%PDF-1.3 1 0 obj << /Kids [ 4 0 R 5 0 R 6 0 R 7 0 R 8 0 R 9 0 R 10 0 R 11 0 R 12 0 R 13 0 R 14 0 R 15 0 R ] /Type /Pages /Count 12 >> endobj 2 0 obj << /Subject (Neural Information Processing Systems http\072\057\057nips\056cc\057) /Publisher (Curran Associates\054 Inc\056) /Language (en\055US) /Created (2019) /EventType (Poster) /Description-Abstract (Using a low\055dimensional parametrization of signals is a generic and powerful way to enhance performance in signal processing and statistical inference\056 A very popular and widely explored type of dimensionality reduction is sparsity\073 another type is generative modelling of signal distributions\056 Generative models based on neural networks\054 such as GANs or variational auto\055encoders\054 are particularly performant and are gaining on applicability\056 In this paper we study spiked matrix models\054 where a low\055rank matrix is observed through a noisy channel\056 This problem with sparse structure of the spikes has attracted broad attention in the past literature\056 Here\054 we replace the sparsity assumption by generative modelling\054 and investigate the consequences on statistical and algorithmic properties\056 We analyze the Bayes\055optimal performance under specific generative models for the spike\056 In contrast with the sparsity assumption\054 we do not observe regions of parameters where statistical performance is superior to the best known algorithmic performance\056 We show that in the analyzed cases the approximate message passing algorithm is able to reach optimal performance\056 We also design enhanced spectral algorithms and analyze their performance and thresholds using random matrix theory\054 showing their superiority to the classical principal component analysis\056 We complement our theoretical results by illustrating the performance of the spectral algorithms when the spikes come from real datasets\056) /Producer (PyPDF2) /Title (The spiked matrix model with generative priors) /Date (2019) /ModDate (D\07220200213020344\05508\04700\047) /Published (2019) /Type (Conference Proceedings) /firstpage (8366) /Book (Advances in Neural Information Processing Systems 32) /Description (Paper accepted and presented at the Neural Information Processing Systems Conference \050http\072\057\057nips\056cc\057\051) /Editors (H\056 Wallach and H\056 Larochelle and A\056 Beygelzimer and F\056 d\047Alch\351\055Buc and E\056 Fox and R\056 Garnett) /Author (Benjamin Aubin\054 Bruno Loureiro\054 Antoine Maillard\054 Florent Krzakala\054 Lenka Zdeborov\341) /lastpage (8377) >> endobj 3 0 obj << /Type /Catalog /Pages 1 0 R >> endobj 4 0 obj << /Contents 16 0 R /Parent 1 0 R /Resources 17 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 54 0 R 55 0 R 56 0 R 57 0 R 58 0 R 59 0 R 60 0 R 61 0 R ] /Type /Page >> endobj 5 0 obj << /Contents 62 0 R /Parent 1 0 R /Resources 63 0 R /MediaBox [ 0 0 612 792 ] /Annots [ 100 0 R 101 0 R 102 0 R 103 0 R ] /Type /Page >> endobj 6 0 obj << /Contents 104 0 R 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