Latent Tree Models Research Articles

A survey of post COVID-19 symptoms from the perspective of traditional medicine

Background: Individuals experiencing post-COVID-19 syndrome may endure lingering health deterioration, leading to challenges in daily activities and impacting mental and physical health, thus potentially burdening themselves, their families, and society. According to traditional medicine (TM), post-COVID-19 represents a recovery period following the flu in COVID. At this stage, the body remains incompletely restored, characterized by depleted vital energy and damaged body fluids, thus affecting the functions of various organ systems. To comprehensively understand post-COVID-19 symptoms from the perspective of traditional medicine and offer valuable insights for diagnosis, treatment, and prevention, this study conducted a survey of post-COVID-19 symptoms using the latent tree model. Methods: A cross-sectional descriptive study was conducted. Data were collected through direct interviews with 282 post-COVID-19 patients over three months at the Ho Chi Minh City Traditional Medicine Hospital from January 2023 to May 2023. Results: Among the collected samples, 38 post-COVID-19 symptoms were recorded, with the five most common symptoms being forgetfulness (58.2%), fatigue (47.5%), hair loss (42.6%), sleep disorders (25.9%), and shortness of breath (25.5%). Analysis using a latent tree model unveiled that within the kidney viscera, forgetfulness and hair loss emerged as primary symptoms, accompanied by tinnitus, anxiety, and hearing impairment. In the spleen viscera, fatigue prevailed as the main symptom, alongside muscle soreness, abdominal fullness, diarrhea, and constipation. In the lung viscera, shortness of breath was identified as the predominant symptom, accompanied by rapid breathing, coughing, breathing difficulties, and a sore throat. In the liver viscera, insomnia was the most perceived symptom, with secondary symptoms including anxiety, headache, and dizziness. In the heart viscera, primary symptoms included attention disorders and insomnia, with secondary symptoms being chest tightness. Conclusion: The most common symptoms observed were forgetfulness, fatigue, hair loss, sleep disorders, and shortness of breath. Post-COVID-19 symptoms affect all five visceras according to traditional medicine. Key words: Post COVID-19 symptoms; Traditional Medicine; Latent tree model.

Spectral top-down recovery of latent tree models.

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, separately recover the structure 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.

A Stan tutorial on Bayesian IRTree models: Conventional models and explanatory extension.

IRTree models have been receiving increasing attention. However, to date, there are limited sources that provide a systematic introduction to Bayesian modeling techniques using modern probabilistic programming frameworks for the implementation of IRTree models. To facilitate the research and application of IRTree models, this paper introduces how to perform two families of Bayesian IRTree models (i.e., response tree models and latent tree models) in Stan and how to extend them in an explanatory way. Some suggestions on executing Stan codes and checking convergence are also provided. An empirical study based on the Oxford Achieving Resilience during COVID-19 data was conducted as an example to further illustrate how to apply Bayesian IRTree models to address research questions. Finally, strengths and future directions are discussed.

Diagnostic traditional medicine criteria of Covid-19 by using a latent tree model

Objectives: Until now, the guideline of the Vietnam Ministry of Health and several pieces of research have confirmed the effectiveness of traditional medicine in managing Covid-19, especially for mild levels. However, the research on differentiating traditional medicine disease patterns of Covid-19 to systemise diagnosis and treatment has not been implemented. Thence, this study aimed to establish diagnostic criteria for mild clinical forms of Covid-19 using latent tree models (LTMs). Materials and methods: Stage 1: Conduct studies on classic medical documents, textbooks and monographs on traditional medicine, to make questionnaires to observe symptoms in Covid-19 patients at a mild stage. Stage 2: Choosing and investigating Covid-19 patients at a mild stage by inclusion criteria. A 65-question survey was used to investigate 438 patients at Ho Chi Minh city Traditional Medicine Hospital, then included data were analysed by using the latent tree model. Results: Literature review exhibited 10 documents (5 classic medical documents, 5 textbooks) with content related to Covid-19. After modelling, 21 latent variables (Y0 to Y20) were established, referring to the groups of included symptom variables. According to ve - khi - dinh - huyet diagnosis theory, 2 traditional medical disease patterns are matching with the literature: the Ve-area disease pattern and the Khi-area disease pattern. Conclusions: The latent tree model analysis pointed out 2 traditional medical disease patterns of Covid-19 at a mild stage, including the Ve-area disease pattern and Khi-area disease pattern.

Developing diagnostic criteria of illness of traditional medicine on patients with carpal tunnel syndrome by a descriptive cross-sectional survey

Carpal tunnel syndrome (CTS) is one of the most common neurodegenerative conditions. However, studies on the classifications and symptoms of CTS from the perspective of traditional medicine are still limited. Our study aims to identify traditional medicine disease nomenclature and symptoms of CTS by the survey form. A descriptive cross-sectional study was conducted at The 3rd branch of University Medical Center HCMC, Thong Nhat Hospital from March 2021 to June 2021. We conducted a study survey on patients diagnosed with primary CTS and agreed to participate in the study with survey questionnaires, data were processed by using Excel 2016 and Lantern 5.0 software. 48 symptoms collected from 94 patients with CTS based on questionnaires were included in the Latent Tree Model. Compared with the medical literature review, there were 40/48 symptoms and 5 patterns appearing in the collected sample. These 5 main patterns: Blood stasis has 4 symptoms, yin deficiency has 6 symptoms, damp heat has 3 symptoms, blood deficiency has 3 symptoms and invasion of meridians of wind cold has 3 symptoms to diagnose. The results of the study have shown that the results of the algorithms are statistically significant when comparing clusters of latent variables with traditional medicine descriptions. Therefore, the use of the results of the machine has a scientific basis in terms of statistics. After analyzing clinical data from 94 patients with Latent Tree Model, it was found that 5 disease patterns appeared with symptoms helping diagnose those disease patterns.

Low-Voltage Distribution Grid Topology Identification With Latent Tree Model

Distribution grid topology information is the basis of grid analysis functions such as power flow and state estimation. Due to lack of monitoring and measurement devices in low-voltage distribution grids (LVDGs), the intermediate nodes connecting LVDG transformers to end-users cannot upload the nodal operation status. The existence of these latent nodes poses a huge challenge to LVDG topology identification. This paper proposes a LVDG latent node and topology identification method based on end-user data from smart meters. Specifically, a special latent-node embedded Bayesian network, defined as latent tree model, is proposed to provide probabilistic representation for all possible LVDG topologies. A search-based algorithm is proposed to generate candidate topologies and then a Bayesian information criterion is proposed to describe the accuracy of the candidate topologies. Meanwhile, the Expectation-Maximization algorithm is introduced to complement measurement lacking latent nodes. Test results in different simulation scenarios and practical LVDGs demonstrate the effectiveness and robustness of the proposed method.

Differentially Private Publication of Vertically Partitioned Data

In this paper, we study the problem of publishing vertically partitioned data under differential privacy, where different attributes of the same set of individuals are held by multiple parties. In this setting, with the assistance of a semi-trusted curator, the involved parties aim to collectively generate an integrated dataset while satisfying differential privacy for each local dataset. Based on the latent tree model (LTM), we present a differentially private latent tree (DPLT) approach, which is, to the best of our knowledge, the first approach to solving this challenging problem. In DPLT, the parties and the curator collaboratively identify the latent tree that best approximates the joint distribution of the integrated dataset, from which a synthetic dataset can be generated. The fundamental advantage of adopting LTM is that we can use the connections between a small number of latent attributes derived from each local dataset to capture the cross-dataset dependencies of the observed attributes in all local datasets such that the joint distribution of the integrated dataset can be learned with little injected noise and low computation and communication costs. DPLT is backed up by a series of novel techniques, including two-phase latent attribute generation (TLAG), tree index based correlation quantification (TICQ) and distributed Laplace perturbation protocol (DLPP). Extensive experiments on real datasets demonstrate that DPLT offers desirable data utility with low computation and communication costs.

Spectral neighbor joining for reconstruction of latent tree Models.

A common assumption in multiple scientific applications is that the distribution of observed data can be modeled by a latent tree graphical model. An important example is phylogenetics, where the tree models the evolutionary lineages of a set of observed organisms. Given a set of independent realizations of the random variables at the leaves of the tree, a key challenge is to infer the underlying tree topology. In this work we develop Spectral Neighbor Joining (SNJ), a novel method to recover the structure of latent tree graphical models. Given a matrix that contains a measure of similarity between all pairs of observed variables, SNJ computes a spectral measure of cohesion between groups of observed variables. We prove that SNJ is consistent, and derive a sufficient condition for correct tree recovery from an estimated similarity matrix. Combining this condition with a concentration of measure result on the similarity matrix, we bound the number of samples required to recover the tree with high probability. We illustrate via extensive simulations that in comparison to several other reconstruction methods, SNJ requires fewer samples to accurately recover trees with a large number of leaves or long edges.

Modeling of Multilayer Multicontent Latent Tree and Its Applications

Latent tree model (LTM) is a probabilistic tree-structured graphical model, which can reveal the hidden hierarchical causal relations among data contents and play a key role in explainable artificial intelligence. However, because current LTM modeling techniques are only suitable for single-content variable, the applications of LTMs are somewhat limited. Toward this end, a multilayer LTM (ML-LTM) is first presented to deal with the hierarchical clustering issues of multicontent variables. Second, we further develop an ML-LTM-based multicontent recommendation system. Our experiment results show that the proposed ML-LTM can achieve 90% recommendation accuracy, but the current LTM can only has 20%. Third, we propose an incremental update approach for ML-LTM that can save five-sixth updating time comparing with the whole-model retraining approach for achieving the same recommendation accuracy.

A Top-Down Binary Hierarchical Topic Model for Biomedical Literature

Over the past two decades, a number of advances in topic modeling have produced sophisticated models that are capable of generating topic hierarchies. In particular, hierarchical Latent Dirichlet Allocation (hLDA) builds a topic tree based on the nested Chinese Restaurant Process (nCRP) or other sampling processes to generate a topic hierarchy that allows arbitrarily large branch structures and adaptive dataset growth. In addition, hierarchical topic models based on the latent tree model, such as Hierarchical Latent Tree Analysis (HLTA), have been developed over the last five years. However, these models do not work well in cases with millions of documents and hundreds of thousands of terms. In addition, the topic trees generated by these models are always poorly interpretable, and the relationships among topics in different levels are relatively simple. The biomedical literature, including Medline abstracts, has large-scale documents in two major categories: biological laboratory research and medical clinical research. We propose a top-down binary hierarchical topic model (biHTM) for biomedical literature by iteratively applying a flat topic model and adaptively processing subtrees of the hierarchy. The biHTM topic hierarchy of complete Medline abstracts with more than 14 topic node levels shows good bimodality and interpretability. Compared to hLDA and HLTA, biHTM shows promising results in experiments assessed in terms of runtime and quality.

Incremental Learning of Latent Forests

In the analysis of real-world data, it is useful to learn a latent variable model that represents the data generation process. In this setting, latent tree models are useful because they are able to capture complex relationships while being easily interpretable. In this paper, we propose two incremental algorithms for learning forests of latent trees. Unlike current methods, the proposed algorithms are based on the variational Bayesian framework, which allows them to introduce uncertainty into the learning process and work with mixed data. The first algorithm, incremental learner , determines the forest structure and the cardinality of its latent variables in an iterative search process. The second algorithm, constrained incremental learner , modifies the previous method by considering only a subset of the most prominent structures in each step of the search. Although restricting each iteration to a fixed number of candidate models limits the search space, we demonstrate that the second algorithm returns almost identical results for a small fraction of the computational cost. We compare our algorithms with existing methods by conducting a comparative study using both discrete and continuous real-world data. In addition, we demonstrate the effectiveness of the proposed algorithms by applying them to data from the 2018 Spanish Living Conditions Survey. All code, data, and results are available at https://github.com/ferjorosa/incremental-latent-forests .

Traditional Chinese Medicine syndrome elements of male infertility revealed by latent tree model analysis

OBJECTIVETo explore the features of Traditional Chinese Medicine (TCM) syndromes in male infertility using computer-based analyses. METHODSLatent class analysis was used to analyze the TCM syndrome data from 813 patients with male infertility and establish a latent tree model. RESULTSA latent tree model with a Bayesian information criterion score of – 11 263 was created. This model revealed that the characteristics of basic TCM syndromes in patients with male infertility were kidney Yang deficiency, kidney Qi deficiency, spleen Yang deficiency, liver Qi stagnation, Qi stagnation and blood stasis, and dump-heat; moreover, most patients with male infertility had complex syndromes (spleen-kidney Yang deficiency and liver Qi stagnation) rather than simple single syndromes. CONCLUSIONThe hidden tree model analysis revealed the objective and quantitative complex relationships between the TCM symptoms of male infertility, and obtained the quantification and objective evidence of TCM syndromes in male infertility.

Experiments with learning graphical models on text

A rich variety of models are now in use for unsupervised modelling of text documents, and, in particular, a rich variety of graphical models exist, with and without latent variables. To date, there is inadequate understanding about the comparative performance of these, partly because they are subtly different, and they have been proposed and evaluated in different contexts. This paper reports on our experiments with a representative set of state of the art models: chordal graphs, matrix factorisation, and hierarchical latent tree models. For the chordal graphs, we use different scoring functions. For matrix factorisation models, we use different hierarchical priors, asymmetric priors on components. We use Boolean matrix factorisation rather than topic models, so we can do comparable evaluations. The experiments perform a number of evaluations: probability for each document, omni-directional prediction which predicts different variables, and anomaly detection. We find that matrix factorisation performed well at anomaly detection but poorly on the prediction task. Chordal graph learning performed the best generally, and probably due to its lower bias, often out-performed hierarchical latent trees.

UC-LTM: Unidimensional clustering using latent tree models for discrete data

This paper is concerned with model-based clustering of discrete data. Latent class models (LCMs) are usually used for this task. An LCM consists of a latent variable and a number of attributes. It makes the overly restrictive assumption that the attributes are conditionally independent given the latent variable. We propose a novel method to relax this assumption. The key idea is to partition the attributes into groups such that correlations among the attributes in each group can be properly modeled by using a single latent variable. The latent variables for the attribute groups are then used to build a number of models, and one of them is chosen to produce the clustering results. The new method produces unidimensional clustering using latent tree models and is named UC-LTM. Extensive empirical studies were conducted to compare UC-LTM with several model-based and distance-based clustering methods. UC-LTM outperforms the alternative methods in most cases, and the differences are often large. Further, analysis on real-world social capital data further shows improved results given by UC-LTM over results given by LCMs in a previous study.

Latent Regression Forest: Structured Estimation of 3D Hand Poses

In this paper we present the latent regression forest (LRF), a novel framework for real-time, 3D hand pose estimation from a single depth image. Prior discriminative methods often fall into two categories: holistic and patch-based. Holistic methods are efficient but less flexible due to their nearest neighbour nature. Patch-based methods can generalise to unseen samples by consider local appearance only. However, they are complex because each pixel need to be classified or regressed during testing. In contrast to these two baselines, our method can be considered as a structured coarse-to-fine search, starting from the centre of mass of a point cloud until locating all the skeletal joints. The searching process is guided by a learnt latent tree model which reflects the hierarchical topology of the hand. Our main contributions can be summarised as follows: (i) Learning the topology of the hand in an unsupervised, data-driven manner. (ii) A new forest-based, discriminative framework for structured search in images, as well as an error regression step to avoid error accumulation. (iii) A new multi-view hand pose dataset containing 180 K annotated images from 10 different subjects. Our experiments on two datasets show that the LRF outperforms baselines and prior arts in both accuracy and efficiency.

Latent tree models for hierarchical topic detection

We present a novel method for hierarchical topic detection where topics are obtained by clustering documents in multiple ways. Specifically, we model document collections using a class of graphical models called hierarchical latent tree models (HLTMs). The variables at the bottom level of an HLTM are observed binary variables that represent the presence/absence of words in a document. The variables at other levels are binary latent variables that represent word co-occurrence patterns or co-occurrences of such patterns. Each latent variable gives a soft partition of the documents, and document clusters in the partitions are interpreted as topics. Latent variables at high levels of the hierarchy capture long-range word co-occurrence patterns and hence give thematically more general topics, while those at low levels of the hierarchy capture short-range word co-occurrence patterns and give thematically more specific topics. In comparison with LDA-based methods, a key advantage of the new method is that it represents co-occurrence patterns explicitly using model structures. Extensive empirical results show that the new method significantly outperforms the LDA-based methods in term of model quality and meaningfulness of topics and topic hierarchies.

Marginal likelihood and model selection for Gaussian latent tree and forest models

Gaussian latent tree models, or more generally, Gaussian latent forest models have Fisher-information matrices that become singular along interesting submodels, namely, models that correspond to subforests. For these singularities, we compute the real log-canonical thresholds (also known as stochastic complexities or learning coefficients) that quantify the large-sample behavior of the marginal likelihood in Bayesian inference. This provides the information needed for a recently introduced generalization of the Bayesian information criterion. Our mathematical developments treat the general setting of Laplace integrals whose phase functions are sums of squared differences between monomials and constants. We clarify how in this case real log-canonical thresholds can be computed using polyhedral geometry, and we show how to apply the general theory to the Laplace integrals associated with Gaussian latent tree and forest models. In simulations and a data example, we demonstrate how the mathematical knowledge can be applied in model selection.

VISTopic: A visual analytics system for making sense of large document collections using hierarchical topic modeling

Effective analysis of large text collections remains a challenging problem given the growing volume of available text data. Recently, text mining techniques have been rapidly developed for automatically extracting key information from massive text data. Topic modeling, as one of the novel techniques that extracts a thematic structure from documents, is widely used to generate text summarization and foster an overall understanding of the corpus content. Although powerful, this technique may not be directly applicable for general analytics scenarios since the topics and topic–document relationship are often presented probabilistically in models. Moreover, information that plays an important role in knowledge discovery, for example, times and authors, is hardly reflected in topic modeling for comprehensive analysis. In this paper, we address this issue by presenting a visual analytics system, VISTopic, to help users make sense of large document collections based on topic modeling. VISTopic first extracts a set of hierarchical topics using a novel hierarchical latent tree model (HLTM) (Liu et al., 2014). In specific, a topic view accounting for the model features is designed for overall understanding and interactive exploration of the topic organization. To leverage multi-perspective information for visual analytics, VISTopic further provides an evolution view to reveal the trend of topics and a document view to show details of topical documents. Three case studies based on the dataset of IEEE VIS conference demonstrate the effectiveness of our system in gaining insights from large document collections.

Spectral methods for learning discrete latent tree models

Spectral methods for learning discrete latent tree models

Gaussian tree constraints applied to acoustic linguistic functional data

Evolutionary models of languages are usually considered to take the form of trees. With the development of so-called tree constraints the plausibility of the tree model assumptions can be assessed by checking whether the moments of observed variables lie within regions consistent with Gaussian latent tree models. In our linguistic application, the data set comprises acoustic samples (audio recordings) from speakers of five Romance languages or dialects. The aim is to assess these functional data for compatibility with a hereditary tree model at the language level. A novel combination of canonical function analysis (CFA) with a separable covariance structure produces a representative basis for the data. The separable-CFA basis is formed of components which emphasize language differences whilst maintaining the integrity of the observational language-groupings. A previously unexploited Gaussian tree constraint is then applied to component-by-component projections of the data to investigate adherence to an evolutionary tree. The results highlight some aspects of Romance language speech that appear compatible with an evolutionary tree model but indicate that it would be inappropriate to model all features as such.