Training a neural network on subsets of features, and then comparing it to the full neural network? Let's say I have a neural network with many features, but the features can be grouped into roughly 4 subsets A, B, C, D. I want to train the neural network using features A, B, C and compare how correlated the output is with the full neural network. It's kind of like cross validation, but using hold-out features instead of hold-out samples. The idea is to learn which features are affecting the output the most. Is this a viable idea, and is there any literature in this direction?
 A: It is a strange thing to do. 
The essence of Neural network is automatically do feature selection and transformation according to training samples. Why we want to do that manually?
One way I can think about the reason is doing manual feature hold out can be used to regularize the model to prevent over fitting. Is that your intention? If Yes, directly change the regularization parameter may be a better option.
Here is a tutorial for regularized neural network. The regularized cost function can be found around 3:15 in the video.
A: Agree with @hxd1011!
One occasion that I think it makes sense is when your dataset is not big enough for your neural network to figure out the relationships between inputs and output(s) by itself. In this case, you might want to try feeding the neural network with a subset of your inputs.
A: I have a similar issue. I have Calculation, based on a formula that depends on X which in turn depends on A, B, C, D as subset features. The prediction has to be made based on X.
A good analogy can be delivery time calculated by FedEx based on Postal Code. While the actual duration is based on statistical information of the postal code like rural or urban, distance from retail office, driving distance, road condition, service time etc. etc.
How can we turn this into a machine learning model from historical data and actual delivery duration experienced, without writing a big formula for calculation.
