  Quantitative evaluations of differences and/or similarities between data
samples define and shape optimisation problems associated with learning data
distributions. Current methods to compare data often suffer from limitations in
capturing such distributions or lack desirable mathematical properties for
optimisation (e.g. smoothness, differentiability, or convexity). In this paper,
we introduce a new method to measure (dis)similarities between paired samples
inspired by Wiener-filter theory. The convolutional nature of Wiener filters
allows us to comprehensively compare data samples in a globally correlated way.
We validate our approach in four machine learning applications: data
compression, medical imaging imputation, translated classification, and
non-parametric generative modelling. Our results demonstrate increased
resolution in reconstructed images with better perceptual quality and higher
data fidelity, as well as robustness against translations, compared to
conventional mean-squared-error analogue implementations.
