Online Optimization Methods for the Quantification Problem
Purushottam Kar, Shuai Li, Harikrishna Narasimhan, Sanjay, Chawla, Fabrizio Sebastiani

TL;DR
This paper introduces the first online stochastic algorithms for directly optimizing quantification-specific performance measures, advancing the theory and demonstrating superior results on benchmark and real datasets.
Contribution
It presents novel online algorithms for quantification measure optimization, with theoretical convergence guarantees and improved empirical performance.
Findings
Algorithms outperform existing methods on benchmark datasets.
Theoretical analysis confirms optimal convergence.
Hybrid measures effectively balance quantification and classification.
Abstract
The estimation of class prevalence, i.e., the fraction of a population that belongs to a certain class, is a very useful tool in data analytics and learning, and finds applications in many domains such as sentiment analysis, epidemiology, etc. For example, in sentiment analysis, the objective is often not to estimate whether a specific text conveys a positive or a negative sentiment, but rather estimate the overall distribution of positive and negative sentiments during an event window. A popular way of performing the above task, often dubbed quantification, is to use supervised learning to train a prevalence estimator from labeled data. Contemporary literature cites several performance measures used to measure the success of such prevalence estimators. In this paper we propose the first online stochastic algorithms for directly optimizing these quantification-specific performance…
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