Modeling local predictive ability using power-transformed Gaussian processes
Title: Modeling local predictive ability using power-transformed Gaussian processes
SNIC Project: LiU-compute-2022-33
Project Type: LiU Compute
Principal Investigator: Mattias Villani <mattias.villani@stat.su.se>
Affiliation: Stockholms universitet
Duration: 2022-10-19 – 2023-01-01
Classification: 10106
Keywords:

Abstract

A Gaussian process is proposed to model the posterior distribution of the local predictive ability of a model or expert, conditional on a vector of covariates, from historical predictions in the form of log predictive scores. Assuming Gaussian expert predictions and a Gaussian data generating process, a linear transformation of the predictive score follows a noncentral chi-squared distribution with one degree of freedom. Motivated by this we develop a non-central chi-squared Gaussian process regression to flexibly model local predictive ability, with the posterior distribution of the latent GP function and kernel hyperparameters sampled by Hamiltonian Monte Carlo. We show that a cube-root transformation of the log scores is approximately Gaussian with homoscedastic variance, which makes it possible to estimate the model much faster by marginalizing the latent GP function analytically. Linear pools based on learned local predictive ability are applied to predict daily bike usage in Washington DC.