  In this work, we demonstrate that a major limitation of regression using a
mean-squared error loss is its sensitivity to the scale of its targets. This
makes learning settings consisting of target's whose values take on varying
scales challenging. A recently-proposed alternative loss function, known as
histogram loss, avoids this issue. However, its computational cost grows
linearly with the number of buckets in the histogram, which renders prediction
with real-valued targets intractable. To address this issue, we propose a novel
approach to training deep learning models on real-valued regression targets,
autoregressive regression, which learns a high-fidelity distribution by
utilizing an autoregressive target decomposition. We demonstrate that this
training objective allows us to solve regression tasks involving targets with
different scales.
