Interpolation of Random Hyperplanes
نویسنده
چکیده
Let {(Zi,Wi) : i = 1, . . . , n} be uniformly distributed in [0, 1]d × G(k, d), where G(k, d) denotes the space of k-dimensional linear subspaces of Rd. For a differentiable function f : [0, 1]k → [0, 1]d, we say that f interpolates (z,w) ∈ [0, 1]d × G(k, d) if there exists x ∈ [0, 1]k such that f(x) = z and ~ f(x) = w, where ~ f(x) denotes the tangent space at x defined by f . For a smoothness class F of Hölder type, we obtain probability bounds on the maximum number of points a function f ∈ F interpolates.
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