Seminar • Algorithms and Complexity • Optimal PAC Bounds without Uniform Convergence

Wednesday, July 5, 2023 12:00 pm - 1:00 pm EDT (GMT -04:00)

Please note: This seminar will take place in DC 1302 and online.

Ishaq Aden-Ali, PhD candidate
Electrical Engineering and Computer Sciences
University of California, Berkeley

In statistical learning theory, determining the sample complexity of realizable binary classification for VC classes was a long-standing open problem. The results of Simon and Hanneke established sharp upper bounds in this setting. However, the reliance of their argument on the uniform convergence principle limits its applicability to more general learning settings such as multiclass classification. In this talk, we will discuss a simple technique that addresses this issue. We will present optimal high probability risk bounds through a framework that surpasses the limitations of uniform convergence arguments.

In addition to binary classification, we will see applications in three settings where uniform convergence is provably suboptimal. For multiclass classification, we prove an optimal risk bound scaling with the one-inclusion hypergraph density of the class, improving on the suboptimal analysis of Daniely and Shalev-Shwartz. In partial concept classification, we determine the optimal sample complexity bound, resolving a question posed by Alon, Hanneke, Holzman, and Moran. In the context of realizable bounded regression with absolute loss, we derive an optimal risk bound that relies on a modified version of the scale-sensitive dimension, refining a result of Bartlett and Long. Our rates surpass standard uniform convergence-based results due to the smaller complexity measure in our risk bound.

Joint work with Yeshwanth Cherapanamjeri, Abhishek Shetty, and Nikita Zhivotovskiy.