Essays on data-driven optimization

The estimation of a data matrix contains two parts: the well estimated and the poorly estimated. The latter is usually throwing away because the estimations are off. As argued in this paper, ignoring is the wrong thing to do as the poorly estimated part is orthogonal to the well estimated. I will show how to use such orthogonality information via robust optimization and provide application in portfolio optimization, least-square regression, and dimension reduction. Across a large number of experiments, utilizing the orthogonality information consistently improves the performance.