Full (exact) conformal set vs. split or cross-validated conformal set Non-connectedness of the conformal prediction set. This was initially suggested in [18, Remark 1]. We follow the actual practice in the literature [14, Remark 5]. We did not observe violations. We will also summarize the proposed algorithm in a direct pseudo-code.

We also provide a detailed analysis quantifying its complexity.

If you are predicting the label $y$ of a new object with $\hat y$, how confident are you that $y = \hat y$? Conformal prediction methods provide an elegant framework for answering such question by building a $100 (1 - \alpha)\%$ confidence region without assumptions on the distribution of the data. It is based on a refitting procedure that parses all the possibilities for $y$ to select the most likely ones. Although providing strong coverage guarantees, conformal set is impractical to compute exactly for many regression problems. We propose efficient algorithms to compute conformal prediction set using approximated solution of (convex) regularized empirical risk minimization. Our approaches rely on a new homotopy continuation technique for tracking the solution path w.r.t. sequential changes of the observations. We provide a detailed analysis quantifying its complexity.