Approximating Stochastic Functions with Multivariate Outputs
A novel method for training generative machine learning models
You can reproduce the experiments in this article by cloning https://github.com/narroyo1/pmt.
The previous article in this series named Approximating stochastic functions introduced a novel method to train generative machine learning models capable of approximating any stochastic function with a single output variable. From this point on I will refer to this method as Pin Movement Training or PMT for short. This because of the analogy of placing pins on fabric and moving them that is used to illustrate it.
The method was described for functions with any number of inputs X but with only a single output Y. The present article will generalize PMT for functions with any number of outputs. A summary of the method will be provided and should be enough to understand how it works, but if you would like a more in depth description you can read the previous article.
The generalized method, for reasons you will learn below, utilizes an architecture similar to that of autoencoders. Because of this and because the uniform sampling distribution may be more convenient for many applications, I believe this method is a valid alternative to Variational Autoencoders.
Refresher of the original method
Let's say that we want to use the a neural network to approximate a stochastic function defined as
