# Correlation threshold for Neural Network features selection

I'm trying to do a correlation analysis between inputs and outputs inspecting the data in order to understand which input variables to include. What could be a threshold in the correlation value to consider a variable eligible to be an input for my Neural Network?

Given non-linearity of neural networks, I believe correlation analysis isn't a good way to estimate importance of variables. For example, imagine that you have 2 input variables - x1 and x2 - and following conditions hold:
• cor(x2, y) = 1 if x1 = 1
• cor(x2, y) = 0 otherwise
• x1 = 1 in 10% of cases
That is, x2 is a very good predictor for y, but only given that x1 = 1, which is the case only in 10% of data. Taking into account correlations of x1 and x2 separately won't expose this dependency, and you will most likely drop out both variables.