no code implementations • 6 Mar 2018 • Adam Gustafson, Hariharan Narayanan
We present an affine-invariant random walk for drawing uniform random samples from a convex body $\mathcal{K} \subset \mathbb{R}^n$ that uses maximum volume inscribed ellipsoids, known as John's ellipsoids, for the proposal distribution.
no code implementations • 29 Mar 2018 • Adam Gustafson, Matthew Hirn, Kitty Mohammed, Hariharan Narayanan, Jason Xu
Recently, the following smooth function approximation problem was proposed: given a finite set $E \subset \mathbb{R}^d$ and a function $f: E \rightarrow \mathbb{R}$, interpolate the given information with a function $\widehat{f} \in \dot{C}^{1, 1}(\mathbb{R}^d)$ (the class of first-order differentiable functions with Lipschitz gradients) such that $\widehat{f}(a) = f(a)$ for all $a \in E$, and the value of $\mathrm{Lip}(\nabla \widehat{f})$ is minimal.