Abstract:
In a recent work, Chase, Chornomaz, Hanneke, Moran, and Yehudayoff have shown that a certain attack on the sample compression conjecture cannot succeed. We will not talk about this, but concentrate instead on a central structural result of their paper: the inequality VC* <= 2 VC + 1 for extremal classes. In particular, we will discuss the (open) question of whether this inequality is tight. While probably of limited importance by itself, this question provides a good opportunity to discuss an inherent topological nature of extremal classes, which we consider to be the main subject of this talk.
Apart from the above-mentioned authors of CCHMY, the talk is based on an ongoing collaboration with Biao Ma.
