Uncertainty quantification for forest attribute maps with conformal prediction and k-nearest neighbor method

Abstract

Forest attribute maps relying on remotely sensed data are increasingly required for local decision-making related to the use of forest resources. Such maps always have uncertainty, which can be challenging to quantify. The objective of this work is to introduce the conformal prediction methodology to uncertainty quantification in forest attribute mapping, particularly for the $k$-NN method. We compare several conformal $k$-NN procedures for the mapping of total volume, broadleaved volume and Lorey’s height using Sentinel-2 satellite images and airborne laser scanning data. We show that all procedures produce valid prediction intervals in the sense that they contain the true value with the desired probability, for example 90%. We use multiple measures to quantify how well the prediction intervals adapt to the difficulty of prediction in different forest strata. We found that there are multiple methods for $k$-NN to produce prediction intervals competitive with those produced by conformal quantile regression. These methods include conformal prediction based on the standard deviation or quantiles of the $k$ nearest neighbors with commonly used values of $k$. We present how to produce a forest attribute map with the proposed conformal prediction intervals. We also show a theoretical coverage guarantee for the jackknife conformal $k$-NN procedure. We recommend conformal prediction for unit-level uncertainty quantification of forest attribute maps.