Consider the following situation: we wish to build a confidence interval (CI) for a real-valued pathwise differentiable parameter Ψ evaluated at a law P, ψ = Ψ(P), from a data set O_1, …, O_N of independent random variables drawn from P but, as is often the case nowadays, N is so large that we will not be able to use all data. To overcome this computational hurdle, we decide (a) to select n among N observations randomly with unequal inclusion probabilities and (b) to adapt TMLE from the smaller data set that results from the selection.