  This paper describes a method for performing inference on models chosen by
cross-validation. When the test error being minimized in cross-validation is a
residual sum of squares it can be written as a quadratic form. This allows us
to apply the inference framework in Loftus et al. (2015) for models determined
by quadratic constraints to the model that minimizes CV test error. Our only
requirement on the model training pro- cedure is that its selection events are
regions satisfying linear or quadratic constraints. This includes both Lasso
and forward stepwise, which serve as our main examples throughout. We do not
require knowledge of the error variance $\sigma^2$. The procedures described
here are computationally intensive methods of selecting models adaptively and
performing inference for the selected model. Implementations are available in
an R package.
