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Skimming through, this looks like an attempt at a foundation with a bunch of applications. Meanwhile, it looks to me that the applications can generally be expl
by usgroup 3y ago
Skimming through, this looks like an attempt at a foundation with a bunch of applications. Meanwhile, it looks to me that the applications can generally be explained without the fairly advanced foundation (e.g. stochastic block model, concentration inequalities, and so on).
So, the "with applications to Data Science" is right, and should not be confused with "a bunch of advanced maths that you need to know in order to understand these applications".
- rq1 3y agoIsoperimetric inequalities are fundamental IMHO. They bridge the gap between theory and practice for eg. resp. the behavior of the Lipschitz constants and batch normalization.
- Donald 3y agoDo you have any examples?
- rq1 3y agohttps://proceedings.neurips.cc/paper_files/paper/2018/file/905056c1ac1dad141560467e0a99e1cf-Paper.pdf https://proceedings.neurips.cc/paper_files/paper/2018/file/9... For the relationship between concentration of the measure and this: the main theorems of concentration generalise the CLT beyond the additive case, for any lipschitz operator over iid vars, the first i can even be relaxed. You can find online, works by eg. Gromov and his students for a deeper understanding.