Is there a known relationship between the amount of information gain that comes from new data added to a dataset?
for eg: If I have a plant watering system that tells me:
- An integer of how wet the ground is (like a moisture sensor) and 2) a regular measurement time
I have a new 'feature' 3) The change in moisture content over time.
If I start recording 4) How much water is added for each time interval, I now have 5) How much water is being consumed (in some way).
If I add 6) ambient temperature information, I will start to see 7) water consumed by soil/plant vs 8) evaporated.
at this point I can start to deduct 9) an evaporation coefficient relative to ambient temp, and from that, I can start to generate 10) how much water the plant uses per day but also things like 11) how much water can keep the ground cool enough to reduce evaporation (perhaps).
So at some point, the amount of inferred information becomes greater than the number of inputs supplied.
Is there some known formula to understand how much information gain adding new data supplies, regardless of its eventual relevance?