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.

翻译：摘要：数据样本间差异和/或相似性的定量评估，定义了与学习数据分布相关的优化问题，并塑造其形态。当前比较数据的方法在捕捉此类分布时往往存在局限性，或缺乏优化所需的理想数学特性（如光滑性、可微性或凸性）。本文提出一种受维纳滤波器理论启发的新方法，用于度量配对样本间的（不）相似性。维纳滤波器的卷积特性使我们能够以全局相关的方式全面比较数据样本。我们在四种机器学习应用中验证了该方法：数据压缩、医学图像插补、变换分类以及非参数生成建模。结果表明，与传统的均方误差类比实现相比，本方法在重建图像中实现了更高的分辨率，具有更优的感知质量和更高的数据保真度，同时具备对图像平移的鲁棒性。