Title: Probabilistic Formulations of Regression with Mixed Guidance,
Abstract: Regression problems assume every instance is annotated (labeled) with a real
value, a form of annotation we call \emph{strong guidance}. In order for these
annotations to be accurate, they must be the result of a precise experiment or
measurement. However, in some cases additional \emph{weak guidance} might be
given by imprecise measurements, a domain expert or even crowd sourcing.
Current formulations of regression are unable to use both types of guidance. We
propose a regression framework that can also incorporate weak guidance based on
relative orderings, bounds, neighboring and similarity relations. Consider
learning to predict ages from portrait images, these new types of guidance
allow weaker forms of guidance such as stating a person is in their 20s or two
people are similar in age. These types of annotations can be easier to generate
than strong guidance. We introduce a probabilistic formulation for these forms
of weak guidance and show that the resulting optimization problems are convex.
Our experimental results show the benefits of these formulations on several
data sets.