  Conformal prediction is a general method that converts almost any point
predictor to a prediction set. The resulting set keeps good statistical
properties of the original estimator under standard assumptions, and guarantees
valid average coverage even when the model is misspecified. A main challenge in
applying conformal prediction in modern applications is efficient computation,
as it generally requires an exhaustive search over the entire output space. In
this paper we develop an exact and computationally efficient conformalization
of the Lasso and elastic net. The method makes use of a novel piecewise linear
homotopy of the Lasso solution under perturbation of a single input sample
point. As a by-product, we provide a simpler and better justified online Lasso
algorithm, which may be of independent interest. Our derivation also reveals an
interesting accuracy-stability trade-off in conformal inference, which is
analogous to the bias-variance trade-off in traditional parameter estimation.
The practical performance of the new algorithm is demonstrated using both
synthetic and real data examples.
