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- W2092479085 abstract "We prove the existence of a class $A$ of subsets of $mathbb{R}^d$ of VC dimension 1 such that the symmetric convex hull $F$ of the class of characteristic functions of sets in $A$ is rich in the following sense. For any absolutely continuous probability measure $mu$ on $mathbb{R}^d$, measurable set $B$ and $varepsilon gt 0$, there exists a function $f$ in $F$ such that the measure of the symmetric difference of $B$ and the set where $f$ is positive is less than $varepsilon$. The question was motivated by the investigation of the theoretical properties of certain algorithms in machine learning." @default.
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- W2092479085 date "2003-01-01" @default.
- W2092479085 modified "2023-10-18" @default.
- W2092479085 title "A note on the richness of convex hulls of VC classes" @default.
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- W2092479085 doi "https://doi.org/10.1214/ecp.v8-1097" @default.
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