  This paper provides estimation and inference methods for the best linear
predictor (approximation) of a structural function, such as conditional average
structural and treatment effects, and structural derivatives, based on modern
machine learning (ML) tools. We represent this structural function as a
conditional expectation of an unbiased signal that depends on a nuisance
parameter, which we estimate by modern machine learning techniques. We first
adjust the signal to make it insensitive (Neyman-orthogonal) with respect to
the first-stage regularization bias. We then project the signal onto a set of
basis functions, growing with sample size, which gives us the best linear
predictor of the structural function. We derive a complete set of results for
estimation and simultaneous inference on all parameters of the best linear
predictor, conducting inference by Gaussian bootstrap. When the structural
function is smooth and the basis is sufficiently rich, our estimation and
inference result automatically targets this function. When basis functions are
group indicators, the best linear predictor reduces to group average
treatment/structural effect, and our inference automatically targets these
parameters. We demonstrate our method by estimating uniform confidence bands
for the average price elasticity of gasoline demand conditional on income.
