  We introduce an ensemble learning method based on Gaussian Process Regression
(GPR) for predicting conditional expected stock returns given stock-level and
macro-economic information. Our ensemble learning approach significantly
reduces the computational complexity inherent in GPR inference and lends itself
to general online learning tasks. We conduct an empirical analysis on a large
cross-section of US stocks from 1962 to 2016. We find that our method dominates
existing machine learning models statistically and economically in terms of
out-of-sample $R$-squared and Sharpe ratio of prediction-sorted portfolios.
Exploiting the Bayesian nature of GPR, we introduce the mean-variance optimal
portfolio with respect to the predictive uncertainty distribution of the
expected stock returns. It appeals to an uncertainty averse investor and
significantly dominates the equal- and value-weighted prediction-sorted
portfolios, which outperform the S&P 500.
