BEGIN:VCALENDAR VERSION:2.0 PRODID:-//wp-events-plugin.com//7.2.3.1//EN TZID:Europe/Paris X-WR-TIMEZONE:Europe/Paris BEGIN:VEVENT UID:5502@i2m.univ-amu.fr DTSTART;TZID=Europe/Paris:20130425T140000 DTEND;TZID=Europe/Paris:20130425T150000 DTSTAMP:20241029T170811Z URL:https://www.i2m.univ-amu.fr/evenements/r-gribonval-inria-rennes-sparse -dictionary-learning-in-the-presence-of-noise-and-outliers/ SUMMARY: (...): R. Gribonval (INRIA Rennes) : Sparse dictionary learning in the presence of noise and outliers DESCRIPTION:: Sparse dictionary learning in the presence of noise and outli ers.\nBy Rémi Gribonval\\\, INRIA Rennes - Bretagne Atlantique.\n\nA popu lar approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms sele cted from a learned dictionary. While this paradigm has led to numerous em pirical successes in various fields ranging from image to audio processing \\\, there have only been a few theoretical arguments supporting these evi dences. In particular\\\, sparse coding\\\, or sparse dictionary learning\ \\, relies on a non-convex procedure whose local minima have not been full y analyzed yet. Considering a probabilistic model of sparse signals\\\, we show that\\\, with high probability\\\, sparse coding admits a local mini mum around the reference dictionary generating the signals. Our study take s into account the case of over-complete dictionaries and noisy signals\\\ , thus extending previous work limited to noiseless settings and/or under- complete dictionaries. The analysis we conduct is non-asymptotic and makes it possible to understand how the key quant\nities of the problem\\\, suc h as the coherence or the level of noise\\\, can scale with respect to the dimension of the signals\\\, the number of atoms\\\, the sparsity and the number of observations.\n\nThis is joint work with Rodolphe Jenatton & \; Francis Bach.\n\nDownload slides CATEGORIES:Séminaire,Signal et Apprentissage END:VEVENT BEGIN:VTIMEZONE TZID:Europe/Paris X-LIC-LOCATION:Europe/Paris BEGIN:DAYLIGHT DTSTART:20130331T030000 TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST END:DAYLIGHT END:VTIMEZONE END:VCALENDAR