{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/nonlinear-ica-using-auxiliary-variables-and","title":"Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning","arxiv_id":"1805.08651","date":"2018-05-22","proceeding":null,"authors":["Aapo Hyvarinen","Hiroaki Sasaki","Richard E. Turner"],"abstract":"Nonlinear ICA is a fundamental problem for unsupervised representation\nlearning, emphasizing the capacity to recover the underlying latent variables\ngenerating the data (i.e., identifiability). Recently, the very first\nidentifiability proofs for nonlinear ICA have been proposed, leveraging the\ntemporal structure of the independent components. Here, we propose a general\nframework for nonlinear ICA, which, as a special case, can make use of temporal\nstructure. It is based on augmenting the data by an auxiliary variable, such as\nthe time index, the history of the time series, or any other available\ninformation. We propose to learn nonlinear ICA by discriminating between true\naugmented data, or data in which the auxiliary variable has been randomized.\nThis enables the framework to be implemented algorithmically through logistic\nregression, possibly in a neural network. We provide a comprehensive proof of\nthe identifiability of the model as well as the consistency of our estimation\nmethod. The approach not only provides a general theoretical framework\ncombining and generalizing previously proposed nonlinear ICA models and\nalgorithms, but also brings practical advantages.","url_abs":"http://arxiv.org/abs/1805.08651v3","url_pdf":"http://arxiv.org/pdf/1805.08651v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"nonlinear-ica-using-auxiliary-variables-and","repo_url":"https://github.com/kondratevakate/fmri-component-analysis","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"contrastive-learning","task_name":"Contrastive Learning"},{"task_slug":"representation-learning","task_name":"Representation Learning"},{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"}],"methods":[{"method_slug":"ica","method_name":"ICA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1805.08651","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}