  The "double descent" risk curve was proposed to qualitatively describe the
out-of-sample prediction accuracy of variably-parameterized machine learning
models. This article provides a precise mathematical analysis for the shape of
this curve in two simple data models with the least squares/least norm
predictor. Specifically, it is shown that the risk peaks when the number of
features $p$ is close to the sample size $n$, but also that the risk decreases
towards its minimum as $p$ increases beyond $n$. This behavior is contrasted
with that of "prescient" models that select features in an a priori optimal
order.
