SCAIM Seminar: Aleksandr (Sasha) Aravkin

Abstract:

For many inverse problems, accuracy of data is required by standard methods, yet rarely achievable in practice. In many applications, data may contain large artifacts, such as outliers caused by measurement errors, or physical phenomena not explained by the predictive model. In this setting, robust methods, i.e. methods that find reasonable results even in the face of gross errors, are an appealing alternative to pre-processing, outlier removal, or very complex modeling.

In this talk, we will discuss two applications: geophysical imaging and inference for dynamical systems. In both cases, we will show how to design robust methods by modifying the statistical error models. We can then get robust solutions by finding the maximum likelihood estimates for parameters in these modified models. In order to solve these problems quickly, optimization techniques must exploit the underlying problem structure. We will highlight this structure for both classes of applications, and present numerical results to show how the methods work in practice.