Learning to Quantify: Estimating Class Prevalence via Supervised Learning

Abstract

Quantification (also known as "supervised prevalence estimation" [2], or "class prior estimation" [7]) is the task of estimating, given a set σ of unlabelled items and a set of classes C = c1, . . . , c |C| , the relative frequency (or "prevalence") p(ci ) of each class ci C, i.e., the fraction of items in σ that belong to ci . When each item belongs to exactly one class, since 0 ≤ p(ci ) ≤ 1 and Í ci C p(ci ) = 1, p is a distribution of the items in σ across the classes in C (the true distribution), and quantification thus amounts to estimating p (i.e., to computing a predicted distribution p?). Quantification is important in many disciplines (such as e.g., market research, political science, the social sciences, and epidemiology) which usually deal with aggregate (as opposed to individual) data. In these contexts, classifying individual unlabelled instances is usually not a primary goal, while estimating the prevalence of the classes of interest in the data is. For instance, when classifying the tweets about a certain entity (e.g., a political candidate) as displaying either a Positive or a Negative stance towards the entity, we are usually not much interested in the class of a specific tweet: instead, we usually want to know the fraction of these tweets that belong to the class [14].