Spectral neighbor joining for reconstruction of latent tree Models

Area of Science:

• Computational Biology
• Graph Theory
• Statistical Modeling

Background:

• Latent tree graphical models are frequently used in scientific applications, notably in phylogenetics for modeling organismal evolutionary lineages.
• Inferring the underlying tree topology from observed data at the leaves is a critical challenge.

Purpose of the Study:

• To introduce Spectral Neighbor Joining (SNJ), a new method for recovering the structure of latent tree graphical models.
• To establish theoretical guarantees for SNJ's consistency and sample complexity.

Main Methods:

• SNJ utilizes a similarity matrix between observed variables to compute a spectral measure of cohesion between variable groups.
• The method's consistency is proven, and a sufficient condition for correct tree recovery from estimated similarity matrices is derived.

Main Results:

• SNJ demonstrates consistency in tree structure recovery.
• A bound on the required number of samples for high-probability tree recovery is established by combining theoretical conditions with measure concentration results.
• Simulations show SNJ outperforms existing methods, requiring fewer samples for accurate tree recovery, especially for trees with many leaves or long edges.

Conclusions:

• SNJ provides a statistically sound and computationally efficient approach for inferring latent tree graphical models.
• The method offers improved sample efficiency compared to existing techniques, making it valuable for complex phylogenetic and related applications.