A Bayesian Perspective on Noise2Noise: Theory and Extensions

The time and resource costs of obtaining pristine training data in machine learning are high. In signal recovery tasks, Noise2Noise proposed by Lehtinen et al. aims to reduce the data cost by learning the regression over two noisy measurements corresponding to the same latent variable. Close examination shows that Lehtinen's original derivation requires a strictly "frequentist" conjecture—i.e. deterministic treatment of the latent variable. This paper presents a Bayesian counter-piece to the original Noise2Noise formulation, with a fully stochastic treatment of the latent variable. We propose to extend Noise2Noise further to unbiased estimate of risk (Noise2Noise2MSE), covariance analysis (Noise2Noise2Cov), and minimum mean squared error estimate (Noise2Noise2MMSE), all derived from pairs of noisy measurements only.