I have a rather straight-forward algorithm for finding the maximum-likelihood parameter of a probability distribution using sub-sampling. I'm fairly confident this algorithm is not novel and was hoping someone might recognize it from the following description. I will use biased coin-flipping as the example, as it is probably the easiest to understand.
Assume we have observed $N$ coin flips. Call the set of observations $S$. We would like to compute an approximation the Bernoulli parameter $p^*$ which maximizes the likelihood of the observed data without overfitting.
- Select a trial value $p$ for the parameter.
- Uniformly randomly select $n$ samples from $S$. Call this sub-sampled set $s$.
- Compute the maximum-likelihood parameter $\theta(s)$ for the sub-sample.
- Using $\lVert p - \theta(s) \rVert^2$ (or similar) as error, compute one step of gradient-descent to update $p$
- Repeat steps 2-4 until desired convergence
Can anyone recognize this as a specific case of a well-known algorithm?