A critical view on invexity

The aim of this note is to emphasize the fact that in many papers on invexity published in prestigious journals there are not clear definitions, trivial or not clear statements and wrong proofs. We also point out the unprofessional way of answering readers' questions by some authors. We think that this is caused mainly by the lack of criticism of the invexity communityComment: The paper was submitted to JOTA in December 2007 and practically accepted by the AE handling it in March 2008. Being a critical paper, the EiC asked the authors of the criticised articles to say their opinion. With the change of the EiC's, apparently the paper was not transmitted to the new Ei

Online Optimization Methods for the Quantification Problem

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 measures. We also provide algorithms that optimize hybrid performance measures that seek to balance quantification and classification performance. Our algorithms present a significant advancement in the theory of multivariate optimization and we show, by a rigorous theoretical analysis, that they exhibit optimal convergence. We also report extensive experiments on benchmark and real data sets which demonstrate that our methods significantly outperform existing optimization techniques used for these performance measures.Comment: 26 pages, 6 figures. A short version of this manuscript will appear in the proceedings of the 22nd ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 201