Neighborhood Stability in Double/Debiased Machine Learning with Dependent Data

This paper studies double/debiased machine learning (DML) methods applied to weakly dependent data. We allow observations to be situated in a general metric space that accommodates spatial and network data. Existing work implements cross-fitting by excluding from the training fold observations sufficiently close to the evaluation fold. We find in simulations that this can result in exceedingly small training fold sizes, particularly with network data. We therefore seek to establish the validity of DML without cross-fitting, building on recent work by Chen et al. (2022). They study i.i.d. data and require the machine learner to satisfy a natural stability condition requiring insensitivity to data perturbations that resample a single observation. We extend these results to dependent data by strengthening stability to "neighborhood stability," which requires insensitivity to resampling observations in any slowly growing neighborhood. We show that existing results on the stability of various machine learners can be adapted to verify neighborhood stability.