Constructive universal distribution generation through deep ReLU networks
We present an explicit deep network construction that transforms uniformly distributed one-dimensional noise into an arbitrarily close approximation of any two-dimensional target distribution of finite differential entropy and Lipschitz-continuous pdf. The key ingredient of our design is a generalization of the "space-filling'' property of sawtooth functions introduced in (Bailey & Telgarsky, 2018). We elicit the importance of depth in our construction in driving the Wasserstein distance between the target distribution and its approximation realized by the proposed neural network to zero. Finally, we outline how our construction can be extended to output distributions of arbitrary dimension.
PDF ICML 2020 PDFTasks
Datasets
Add Datasets
introduced or used in this paper
Results from the Paper
Submit
results from this paper
to get state-of-the-art GitHub badges and help the
community compare results to other papers.
Methods
No methods listed for this paper. Add
relevant methods here
