kun Zhang -
2023 Oral: Generalizing Nonlinear ICA Beyond Structural Sparsity »
Yujia Zheng · Kun Zhang -
2022 Spotlight: Latent Hierarchical Causal Structure Discovery with Rank Constraints »
Biwei Huang · Charles Jia Han Low · Feng Xie · Clark Glymour · Kun Zhang -
2022 : Kun Zhang: Causal Principles Meet Deep Learning: Successes and Challenges. »
Kun Zhang -
2022 : Kun Zhang: Causal Principles Meet Deep Learning: Successes and Challenges. »
Kun Zhang -
2022 Workshop: Causal Machine Learning for Real-World Impact »
Nick Pawlowski · Jeroen Berrevoets · Caroline Uhler · Kun Zhang · Mihaela van der Schaar · Cheng Zhang -
2022 Poster: Independence Testing-Based Approach to Causal Discovery under Measurement Error and Linear Non-Gaussian Models »
Haoyue Dai · Peter Spirtes · Kun Zhang -
2022 Poster: Latent Hierarchical Causal Structure Discovery with Rank Constraints »
Biwei Huang · Charles Jia Han Low · Feng Xie · Clark Glymour · Kun Zhang -
2022 Poster: MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Models »
Erdun Gao · Ignavier Ng · Mingming Gong · Li Shen · Wei Huang · Tongliang Liu · Kun Zhang · Howard Bondell -
2022 Poster: Causal Discovery in Linear Latent Variable Models Subject to Measurement Error »
Yuqin Yang · AmirEmad Ghassami · Mohamed Nafea · Negar Kiyavash · Kun Zhang · Ilya Shpitser -
2022 Poster: Unsupervised Image-to-Image Translation with Density Changing Regularization »
Shaoan Xie · Qirong Ho · Kun Zhang -
2022 Poster: Factored Adaptation for Non-Stationary Reinforcement Learning »
Fan Feng · Biwei Huang · Kun Zhang · Sara Magliacane -
2022 Poster: Counterfactual Fairness with Partially Known Causal Graph »
Aoqi Zuo · Susan Wei · Tongliang Liu · Bo Han · Kun Zhang · Mingming Gong -
2022 Poster: Temporally Disentangled Representation Learning »
Weiran Yao · Guangyi Chen · Kun Zhang -
2022 Poster: Truncated Matrix Power Iteration for Differentiable DAG Learning »
Zhen Zhang · Ignavier Ng · Dong Gong · Yuhang Liu · Ehsan Abbasnejad · Mingming Gong · Kun Zhang · Javen Qinfeng Shi -
2021 Poster: Reliable Causal Discovery with Improved Exact Search and Weaker Assumptions »
Ignavier Ng · Yujia Zheng · Jiji Zhang · Kun Zhang -
2020 : Oral: Ignavier Ng »
Ignavier Ng -
2020 Workshop: Causal Discovery and Causality-Inspired Machine Learning »
Biwei Huang · Sara Magliacane · Kun Zhang · Danielle Belgrave · Elias Bareinboim · Daniel Malinsky · Thomas Richardson · Christopher Meek · Peter Spirtes · Bernhard Schölkopf -
2020 Poster: On the Role of Sparsity and DAG Constraints for Learning Linear DAGs »
Ignavier Ng · AmirEmad Ghassami · Kun Zhang -
2019 : Coffee break, posters, and 1-on-1 discussions »
Julius von Kügelgen · David Rohde · Candice Schumann · Grace Charles · Victor Veitch · Vira Semenova · Mert Demirer · Vasilis Syrgkanis · Suraj Nair · Aahlad Puli · Masatoshi Uehara · Aditya Gopalan · Yi Ding · Ignavier Ng · Khashayar Khosravi · Eli Sherman · Shuxi Zeng · Aleksander Wieczorek · Hao Liu · Kyra Gan · Jason Hartford · Miruna Oprescu · Alexander D'Amour · Jörn Boehnke · Yuta Saito · Théophile Griveau-Billion · Chirag Modi · Shyngys Karimov · Jeroen Berrevoets · Logan Graham · Imke Mayer · Dhanya Sridhar · Issa Dahabreh · Alan Mishler · Duncan Wadsworth · Khizar Qureshi · Rahul Ladhania · Gota Morishita · Paul Welle -
2017 Poster: Learning Causal Structures Using Regression Invariance »
AmirEmad Ghassami · Saber Salehkaleybar · Negar Kiyavash · Kun Zhang