Modeling local predictive ability using power-transformed Gaussian processes
arxiv(2024)
摘要
A Gaussian process is proposed as a model for the posterior distribution of
the local predictive ability of a model or expert, conditional on a vec- tor of
covariates, from historical predictions in the form of log predictive scores.
Assuming Gaussian expert predictions and a Gaussian data generat- ing process,
a linear transformation of the predictive score follows a noncen- tral
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.
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