There is not, because there could always be some underlying tricky generator that you just haven't discovered, and discovering that pattern is basically equival

There is not, because there could always be some underlying tricky generator that you just haven't discovered, and discovering that pattern is basically equivalent to solving the halting problem. (See https://en.wikipedia.org/wiki/Kolmogorov_complexity#Uncomputability_of_Kolmogorov_complexity https://en.wikipedia.org/wiki/Kolmogorov_complexity#Uncomput...) As a trivial example, if your dataset is one trillion binary digits of pi, it is essentially incompressible by any regular compressor, but you can fit a generator well under 1 kB.