Optimization for Big Data Analytics and its Applications
In the past several decades, many advanced technologies have been developed to collect and store data continuously, and data and decisions are more strongly linked together than ever before. In most cases, the data includes a lot of uncertainties, such as missing or incomplete information, measurement errors, communication errors, noise, etc. Traditional data mining or machine learning methods for decisions are dealing with the exact information of data. Only to some extent, the data uncertainty, modeled by some support sets, mean or moment values, has been considered for robust decisions. In this talk, we discuss statistical models for data uncertainties and data-driven optimization approaches for decision-making under uncertainty, especially in the case of big data. Some robust and distributionally robust optimization models and algorithms for support vector machines will be introduced, and numerical experiments for some applications will be performed to validate the proposed approaches.