  The multiresolution Gaussian process (GP) has gained increasing attention as
a viable approach towards improving the quality of approximations in GPs that
scale well to large-scale data. Most of the current constructions assume full
independence across resolutions. This assumption simplifies the inference, but
it underestimates the uncertainties in transitioning from one resolution to
another. This in turn results in models which are prone to overfitting in the
sense of excessive sensitivity to the chosen resolution, and predictions which
are non-smooth at the boundaries. Our contribution is a new construction which
instead assumes conditional independence among GPs across resolutions. We show
that relaxing the full independence assumption enables robustness against
overfitting, and that it delivers predictions that are smooth at the
boundaries. Our new model is compared against current state of the art on 2
synthetic and 9 real-world datasets. In most cases, our new conditionally
independent construction performed favorably when compared against models based
on the full independence assumption. In particular, it exhibits little to no
signs of overfitting.
