# Spectral Top-Down Recovery of Latent Tree Models

arXiv: https://arxiv.org/abs/2102.13276 · HTML: https://mlsanity.com/paper/2102.13276/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 71 references that are in the map.
- First posted on arXiv 26 Feb 2021.

## Builds on (most cited first, 3 of 3)

- [A Survey on Latent Tree Models and Applications](https://mlsanity.com/paper/1402.0577/) (2014)
- [Spectral neighbor joining for reconstruction of latent tree models](https://mlsanity.com/paper/2002.12547/) (2020)
- [The Spectral Underpinning of word2vec](https://mlsanity.com/paper/2002.12317/) (2020)

## Built on by (most cited first, 2 of 2)

- [T-Stochastic Graphs](https://mlsanity.com/paper/2309.01301/) (2023)
- [SDSR: A Spectral Divide-and-Conquer Approach for Species Tree Reconstruction](https://mlsanity.com/paper/2603.10215/) (2026)

## Abstract (arXiv)

Modeling the distribution of high dimensional data by a latent tree graphical model is a prevalent approach in multiple scientific domains. A common task is to infer the underlying tree structure, given only observations of its terminal nodes. Many algorithms for tree recovery are computationally intensive, which limits their applicability to trees of moderate size. For large trees, a common approach, termed divide-and-conquer, is to recover the tree structure in two steps. First, recover the structure separately of multiple, possibly random subsets of the terminal nodes. Second, merge the resulting subtrees to form a full tree. Here, we develop Spectral Top-Down Recovery (STDR), a deterministic divide-and-conquer approach to infer large latent tree models. Unlike previous methods, STDR partitions the terminal nodes in a non random way, based on the Fiedler vector of a suitable Laplacian matrix related to the observed nodes. We prove that under certain conditions, this partitioning is consistent with the tree structure. This, in turn, leads to a significantly simpler merging procedure of the small subtrees. We prove that STDR is statistically consistent and bound the number of samples required to accurately recover the tree with high probability. Using simulated data from several common tree models in phylogenetics, we demonstrate that STDR has a significant advantage in terms of runtime, with improved or similar accuracy.