Convolve and Conquer: Data Comparison with Wiener Filters
This addresses limitations in data comparison methods for machine learning applications, offering improved mathematical properties and performance, though it appears incremental as it builds on existing filter theory.
The paper tackled the problem of comparing data samples for optimization by introducing a Wiener-filter-inspired method, which demonstrated increased resolution in reconstructed images with better perceptual quality and higher data fidelity, as well as robustness against translations in applications like data compression and medical imaging.
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.