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用于神经网络贝叶斯学习与 MCMC 的迹类高斯先验AI 解读

Abstract This paper introduces a new neural network based prior for real valued functions. Each weight and bias of the neural network has an independent Gaussian prior, with the key novelty that the variances decrease in the width of the network in such a way that the resulting function is well defined in the limit of an infinite width network. We show that the induced posterior over functions is amenable to Monte Carlo sampling using Hilbert space Markov chain Monte Carlo…

非可微先验下贝叶斯推断的梯度型 MCMCAI 解读

The use of nondifferentiable priors in Bayesian statistics has become increasingly popular, in particular in Bayesian imaging analysis. Current state-of-the-art methods are approximate in the sense that they replace the posterior with a smooth approximation via Moreau-Yosida envelopes, and apply gradient-based discretized diffusions to sample from the resulting distribution. We characterize the error of the Moreau-Yosida approximation and propose a novel implementation using…