Distributional Robustification with Fisher-Rao Ambiguity Sets

Professor Yue, Man Chung   (Principal Investigator (PI))

36

2021-01-01

439702

Distributional Robustification with Fisher-Rao Ambiguity Sets

Distributionally Robust Opt, Data-driven Optimization, Manifold Optimization, Geodesic Convex Optimization

Physical Sciences

Physical Sciences (P)

25302420

Early Career Scheme (ECS) 2020/21

On-going

1. Motivated by the limitations of the existing literature on distributional robustification and by the attractive properties of the celebrated Fisher-Rao distance, a new type of ambiguity set, called the Fisher-Rao ambiguity set, for distributional robustification will be explored from both modeling and algorithmic perspectives. 2. Two new statistical tools emerged from the idea of distributional robustification with Fisher-Rao ambiguity sets will be focused and investigated thoroughly. One is the distributionally robust quadratic discriminant analysis recently proposed by the PI and his co-authors. The other is a distributionally robust covariance matrix estimator newly proposed in the project. In particular, statistical guarantees of these tools, such as finitesample bounds and asymptotic convergences, are studied. Numerical experiments on real datasets will also be conducted to examine their practical performance. 3. To accommodate the high-dimensional and large-scale data setting, dedicated algorithms will be developed to efficiently solve the distributionally robust optimization problems associated with the two new statistical tools. Geometric properties of these specific optimization problems, such as the KL and error bound conditions, will be studied. Theoretical results and algorithmic techniques applicable to general geodesically convex manifold optimization problems will also be developed.