  Loss functions are a cornerstone of machine learning and the starting point
of most algorithms. Statistics and Bayesian decision theory have contributed,
via properness, to elicit over the past decades a wide set of admissible losses
in supervised learning, to which most popular choices belong (logistic, square,
Matsushita, etc.). Rather than making a potentially biased ad hoc choice of the
loss, there has recently been a boost in efforts to fit the loss to the domain
at hand while training the model itself. The key approaches fit a canonical
link, a function which monotonically relates the closed unit interval to R and
can provide a proper loss via integration. In this paper, we rely on a broader
view of proper composite losses and a recent construct from information
geometry, source functions, whose fitting alleviates constraints faced by
canonical links. We introduce a trick on squared Gaussian Processes to obtain a
random process whose paths are compliant source functions with many desirable
properties in the context of link estimation. Experimental results demonstrate
substantial improvements over the state of the art.
