In this section, we show how the Rademacher and Gaussian complexities can be used to bound the statistical risk of a constrained least squares estimator over FL,V.
We now show that the minimax risk from \prettyrefthm:singleupper is nearly optimal, up to a polynomial factor in v. Using the fact that ramp functions are invariant under composition, ϕ(z)=ϕ(ϕ(z)) for all real z, the constructions used for the follo…
The risk bound framework of this paper is self-contained, yet borrows heavily from the unpublished manuscript  written with Cong Huang and Gerald Cheang, which was judged to be too long for the Annals of Statistics. The Annals did show favorable…
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