Distribution Free Prediction Bands
This work addresses the need for reliable prediction intervals in statistical modeling, offering an automated alternative to classical methods like linear regression, though it is incremental in building on conformal prediction.
The paper tackles the problem of constructing distribution-free, nonparametric prediction bands with finite sample guarantees, resulting in the COPS estimator that provides stronger finite sample coverage than existing methods and converges to an oracle band at a minimax optimal rate under regularity conditions.
We study distribution free, nonparametric prediction bands with a special focus on their finite sample behavior. First we investigate and develop different notions of finite sample coverage guarantees. Then we give a new prediction band estimator by combining the idea of "conformal prediction" (Vovk et al. 2009) with nonparametric conditional density estimation. The proposed estimator, called COPS (Conformal Optimized Prediction Set), always has finite sample guarantee in a stronger sense than the original conformal prediction estimator. Under regularity conditions the estimator converges to an oracle band at a minimax optimal rate. A fast approximation algorithm and a data driven method for selecting the bandwidth are developed. The method is illustrated first in simulated data. Then, an application shows that the proposed method gives desirable prediction intervals in an automatic way, as compared to the classical linear regression modeling.