We study a non-parametric multi-armed bandit problem with stochastic covariates, where key complexity driver is the smoothness of payoff functions respect to covariates. Previous studies have focused on deriving minimax-optimal algorithms in cases it priori known how smooth are. In practice, however, typically not advance, and misspecification may severely deteriorate performance existing metho...

OBJECTIVE We investigated whether surface smoothness of articular cartilage in the medial tibiofemoral compartment quantified from magnetic resonance imaging (MRI) could be appropriate as a diagnostic marker of osteoarthritis (OA). METHOD At baseline, 159 community-based subjects aged 21 to 81 with normal or OA-affected knees were recruited to provide a broad range of OA states. Smoothness wa...

a palladium composite membrane was prepared via electroless plating technique using organic-inorganic method during activation process. the ceramic support surface was modified by two tio2-boehmite and one γ-alumina layers to avoid pd penetration in support pores. thin and defect-free pd composite membrane was obtained by creating a relative smoothness on the ceramic support and using pd nanopa...

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We prove that some multivariate linear tensor product problems are tractable in the worst case setting if they are defined as tensor products of univariate problems with logarithmically increasing smoothness. This is demonstrated for the approximation problem defined over Korobov spaces and for the approximation problem of certain diagonal operators. For these two problems we show necessary and...

in hilbert space l2(rn), we prove the equivalence between the mod-ulus of smoothness and the k-functionals constructed by the sobolev space cor-responding to the fourier transform. for this purpose, using a spherical meanoperator.