Latent tree models

Latent tree models are graphical models defined on trees, in which only a subset of variables is observed. They were first discussed by Judea Pearl as tree-decomposable distributions to generalise star-decomposable distributions such as the latent class model. Latent tree models, or their submodels, are widely used in: phylogenetic analysis, network tomography, computer vision, causal modeling, and data clustering. They also contain other well-known classes of models like hidden Markov models, Brownian motion tree model, the Ising model on a tree, and many popular models used in phylogenetics. This article offers a concise introduction to the theory of latent tree models. We emphasise the role of tree metrics in the structural description of this model class, in designing learning algorithms, and in understanding fundamental limits of what and when can be learned

The correlation space of Gaussian latent tree models and model selection without fitting

We provide a complete description of possible covariance matrices consistent with a Gaussian latent tree model for any tree. We then present techniques for utilising these constraints to assess whether observed data is compatible with that Gaussian latent tree model. Our method does not require us first to fit such a tree. We demonstrate the usefulness of the inverse-Wishart distribution for performing preliminary assessments of tree-compatibility using semialgebraic constraints. Using results from Drton et al. (2008) we then provide the appropriate moments required for test statistics for assessing adherence to these equality constraints. These are shown to be effective even for small sample sizes and can be easily adjusted to test either the entire model or only certain macrostructures hypothesized within the tree. We illustrate our exploratory tetrad analysis using a linguistic application and our confirmatory tetrad analysis using a biological application.Comment: 15 page

Latent Tree Learning with Differentiable Parsers: Shift-Reduce Parsing and Chart Parsing

Latent tree learning models represent sentences by composing their words according to an induced parse tree, all based on a downstream task. These models often outperform baselines which use (externally provided) syntax trees to drive the composition order. This work contributes (a) a new latent tree learning model based on shift-reduce parsing, with competitive downstream performance and non-trivial induced trees, and (b) an analysis of the trees learned by our shift-reduce model and by a chart-based model.Comment: ACL 2018 workshop on Relevance of Linguistic Structure in Neural Architectures for NL

Context Trees: Augmenting Geospatial Trajectories with Context

Exposing latent knowledge in geospatial trajectories has the potential to provide a better understanding of the movements of individuals and groups. Motivated by such a desire, this work presents the context tree, a new hierarchical data structure that summarises the context behind user actions in a single model. We propose a method for context tree construction that augments geospatial trajectories with land usage data to identify such contexts. Through evaluation of the construction method and analysis of the properties of generated context trees, we demonstrate the foundation for understanding and modelling behaviour afforded. Summarising user contexts into a single data structure gives easy access to information that would otherwise remain latent, providing the basis for better understanding and predicting the actions and behaviours of individuals and groups. Finally, we also present a method for pruning context trees, for use in applications where it is desirable to reduce the size of the tree while retaining useful information

Latent Tree Learning with Differentiable Parsers: Shift-Reduce Parsing and Chart Parsing

Latent tree learning models represent sentences by composing their words according to an induced parse tree, all based on a downstream task. These models often outperform baselines which use (externally provided) syntax trees to drive the composition order. This work contributes (a) a new latent tree learning model based on shift-reduce parsing, with competitive downstream performance and non-trivial induced trees, and (b) an analysis of the trees learned by our shift-reduce model and by a chart-based model.Comment: ACL 2018 workshop on Relevance of Linguistic Structure in Neural Architectures for NL

Learning Latent Trees with Stochastic Perturbations and Differentiable Dynamic Programming

We treat projective dependency trees as latent variables in our probabilistic model and induce them in such a way as to be beneficial for a downstream task, without relying on any direct tree supervision. Our approach relies on Gumbel perturbations and differentiable dynamic programming. Unlike previous approaches to latent tree learning, we stochastically sample global structures and our parser is fully differentiable. We illustrate its effectiveness on sentiment analysis and natural language inference tasks. We also study its properties on a synthetic structure induction task. Ablation studies emphasize the importance of both stochasticity and constraining latent structures to be projective trees.Comment: Accepted at ACL 201

Applying latent tree analysis to classify Traditional Chinese Medicine syndromes (Zheng) in patients with psoriasis vulgari

OBJECTIVE To treat patients with psoriasis vulgaris using Traditional Chinese Medicine (TCM), one must stratify patients into subtypes (known as TCM syndromes or Zheng) and apply appropriate TCM treatments to different subtypes. However, no unified symptom-based classification scheme of subtypes (Zheng) exists for psoriasis vulgaris. The present paper aims to classify patients with psoriasis vulgaris into different subtypes via the analysis of clinical TCM symptom and sign data. METHODS A cross-sectional survey was carried out in Beijing from 2005-2008, collecting clinical TCM symptom and sign data from 2764 patients with psoriasis vulgaris. Roughly 108 symptoms and signs were initially analyzed using latent tree analysis, with a selection of the resulting latent variables then used as features to cluster patients into subtypes. RESULTS The initial latent tree analysis yielded a model with 43 latent variables. The second phase of the analysis divided patients into three subtype groups with clear TCM Zheng connotations: 'blood deficiency and wind dryness'; 'blood heat'; and 'blood stasis'. CONCLUSIONS Via two-phase analysis of clinic symptom and sign data, three different Zheng subtypes were identified for psoriasis vulgaris. Statistical characteristics of the three subtypes are presented. This constitutes an evidence-based solution to the syndromedifferentiation problem that exists with psoriasis vulgaris