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.

通过 Wiener 滤波器理论，本文介绍了一种新的方法来计算配对样本之间的相似度或差异，可在全局相关的方式下全面比较数据样本，并在数据压缩、医学影像填充、翻译分类和非参数生成建模等四个机器学习应用中得到验证。实验结果表明，与常规均方误差模拟实现相比，重建图像具有更高的感知质量和更高的数据保真度，并且对平移具有鲁棒性。