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Johnson-Lindenstrauss Lemma Beyond Euclidean Geometry
Chengyuan Deng, Jie Gao, Kevin Lu +2
The Johnson-Lindenstrauss (JL) lemma is a cornerstone of dimensionality reduction in Euclidean space, but its applicability to non-Euclidean data has remained limited. This paper e…
On the Price of Differential Privacy for Hierarchical Clustering
Chengyuan Deng, Jie Gao, Jalaj Upadhyay +2
Hierarchical clustering is a fundamental unsupervised machine learning task with the aim of organizing data into a hierarchy of clusters. Many applications of hierarchical clusteri…
Low Sensitivity Hopsets
Vikrant Ashvinkumar, Aaron Bernstein, Chengyuan Deng +2
Given a weighted graph , a -hopset is an edge set such that for any , where can reach in , there is a path from to in $G \c…
The Discrepancy of Shortest Paths
Greg Bodwin, Chengyuan Deng, Jie Gao +3
The hereditary discrepancy of a set system is a certain quantitative measure of the pseudorandom properties of the system. Roughly, hereditary discrepancy measures how well one can…