Improving data gaussianity using neural networks

Question

I wanted to know if there is a way to use neural networks (deep neural networks or autoencoders) for a data gaussianization. I wonder how could the output data distribution be monitored and integrated in the cost function (minimize the reconstruction error and maximize gaussianity). Should there be some kind of sampling or is there another way ? I couldn't find any paper treating this kind of problems.

& thank you !

Answer 1

Let's assume:

• Gaussianized data has a normal distribution with zero mean and unit variance
• The output layer uses a softmax layer
• The cost function is cross entropy which measures how much the distribution of the output layer is different from the desired output distribution

Now if the desired output is a sample from Gaussian distribution and you run the back-propagation algorithm with cross entropy cost function, the network weight will be trained in such a way that the output distribution is as close as possible to normal distribution.