  Several real-life applications require crafting concise, quantitative scoring
functions (also called rating systems) from measured observations. For example,
an effectiveness score needs to be created for advertising campaigns using a
number of engagement metrics. Experts often need to create such scoring
functions in the absence of labelled data, where the scores need to reflect
business insights and rules as understood by the domain experts. Without a way
to capture these inputs systematically, this becomes a time-consuming process
involving trial and error. In this paper, we introduce a label-free practical
approach to learn a scoring function from multi-dimensional numerical data. The
approach incorporates insights and business rules from domain experts in the
form of easily observable and specifiable constraints, which are used as weak
supervision by a machine learning model. We convert such constraints into loss
functions that are optimized simultaneously while learning the scoring
function. We examine the efficacy of the approach using a synthetic dataset as
well as four real-life datasets, and also compare how it performs vis-a-vis
supervised learning models.
