Guaranteed Coverage Prediction Intervals with Gaussian Process
  Regression
Harris Papadopoulos
Gaussian Process Regression (GPR) is a popular regression method, which
unlike most Machine Learning techniques, provides estimates of uncertainty for
its predictions. These uncertainty estimates however, are based on the
assumption that the model is well-specified, an assumption that is violated in
most practical applications, since the required knowledge is rarely available.
As a result, the produced uncertainty estimates can become very misleading; for
example the prediction intervals (PIs) produced for the 95\% confidence level
may cover much less than 95\% of the true labels. To address this issue, this
paper introduces an extension of GPR based on a Machine Learning framework
called, Conformal Prediction (CP). This extension guarantees the production of
PIs with the required coverage even when the model is completely misspecified.
The proposed approach combines the advantages of GPR with the valid coverage
guarantee of CP, while the performed experimental results demonstrate its
superiority over existing methods.