Seminar by Jeffrey Negrea

Adapting to Failure of the IID Assumption

Assumptions on data are used to develop statistical methods with optimistic performance guarantees. Even if these assumptions do not hold, we often believe that if our models are nearly correct, our methods will perform similarly to those optimistic guarantees. How can we use models that we know to be wrong, but expect to be nearly correct, in a way that is robust and reliable? I will discuss my work on the canonical problem of statistical aggregation, i.e., combining predictions from a large number of models or experts. In my work, we define a continuous spectrum of relaxations of the IID assumption for prediction problems with sequential data, with IID data at one extreme and mechanisms that select worst-case responses to one's actions at the other. We develop methods for statistical aggregation with sequential data that adapt to the level of failure of the IID assumption. We quantify the difficulty of statistical aggregation in all scenarios along the spectrum we introduce, demonstrate that the prevailing methods do not adapt to this spectrum, and present new methods that are adaptively minimax optimal. More broadly, it is shown that it is possible to develop methods that are both adaptive and robust: they realize the benefits of the IID assumption when it holds, without ever compromising performance when the IID assumption fails, and without having to know the degree to which the IID assumption fails in advance.

The presentation is based on the following two manuscripts:

• https://doi.org/10.1214/23-AOS2315
• https://proceedings.neurips.cc/paper/2021/hash/dcd2f3f312b6705fb06f4f9f1b55b55c-Abstract.html