A Survey on Latent Tree Models and Applications

Abstract

In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic graphical models, deserves attention. Its simple structure - a tree - allows simple and efficient inference, while its latent variables capture complex relationships. In the past decade, the latent tree model has been subject to significant theoretical and methodological developments. In this review, we propose a comprehensive study of this model. First we summarize key ideas underlying the model. Second we explain how it can be efficiently learned from data. Third we illustrate its use within three types of applications: latent structure discovery, multidimensional clustering, and probabilistic inference. Finally, we conclude and give promising directions for future researches in this field

A method combining a random forest-based technique with the modeling of linkage disequilibrium through latent variables, to run multilocus genome-wide association studies

“…Learning the tree structure can only be efficiently addressed through iterative ascending clustering of the variables. Mourad and co-workers examined various such clustering-based approaches and their limitations [40]. In the latter work, 15 methods were compared, including FLTM (named CFHLC in the paper cited) ([40], page 183).…”

“…Mourad and co-workers examined various such clustering-based approaches and their limitations [40]. In the latter work, 15 methods were compared, including FLTM (named CFHLC in the paper cited) ([40], page 183). FLTM was the method with the highest scalability.…”

“…On the other hand, it has to be noted that in its very first version (i.e. a window-based version), FLTM was also tested on still larger datasets as in [40] (e.g. describing 100,000 variables [32]).…”

“…There exist candidate structures for a latent tree derived from n observed variables [39]. Learning the tree structure can only be efficiently addressed through iterative ascending clustering of the variables [40]. A similarity measure based on mutual information is usually used to cluster discrete variables.…”

Using Copulas in Data Mining Based on the Observational Calculus

“…Most frequently, they are encountered in connection with classification and regression trees [44]- [46], which differ substantially from HACs in the sense that they make no distributional assumptions about the data. Besides decision trees, however, there exist also several approaches that are similar to HACs in making such assumptions, most importantly maximum weight spanning trees, probabilistic decision graphs, tree belief networks, and latent tree models [47]- [50], encountered in the area of probabilistic graphical models [51], [52]. In this section, we compare the results obtained using HACs with those obtained using two kinds of maximum weight spanning trees, in accordance with the proposal in [53].…”