Sparse Bayesian multidimensional scaling(s)

Area of Science:

• Computational Biology
• Statistical Modeling
• Machine Learning

Background:

• Bayesian multidimensional scaling (BMDS) is a probabilistic dimension reduction method for visualizing object dissimilarities.
• Standard BMDS is computationally intensive, requiring O(N^2) operations, limiting its use with large datasets (N).
• Existing methods struggle with scalability in complex analyses like phylogenetic inference.

Purpose of the Study:

• To develop and evaluate computationally efficient sparse variants of BMDS (sBMDS).
• To assess the trade-off between computational speed and accuracy in sBMDS.
• To demonstrate the applicability of sBMDS in phylogeography and document clustering.

Main Methods:

• Introduced two sparse BMDS (sBMDS) methods: Landmark sBMDS (L-sBMDS) and Banded sBMDS (B-sBMDS).
• sBMDS variants compute log-likelihood and gradients on subsets of the dissimilarity matrix.
• Evaluated performance using Metropolis-Hastings and Hamiltonian Monte Carlo algorithms via simulations and real-world data applications.

Main Results:

• sBMDS achieves significant speedups (3x to 40x) with negligible accuracy loss for datasets up to 5,000 points.
• Computational efficiency of sBMDS scales favorably, outperforming standard BMDS for large N.
• Demonstrated successful application in modeling influenza subtype spread and clustering arXiv manuscripts.

Conclusions:

• sBMDS provides a scalable and accurate alternative to standard BMDS for large-scale data analysis.
• The sparse approach enables efficient uncertainty quantification in complex Bayesian models.
• sBMDS enhances the practical utility of dimension reduction techniques in diverse scientific fields.