Event Date Details:
Refreshments served at 3:15 p.m.
- Sobel Seminar Room; South Hall 5607F
- Department Seminar Series
Title: Computational approaches in data mining and portfolio selection
Abstract: This talk consists of two parts. In the first part, I will share my experience with the use of high-performance computing (HPC) in high-dimensional data mining problems, which are well known to be difficult both theoretically and computationally. I advocate parallelization as a practical solution to mitigate the computational difficulties, and show that a fair amount of parallelism can be achieved with small efforts by using commodity HPC systems. Success and failure stories of adopting graphics processing units (GPUs) for the fused lasso sparse regression and Hadoop MapReduce for graph algorithms are discussed. In the second part, I will discuss a use of numerical optimization in financial portfolio selection problems in the presence of parameter uncertainty. Robust optimization is employed to explicitly incorporate a model of parameter uncertainty in the problem formulation, and optimizes for the worst-case scenario. This part of the talk considers robust mean-variance portfolio selection involving a trade-off between the worst-case utility and the worst-case regret, or the largest difference between the best utility achievable under the model and that achieved by a given portfolio. I will show that while optimizing for the worst-case utility may yield an overly pessimistic portfolio, optimizing for the worst-case regret may result in a complete loss of robustness. Robust trade-off portfolio compromises these two extremes, enabling more informative selections. I will show that, under a widely used ellipsoidal uncertainty model, the entire optimal trade-off curve can be found via solving a series of semidefinite programs (SDPs), which are computationally tractable. I then extend the model to handle a union of finitely many ellipsoids, and show that trade-off analysis under this quite general uncertainty model also reduces to a series of SDPs. For more general uncertainties, I propose an iterative algorithm based on the cutting-set method.