This article presents novel methods and theories for estimation and inference about parameters in statistical models using machine learning for nuisance parameter estimation when data are dyadic. We propose a dyadic cross-fitting method to remove over-fitting biases under arbitrary dyadic dependence. Together with the use of Neyman orthogonal scores, this novel cross-fitting method enables root- n consistent estimation and inference robustly against dyadic dependence. We demonstrate its versatility by applying it to high-dimensional network formation models and reexamine the determinants of free trade agreements.