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9 votes
2 answers
674 views

Small crown probabilities (and infinite dimensional margin assumption)

My question is: How do I find sharp upper bounds on $P(|q|\leq \epsilon)$ uniformly over a set of gaussian polynomes $q$ of degree two. Notations and definitions (to make the question rigorous) Let ...
0 votes
1 answer
915 views

Can you interpret this divergent integral?

In this ArXiv paper by Wilk and Wlodarczyk (published in Physical Review Letters), equation 16 has essentially the following definition of a function: $$\text{f(x)=}\frac{c}{2Dx^2}\exp[\int^x_0 \frac{\...
1 vote
0 answers
466 views

Bounding point-wise maximum of the absolute difference of two convex functions

Let $\Delta: R \times R \rightarrow R_{+}$ be a positive and convex function (convex in, say, both the arguments) called the loss function. Let $x \in R^d$. Moreover, let $H_1,...,H_r$ be sets of ...

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