The Bayesian committee machine (BCM) is a novel approach to combining estim
ators that were trained on different data sets. Although the BCM can be app
lied to the combination of any kind of estimators, the main foci are gaussi
an process regression and related systems such as regularization networks a
nd smoothing splines for which the degrees of freedom increase with the num
ber of training data. Somewhat surprisingly, we find that the performance o
f the BCM improves if several test points are queried at the same time and
is optimal if the number of test points is at least as large as the degrees
of freedom of the estimator. The BCM also provides a new solution for on-l
ine learning with potential applications to data mining. We apply the BCM t
o systems with fixed basis functions and discuss its relationship to gaussi
an process regression. Finally, we show how the ideas behind the BCM can be
applied in a non-Bayesian setting to extend the input-dependent combinatio
n of estimators.