Search Results for author: Kitty Mohammed

Found 2 papers, 0 papers with code

Structural Risk Minimization for $C^{1,1}(\mathbb{R}^d)$ Regression

no code implementations29 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.

Manifold Learning Using Kernel Density Estimation and Local Principal Components Analysis

no code implementations11 Sep 2017 Kitty Mohammed, Hariharan Narayanan

Ideally, the estimate $\mathcal{M}_\mathrm{put}$ of $\mathcal{M}$ should be an actual manifold of a certain smoothness; furthermore, $\mathcal{M}_\mathrm{put}$ should be arbitrarily close to $\mathcal{M}$ in Hausdorff distance given a large enough sample.

Density Estimation

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