Quantile and moment neural networks for learning functionals of distributions
This work addresses the challenge of learning distribution functionals for applications in probability and statistics, representing an incremental improvement over prior neural network approaches.
The authors tackled the problem of approximating functionals of distributions using neural networks, proposing quantile- and moment-based networks that outperform existing methods on univariate and bivariate distribution test cases.
We study news neural networks to approximate function of distributions in a probability space. Two classes of neural networks based on quantile and moment approximation are proposed to learn these functions and are theoretically supported by universal approximation theorems. By mixing the quantile and moment features in other new networks, we develop schemes that outperform existing networks on numerical test cases involving univariate distributions. For bivariate distributions, the moment neural network outperforms all other networks.