Spectral top-down recovery of latent tree models

Area of Science:

• Computational Biology
• Machine Learning
• Statistical Modeling

Background:

• Latent tree graphical models are used to analyze high-dimensional data across scientific domains.
• Inferring tree structures from observed terminal nodes is challenging due to computational intensity for large trees.

Purpose of the Study:

• To develop an efficient and statistically consistent method for inferring large latent tree models.
• To improve upon existing divide-and-conquer approaches for tree recovery.

Main Methods:

• Introduced Spectral Top-Down Recovery (STDR), a deterministic divide-and-conquer algorithm.
• Utilized the Fiedler vector of a Laplacian matrix for non-random partitioning of terminal nodes.
• Developed a simplified subtree merging procedure based on the partitioning.

Main Results:

• Proved that STDR's partitioning is consistent with the underlying tree structure under specific conditions.
• Demonstrated statistical consistency of STDR and provided bounds on sample complexity.
• Showcased significant runtime advantages with comparable or improved accuracy on simulated phylogenetic data.

Conclusions:

• STDR offers a computationally efficient and accurate solution for inferring large latent tree models.
• The method's theoretical guarantees and practical performance make it valuable for large-scale tree recovery.
• STDR advances the analysis of complex data structures in fields like phylogenetics.