Corpus ID: 59336184

# A maximum principle argument for the uniform convergence of graph Laplacian regressors

@article{Trillos2019AMP,
title={A maximum principle argument for the uniform convergence of graph Laplacian regressors},
author={Nicol{\'a}s Garc{\'i}a Trillos and Ryan Murray},
journal={ArXiv},
year={2019},
volume={abs/1901.10089}
}
• Published in ArXiv 2019
• Mathematics, Computer Science
• We study asymptotic consistency guarantees for a non-parametric regression problem with Laplacian regularization. In particular, we consider $(x_1, y_1), \dots, (x_n, y_n)$ samples from some distribution on the cross product $\mathcal{M} \times \mathbb{R}$, where $\mathcal{M}$ is a $m$-dimensional manifold embedded in $\mathbb{R}^d$. A geometric graph on the cloud $\{x_1, \dots, x_n \}$ is constructed by connecting points that are within some specified distance $\varepsilon_n$. A suitable semi… CONTINUE READING

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