Beyond Mean-Squared-Error, Examining the utility of training generative models of images with a loss function based on Mahalanobis distance
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2018-07-10
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en
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Abstract
Generative models of high-dimensional data, such as images or audio, are an active field
of research in machine learning. Traditionally, modelling images has been treated as a regression
task, such that models are optimized to minimize the Mean-Square-Error (MSE)
loss function, that is, the average squared euclidean distance between model outputs and
data samples. A significant short-coming of MSE is that it assumes that pixels are independent
of one another, whereas natural images contain strict covariance patterns between
pixels (edges, textures, etc.). We examine the utility of learning the parameters of a loss
function based on Mahalanobis distance, which takes pixel covariance into account, as an
alternative to MSE. The Mahalanobis-based loss function is implemented using a Gaussian
mixture model (GMM) with full covariance matrices, which is fitted to the MNIST
dataset of hand-written digits. In order to better isolate the covariance structures learned
by the GMM, the eigenvectors of each component’s covariance matrix are extracted. Additional
mixture models are learned over the extracted eigenvectors, in order to sample
the learned covariance structures directly, improving the perceptual quality of generated
images somewhat. A quantitative comparison of the base and modified GMMs indicates
that the proposed modifications reduce over-fitting (measured by the difference between
train-set and test-set log-likelihood), however, additional research is needed to further improve
sample quality and the model’s fit to the data.
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Faculteit der Sociale Wetenschappen