2021
DOI: 10.48550/arxiv.2107.12466
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High-Dimensional Distribution Generation Through Deep Neural Networks

Abstract: We show that every d-dimensional probability distribution of bounded support can be generated through deep ReLU networks out of a 1-dimensional uniform input distribution. What is more, this is possible without incurring a cost-in terms of approximation error measured in Wasserstein-distance-relative to generating the d-dimensional target distribution from d independent random variables. This is enabled by a vast generalization of the space-filling approach discovered in [2]. The construction we propose elicit… Show more

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