Publications

Here is the list of my publications in reversed chronological order, generated by jekyll-scholar.

2023

Linear Regression on Manifold Structured Data: the Impact of Extrinsic Geometry on Solutions

Liangchen Liu, Juncai He, and Richard Tsai

arXiv preprint arXiv:2307.02478, 2023

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We study linear regression applied to data structured on a manifold. We reveal the impact of the data manifold’s extrinsic geometry on the regression by deriving explicit solution formulas and numerical experiments. Our findings reveal the role of data manifold geometry in ensuring the stability of regression models for out-of-distribution inferences.

2019

Nearest neighbor sampling of point sets using rays (RaySense)

Liangchen Liu, Louis Ly, Colin Macdonald, and 1 more author

arXiv preprint arXiv:1911.10737, 2019

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We propose a new framework for the sampling, compression, and analysis of distributions of point sets and other geometric objects. We provide theoretical explanations to its properties along with guarantees for line integral approximation