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Computing Full Conformal Prediction Set with Approximate Homotopy
Eugene Ndiaye · Ichiro Takeuchi

Wed Dec 11 10:45 AM -- 12:45 PM (PST) @ East Exhibition Hall B + C #41
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 with respect to sequential changes of the observations. We also provide a detailed analysis quantifying its complexity.

Author Information

Eugene Ndiaye (Riken AIP)
Ichiro Takeuchi (Nagoya Institute of Technology)

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