Say we have a dataset that has several continuous features, 2 time features, and binary classes. I want to be clear, this isn't a time series dataset, but time snapshots of when each observation occurred is recorded. The dataset looks like this:
class t1 t2 x1 x2 x3 x4 ... 0 735 311 0.345 0.123 -0.32 132 1 93 101 0.89 1.34 9.345 834 ... ... ... ... ... ... ... ...
t1,t2 as time features and
x1,...xn as the continuous features.
Uncaptured explicitly in the dataset, is the difference between times
t1-t2). This metric is important because if the absolute difference
t1-t2 is less than 20, the class will be 1 more than 90% of the time. In other words, the constructed feature
t1-t2 is a very good indicator of an observations class.
Will a neural network classifier trained on the original, unchanged dataset above, capture the relationship between
t2 to increase model accuracy?
More broadly speaking, do neural networks capture relationships between features?
I appreciate that in this hypothetical case, if I knew apriori about the time difference indicator, I would engineer a new feature that would be the absolute difference in time, and train the network on a dataset with this new feature. But for the sake of argument, say I do not know this in advance.