  Estimation and inference on causal parameters is typically reduced to a
generalized method of moments problem, which involves auxiliary functions that
correspond to solutions to a regression or classification problem. Recent line
of work on debiased machine learning shows how one can use generic machine
learning estimators for these auxiliary problems, while maintaining asymptotic
normality and root-$n$ consistency of the target parameter of interest, while
only requiring mean-squared-error guarantees from the auxiliary estimation
algorithms. The literature typically requires that these auxiliary problems are
fitted on a separate sample or in a cross-fitting manner. We show that when
these auxiliary estimation algorithms satisfy natural leave-one-out stability
properties, then sample splitting is not required. This allows for sample
re-use, which can be beneficial in moderately sized sample regimes. For
instance, we show that the stability properties that we propose are satisfied
for ensemble bagged estimators, built via sub-sampling without replacement, a
popular technique in machine learning practice.
