Published on Fri Sep 20 2019

### Computing Full Conformal Prediction Set with Approximate Homotopy

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Conformal prediction methods provide an elegant framework for answering such question. Conformal set is impractical to compute exactly for many regression problems. We propose efficient algorithms to compute conformal prediction set using approximated solution of regularized empirical risk minimization.

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###### Abstract

If you are predicting the label of a new object with , how confident are you that ? 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 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.