Valid Generalisation from Approximate Interpolation

Valid Generalisation from Approximate Interpolation

Let H and C be sets of functions from domain X to <. We say that H validly generalises C from approximate interpolation if and only if for each η > 0 and , δ ∈ (0, 1) there is m0(η, , δ) such that for any function t ∈ C and any probability distribution P on X, if m ≥ m0 then with Pm-probability at least 1− δ, a sample x = (x1, x2, . . . , xm) ∈ Xm satisfies ∀h ∈ H, |h(xi)− t(xi)| < η, (1 ≤ i ≤ ...

Valid inequalities for MIPs and group polyhedra from approximate liftings

Physically-Valid View Synthesis by Image Interpolation

Image warping is a popular tool for smoothly transforming one image to another. \Morphing" techniques based on geometric image interpolation create compelling visual e ects, but the validity of such transformations has not been established. In particular, does 2D interpolation of two views of the same scene produce a sequence of physically valid in-between views of that scene? In this paper, we...

Valid inequalities based on the interpolation procedure

We study the interpolation procedure of Gomory and Johnson (1972), which generates cutting planes for general integer programs from facets of cyclic group polyhedra. This idea has recently been re-considered by Evans (2002) and Gomory, Johnson and Evans (2003). We compare inequalities generated by this procedure with mixed-integer rounding (MIR) based inequalities discussed in Dash and Gunluk (...

A Generalisation of an Approximate Method to Calculate Inbreeding Coefficients

Where, A is a common ancestor of the parents of X; n is the number of generations from the sire of X to A and n' the number of generations from the dam of X to A. Subsequently, Wright & McPhee (1925) developed a method for calculating an approximate inbreeding coefficient from a pedigree which is completed for only a limited number of generations, the residual pedigree being represented by rand...