I'm trying to get a value for a correlation between a function input and its output. One brute force way to get this is to sample the entire space and find the standard deviation of the resulting outputs.

Is there a less expensive way to find this correlation, perhaps by differentiating the equation?

For more context, I'm trying to see how much a particular input affects each output of a neural network (nothing to do with tuning weights).

  • $\begingroup$ You're probably trying to understand if your neural network represents or not a "smooth function". You may also want to look at terms such as "sensitivity" and "robustness" in the context of neural networks. Maybe these 3 terms will help you find an answer to your question, which you can post below once you find it. If these terms aren't unrelated to your question, please, explain why! $\endgroup$ – nbro Apr 30 at 15:47
  • $\begingroup$ @nbro Not really. I'm just trying to see how important particular inputs are to particular outputs $\endgroup$ – Tobi Apr 30 at 21:35
  • $\begingroup$ You need to define "important" or what you mean by "correlation". Why would the "standard deviation" help in your case? $\endgroup$ – nbro Apr 30 at 22:42
  • $\begingroup$ @nbro to see how much the output deviates as we vary the input. $\endgroup$ – Tobi Apr 30 at 22:43

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