text: 9,22,1134342275474046979,883039700,Lenka Zdeborova,"Generative models are the new sparsity ... or even better actually as shown in our last paper: <LINK> <LINK> @carlonicolini84 You are perfectly right, the prior is based on the whole database, it does not know which particular picture was chosen to be the spike. @DanFrederiksen2 It is not denoising, but we do want to reconstruct the images as in denoising. The point is that the shirt is there better in the lower line than in the upper line which is the standard methods. The noisy data are not shown as they do not come in the form of picture.",https://arxiv.org/abs/1905.12385,"Using a low-dimensional parametrization of signals is a generic and powerful way to enhance performance in signal processing and statistical inference. A very popular and widely explored type of dimensionality reduction is sparsity; another type is generative modelling of signal distributions. Generative models based on neural networks, such as GANs or variational auto-encoders, are particularly performant and are gaining on applicability. In this paper we study spiked matrix models, where a low-rank matrix is observed through a noisy channel. This problem with sparse structure of the spikes has attracted broad attention in the past literature. Here, we replace the sparsity assumption by generative modelling, and investigate the consequences on statistical and algorithmic properties. We analyze the Bayes-optimal performance under specific generative models for the spike. In contrast with the sparsity assumption, we do not observe regions of parameters where statistical performance is superior to the best known algorithmic performance. We show that in the analyzed cases the approximate message passing algorithm is able to reach optimal performance. We also design enhanced spectral algorithms and analyze their performance and thresholds using random matrix theory, showing their superiority to the classical principal component analysis. We complement our theoretical results by illustrating the performance of the spectral algorithms when the spikes come from real datasets. ",The spiked matrix model with generative priors,3,"['Generative models are the new sparsity ... or even better actually as shown in our last paper: <LINK> <LINK>', '@carlonicolini84 You are perfectly right, the prior is based on the whole database, it does not know which particular picture was chosen to be the spike.', '@DanFrederiksen2 It is not denoising, but we do want to reconstruct the images as in denoising. The point is that the shirt is there better in the lower line than in the upper line which is the standard methods. The noisy data are not shown as they do not come in the form of picture.']",19,05,547