Are there generalised rules for generating heuristics from data?

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Heuristics seems to be more of an art than a science, like a gut-feel supported by data; I might be wrong. Are there algorithms for mathematically generating heuristics from data, like pruning a Bayesian network? Things like the Reichenbach Common Cause principle comes to mind. Is there a branch of mathematics that is specifically applicable here? Maybe a generalised way of expressing discrete data as a function in the way a Taylor series estimates a sine wave?

I'll do the reading I just need some pointers. Any help will be appreciated.