# Guaranteed Scalable Learning of Latent Tree Models

arXiv: https://arxiv.org/abs/1406.4566 · HTML: https://mlsanity.com/paper/1406.4566/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2014.

## Built on by (most cited first, 4 of 4)

- [Identification of Nonlinear Latent Hierarchical Models](https://mlsanity.com/paper/2306.07916/) (2023)
- [Recursive Bayesian Networks: Generalising and Unifying Probabilistic Context-Free Grammars and Dynamic Bayesian Networks](https://mlsanity.com/paper/2111.01853/) (2021)
- [Robustifying Algorithms of Learning Latent Trees with Vector Variables](https://mlsanity.com/paper/2106.00885/) (2021)
- [Disentangling Observed Causal Effects from Latent Confounders using Method of Moments](https://mlsanity.com/paper/2101.06614/) (2021)

## Abstract (arXiv)

We present an integrated approach for structure and parameter estimation in latent tree graphical models. Our overall approach follows a "divide-and-conquer" strategy that learns models over small groups of variables and iteratively merges onto a global solution. The structure learning involves combinatorial operations such as minimum spanning tree construction and local recursive grouping; the parameter learning is based on the method of moments and on tensor decompositions. Our method is guaranteed to correctly recover the unknown tree structure and the model parameters with low sample complexity for the class of linear multivariate latent tree models which includes discrete and Gaussian distributions, and Gaussian mixtures. Our bulk asynchronous parallel algorithm is implemented in parallel and the parallel computation complexity increases only logarithmically with the number of variables and linearly with dimensionality of each variable.