Adaptive sampling

Adaptive sampling is a approach to <a href="/facts/Sampling_(statistics)/kIb01xdL">sampling</a> that uses heuristics to provide <a href="/facts/Efficiency_(statistics)/wTmgEqte">efficiency</a>. The term adaptive sampling represents a general approach to the problem of sampling, rather than being a special method itself. Meaning it can be combined with suitable other approaches/methods.
In some real world problems, sampling is implicitly/explicitly needed and used to obtain practical solutions. The sampling process will need resources and efficient usage of these resources is usually crucial. This is why there are multiple sampling methods instead of the brute-force approach.
Let f(x) be a function that is to be sampled. For simplicity, let C(x,s) be the cost for sample x given the previous set of samples s (For simplicity, we can assume that C(x,s) is constant since sampling cost usually does not depend on the previous samples and the sampling input x to the function. In time-critical systems, where the cost for each sample is strongly related to computation time; usually there are other parameters to the function C like the current time...); and G(x, s) be the gain (anti-cost) from sampling the function at x, given the set of previous samples s. For example, it can be assumed that G(x, s)=0 if x has already been sampled. The sampling problem is then maximizing our cumulative gain minus cumulative cost. Which usually comes down to sampling the function n times until the next sample's estimated/deterministic cost C(x,s) is smaller than the gain G(x,s) of that sample.
Adaptive sampling then assumes that given necessary knowledge about the problem, there is a theoretically optimal sequence s of samples that will maximize the information (gain) induced by that sample; and it is possible to estimate s using <a href="/facts/Heuristic/BcBEkv9c">heuristics</a>. Adaptive sampling usually focuses on estimating the next optimal sample input x, given the previous set of samples. Thus, being adaptive to the current knowledge about the function.

Adaptive sampling open-in-new

Adaptive sampling