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.
The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICA
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Max Planck Institute for Biological Cybernetics（马克斯·普朗克生物控制论研究所）；University of Cambridge（剑桥大学）；Max Planck ETH Center for Learning Systems（马克斯·普朗克-苏黎世联邦理工学院学习系统中心）；ETH Zürich（苏黎世联邦理工学院）
Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning
The Gatsby Unit UCL（伦敦大学学院盖茨比研究组）；Dept. of CS and HIIT Univ. Helsinki（赫尔辛基大学计算机科学系及赫尔辛基信息技术研究所）；Div. of Info. Sci. NAIST（奈良先端科学技术大学院大学信息科学部）；Univ. Cambridge & Microsoft Research（剑桥大学及微软研究院）
Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICA
University of Helsinki（赫尔辛基大学）；Télécom SudParis（南巴黎电信学院）；Institut Polytechnique de Paris（巴黎理工学院）；Université Côte d’Azur（蔚蓝海岸大学）；CNRS（法国国家科学研究中心）；University of Cambridge（剑桥大学）；Université Paris-Saclay（巴黎萨克雷大学）
Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA
Mila（米拉人工智能研究所）；DIRO, Université de Montréal（蒙特利尔大学计算机科学与运筹学系）；ServiceNow Research（ServiceNow研究院）；Tübingen AI Center, University of Tübingen（蒂宾根大学蒂宾根人工智能中心）；Google Research（谷歌研究院）
An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysis
Carnegie Mellon University（卡内基梅隆大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；International Max Planck Research School for Intelligent Systems (IMPRS-IS)（马克斯·普朗克智能系统国际研究学校（IMPRS-IS））；European Laboratory for Learning and Intelligent Systems (ELLIS)（欧洲学习与智能系统实验室（ELLIS））
Concept Modulation Models: A Unified Framework for Identifiability and Extrapolation
Department of Statistics and Data Science, Carnegie Mellon University（卡内基梅隆大学统计与数据科学系）；Machine Learning Department, Carnegie Mellon University（卡内基梅隆大学机器学习系）
Encoding Domain Knowledge in Multi-view Latent Variable Models: A Bayesian Approach with Structured Sparsity
German Cancer Research Center (DKFZ)（德国癌症研究中心（DKFZ））；German Cancer Consortium (DKTK)（德国癌症联盟（DKTK））；Goethe University Frankfurt（法兰克福歌德大学）；Frankfurt Cancer Institute（法兰克福癌症研究所）
Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts
Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；The University of Melbourne（墨尔本大学）；Peking University（北京大学）；Carnegie Mellon University（卡内基梅隆大学）
Decoding the Encoding of Functional Brain Networks: an fMRI Classification Comparison of Non-negative Matrix Factorization (NMF), Independent Component Analysis (ICA), and Sparse Coding Algorithms
A Sparsity Principle for Partially Observable Causal Representation Learning
University of Amsterdam（阿姆斯特丹大学）；Institute of Science and Technology Austria（奥地利科技学院）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Samsung - SAIT AI Lab, Montreal（三星SAIT AI实验室（蒙特利尔））；Mila, Université de Montréal（蒙特利尔大学Mila研究所）；ServiceNow Research（ServiceNow研究院）；Seminar for Statistics, ETH Zürich（苏黎世联邦理工学院统计研究所）
SPARLING: Learning Latent Representations with Extremely Sparse Activations
Department of Electrical Engineering and Computer Science（电气工程与计算机科学系）；Massachusetts Institute of Technology（麻省理工学院）；Department of Computer and Information Science（计算机与信息科学系）；University of Pennsylvania（宾夕法尼亚大学）
Synergy Between Sufficient Changes and Sparse Mixing Procedure for Disentangled Representation Learning
Carnegie Mellon University（卡内基梅隆大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Guangdong University of Technology（广东工业大学）
Towards Identifiability of Hierarchical Temporal Causal Representation Learning
Carnegie Mellon University（卡内基梅隆大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Guangdong University of Technology（广东技术大学）；University of California San Diego（加州大学圣地亚哥分校）
Counterfactual Generation with Identifiability Guarantees
Mohamed Bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；King’s College London（伦敦国王学院）；University of Warwick（华威大学）；Carnegie Mellon University（卡内基梅隆大学）
Estimation of Structural Causal Model via Sparsely Mixing Independent Component Analysis
The Graduate University for Advanced Studies (SOKENDAI)（综合研究大学院大学）；The Institute of Statistical Mathematics（统计数理研究所）；RIKEN Center for Advanced Intelligence Project (AIP)（日本理化学研究所先进智能研究中心）
