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Activity Number: 28 - SPEED: Statistical Computing and Statistics in Genomics Part 1
Type: Contributed
Date/Time: Sunday, August 7, 2022 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Computing
Abstract #323659
Title: Bayesian Hyperbolic Multi-Dimensional Scaling
Author(s): Bolun Liu* and Tyler McCormick and Adrian E. Raftery and Shane Lubold
Companies: Departments of Statistics, University of Washington and University of Washington and University of Washington and University of Washington
Keywords: Multi-Dimensional Scaling; Bayesian Modeling; Markov chain Monte Carlo; Hyperbolic Embedding; Hierarchical Data; Graph

We describe BHMDS (Bayesian Hyperbolic Multi-Dimensional Scaling), a Bayesian framework that embeds similarity or dissimilarity data into hyperbolic space. BHMDS quantifies the uncertainty of the observed dissimilarity measures and allows credible interval constructions. It achieves a reasonable coverage rate and is well-calibrated. Moreover, it outperforms its Euclidean counterparts when data has a tree-like or hierarchical structure. To enable BHMDS with large dissimilarity data, we describe an approximated case-control likelihood in the Markov chain Monte Carlo estimation of the BHMDS model to reduce its computational time. We further apply BHMDS with several tasks involved with Phylogenetic and Natural Language Processing data and use BHMDS to measure the uncertainty of the outcomes.

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