BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Aapo Hyvärinen (University of Helsinki) DTSTART:20200804T163000Z DTEND:20200804T174500Z DTSTAMP:20260423T021059Z UID:IASML/16 DESCRIPTION:Title: N onlinear independent component analysis\nby Aapo Hyvärinen (Universit y of Helsinki) as part of IAS Seminar Series on Theoretical Machine Learni ng\n\n\nAbstract\nUnsupervised learning\, in particular learning general n onlinear representations\, is one of the deepest problems in machine learn ing. Estimating latent quantities in a generative model provides a princip led framework\, and has been successfully used in the linear case\, e.g. w ith independent component analysis (ICA) and sparse coding. However\, exte nding ICA to the nonlinear case has proven to be extremely difficult: A st raight-forward extension is unidentifiable\, i.e. it is not possible to re cover those latent components that actually generated the data. Here\, we show that this problem can be solved by using additional information eithe r in the form of temporal structure or an additional observed variable. We start by formulating two generative models in which the data is an arbitr ary but invertible nonlinear transformation of time series (components) wh ich are statistically independent of each other. Drawing from the theory o f linear ICA\, we formulate two distinct classes of temporal structure of the components which enable identification\, i.e. recovery of the original independent components. We further generalize the framework to the case w here instead of temporal structure\, an additional "auxiliary" variable is observed and used by means of conditioning (e.g. audio in addition to vid eo). Our methods are closely related to "self-supervised" methods heuristi cally proposed in computer vision\, and also provide a theoretical foundat ion for such methods in terms of estimating a latent-variable model. Likew ise\, we show how variants of deep latent-variable models such as VAE's ca n be seen as nonlinear ICA\, and made identifiable by suitable conditionin g.\n LOCATION:https://researchseminars.org/talk/IASML/16/ END:VEVENT END:VCALENDAR