Academic literature on the topic 'Dirichlet modeling'

Thesis (Ph.D.)--City University of Hong Kong, 2009.<br>"Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [85]-91)

Functional analyses have gained more interest as we have easier access to massive data sets. However, such data sets often contain large heterogeneities, noise, and dimensionalities. When generalizing the analyses from vectors to functions, classical methods might not work directly. This dissertation considers noisy information reduction in functional analyses from two perspectives: functional variable selection to reduce the dimensionality and functional clustering to group similar observations and thus reduce the sample size. The complicated data structures and relations can be easily modeled by a Bayesian hierarchical model, or developed from a more generic one by changing the prior distributions. Hence, this dissertation focuses on the development of Bayesian approaches for functional analyses due to their flexibilities. A nonparametric Bayesian approach, such as the Dirichlet process mixture (DPM) model, has a nonparametric distribution as the prior. This approach provides flexibility and reduces assumptions, especially for functional clustering, because the DPM model has an automatic clustering property, so the number of clusters does not need to be specified in advance. Furthermore, a weighted Dirichlet process mixture (WDPM) model allows for more heterogeneities from the data by assuming more than one unknown prior distribution. It also gathers more information from the data by introducing a weight function that assigns different candidate priors, such that the less similar observations are more separated. Thus, the WDPM model will improve the clustering and model estimation results. In this dissertation, we used an advanced nonparametric Bayesian approach to study functional variable selection and functional clustering methods. We proposed 1) a stochastic search functional selection method with application to 1-M matched case-crossover studies for aseptic meningitis, to examine the time-varying unknown relationship and find out important covariates affecting disease contractions; 2) a functional clustering method via the WDPM model, with application to three pathways related to genetic diabetes data, to identify essential genes distinguishing between normal and disease groups; and 3) a combined functional clustering, with the WDPM model, and variable selection approach with application to high-frequency spectral data, to select wavelengths associated with breast cancer racial disparities.<br>Doctor of Philosophy<br>As we have easier access to massive data sets, functional analyses have gained more interest to analyze data providing information about curves, surfaces, or others varying over a continuum. However, such data sets often contain large heterogeneities and noise. When generalizing the analyses from vectors to functions, classical methods might not work directly. This dissertation considers noisy information reduction in functional analyses from two perspectives: functional variable selection to reduce the dimensionality and functional clustering to group similar observations and thus reduce the sample size. The complicated data structures and relations can be easily modeled by a Bayesian hierarchical model due to its flexibility. Hence, this dissertation focuses on the development of nonparametric Bayesian approaches for functional analyses. Our proposed methods can be applied in various applications: the epidemiological studies on aseptic meningitis with clustered binary data, the genetic diabetes data, and breast cancer racial disparities.

La détection de nouveauté est le problème non supervisé d’identification d’anomalies dans des données de test qui diffèrent de manière significative des données d’apprentissage. La représentation de données temporelles ou de données de types mixtes, telles des données numériques et catégorielles, est une tâche complexe. Outre le type de données supporté, l'efficacité des méthodes de détection de nouveauté repose également sur la capacité à dissocier avec précision les anomalies des échantillons nominaux, l'interprétabilité, la scalabilité et la robustesse aux anomalies présentes dans les données d'entraînement. Dans cette thèse, nous explorons de nouvelles façons de répondre à ces contraintes. Plus spécifiquement, nous proposons (i) une étude de l'état de l'art des méthodes de détection de nouveauté, appliquée aux données de types mixtes, et évaluant la scalabilité, la consommation mémoire et la robustesse des méthodes (ii) une étude des méthodes de détection de nouveauté adaptées aux séquences d'évènements (iii) une méthode de détection de nouveauté probabiliste et non paramétrique pour les données de types mixtes basée sur des mélanges de processus de Dirichlet et des distributions de famille exponentielle et (iv) un modèle de détection de nouveauté basé sur un autoencodeur dans lequel l'encodeur et le décodeur sont modélisés par des processus Gaussiens profonds. L’apprentissage de ce modèle est effectué par extension aléatoire des dimensions et par inférence stochastique variationnelle. Cette méthode est adaptée aux dimensions de types mixtes et aux larges volumes de données<br>Novelty detection is the unsupervised problem of identifying anomalies in test data which significantly differ from the training set. While numerous novelty detection methods were designed to model continuous numerical data, tackling datasets composed of mixed-type features, such as numerical and categorical data, or temporal datasets describing discrete event sequences is a challenging task. In addition to the supported data types, the key criteria for efficient novelty detection methods are the ability to accurately dissociate novelties from nominal samples, the interpretability, the scalability and the robustness to anomalies located in the training data. In this thesis, we investigate novel ways to tackle these issues. In particular, we propose (i) a survey of state-of-the-art novelty detection methods applied to mixed-type data, including extensive scalability, memory consumption and robustness tests (ii) a survey of state-of-the-art novelty detection methods suitable for sequence data (iii) a probabilistic nonparametric novelty detection method for mixed-type data based on Dirichlet process mixtures and exponential-family distributions and (iv) an autoencoder-based novelty detection model with encoder/decoder modelled as deep Gaussian processes. The learning of this last model is made tractable and scalable through the use of random feature approximations and stochastic variational inference. The method is suitable for large-scale novelty detection problems and data with mixed-type features. The experiments indicate that the proposed model achieves competitive results with state-of-the-art novelty detection methods

With the rapid development of modern high-throughput technologies, scientists can now collect high-dimensional complex data in different forms, such as medical images, genomics measurements. However, acquisition of more data does not automatically lead to better knowledge discovery. One needs efficient and reliable analytical tools to extract useful information from complex datasets. The main objective of this dissertation is to develop innovative Bayesian methodologies to enable effective and efficient knowledge discovery from complex high-dimensional data. It contains two parts—the development of computationally efficient functional mixed models and the modeling of data heterogeneity via Dirichlet Diffusion Tree. The first part focuses on tackling the computational bottleneck in Bayesian functional mixed models. We propose a computational framework called variational functional mixed model (VFMM). This new method facilitates efficient data compression and high-performance computing in basis space. We also propose a new multiple testing procedure in basis space, which can be used to detect significant local regions. The effectiveness of the proposed model is demonstrated through two datasets, a mass spectrometry dataset in a cancer study and a neuroimaging dataset in an Alzheimer's disease study. The second part is about modeling data heterogeneity by using Dirichlet Diffusion Trees. We propose a Bayesian latent tree model that incorporates covariates of subjects to characterize the heterogeneity and uncover the latent tree structure underlying data. This innovative model may reveal the hierarchical evolution process through branch structures and estimate systematic differences between groups of samples. We demonstrate the effectiveness of the model through the simulation study and a brain tumor real data.<br>Doctor of Philosophy<br>With the rapid development of modern high-throughput technologies, scientists can now collect high-dimensional data in different forms, such as engineering signals, medical images, and genomics measurements. However, acquisition of such data does not automatically lead to efficient knowledge discovery. The main objective of this dissertation is to develop novel Bayesian methods to extract useful knowledge from complex high-dimensional data. It has two parts—the development of an ultra-fast functional mixed model and the modeling of data heterogeneity via Dirichlet Diffusion Trees. The first part focuses on developing approximate Bayesian methods in functional mixed models to estimate parameters and detect significant regions. Two datasets demonstrate the effectiveness of proposed method—a mass spectrometry dataset in a cancer study and a neuroimaging dataset in an Alzheimer's disease study. The second part focuses on modeling data heterogeneity via Dirichlet Diffusion Trees. The method helps uncover the underlying hierarchical tree structures and estimate systematic differences between the group of samples. We demonstrate the effectiveness of the method through the brain tumor imaging data.

Online quality assurance is crucial for elevating product quality and boosting process productivity in advanced manufacturing. However, the inherent complexity of advanced manufacturing, including nonlinear process dynamics, multiple process attributes, and low signal/noise ratio, poses severe challenges for both maintaining stable process operations and establishing efficacious online quality assurance schemes. To address these challenges, four different advanced manufacturing processes, namely, fused filament fabrication (FFF), binder jetting, chemical mechanical planarization (CMP), and the slicing process in wafer production, are investigated in this dissertation for applications of online quality assurance, with utilization of various sensors, such as thermocouples, infrared temperature sensors, accelerometers, etc. The overarching goal of this dissertation is to develop innovative integrated methodologies tailored for these individual manufacturing processes but addressing their common challenges to achieve satisfying performance in online quality assurance based on heterogeneous sensor data. Specifically, three new methodologies are created and validated using actual sensor data, namely, (1) Real-time process monitoring methods using Dirichlet process (DP) mixture model for timely detection of process changes and identification of different process states for FFF and CMP. The proposed methodology is capable of tackling non-Gaussian data from heterogeneous sensors in these advanced manufacturing processes for successful online quality assurance. (2) Spatial Dirichlet process (SDP) for modeling complex multimodal wafer thickness profiles and exploring their clustering effects. The SDP-based statistical control scheme can effectively detect out-of-control wafers and achieve wafer thickness quality assurance for the slicing process with high accuracy. (3) Augmented spatiotemporal log Gaussian Cox process (AST-LGCP) quantifying the spatiotemporal evolution of porosity in binder jetting parts, capable of predicting high-risk areas on consecutive layers. This work fills the long-standing research gap of lacking rigorous layer-wise porosity quantification for parts made by additive manufacturing (AM), and provides the basis for facilitating corrective actions for product quality improvements in a prognostic way. These developed methodologies surmount some common challenges of advanced manufacturing which paralyze traditional methods in online quality assurance, and embody key components for implementing effective online quality assurance with various sensor data. There is a promising potential to extend them to other manufacturing processes in the future.<br>Ph. D.

Les travaux de cette thèse présentent le développement d'algorithmes de classification de documents d'une part, ou d'analyse de réseaux complexes d'autre part, en s'appuyant sur la prétopologie, une théorie qui modélise le concept de proximité. Le premier travail développe un cadre pour la classification de documents en combinant une approche de topicmodeling et la prétopologie. Notre contribution propose d'utiliser des distributions de sujets extraites à partir d'un traitement topic-modeling comme entrées pour des méthodes de classification. Dans cette approche, nous avons étudié deux aspects : déterminer une distance adaptée entre documents en étudiant la pertinence des mesures probabilistes et des mesures vectorielles, et effet réaliser des regroupements selon plusieurs critères en utilisant une pseudo-distance définie à partir de la prétopologie. Le deuxième travail introduit un cadre général de modélisation des Réseaux Complexes en développant une reformulation de la prétopologie stochastique, il propose également un modèle prétopologique de cascade d'informations comme modèle général de diffusion. De plus, nous avons proposé un modèle agent, Textual-ABM, pour analyser des réseaux complexes dynamiques associés à des informations textuelles en utilisant un modèle auteur-sujet et nous avons introduit le Textual-Homo-IC, un modèle de cascade indépendant de la ressemblance, dans lequel l'homophilie est fondée sur du contenu textuel obtenu par un topic-model<br>The work of this thesis presents the development of algorithms for document classification on the one hand, or complex network analysis on the other hand, based on pretopology, a theory that models the concept of proximity. The first work develops a framework for document clustering by combining Topic Modeling and Pretopology. Our contribution proposes using topic distributions extracted from topic modeling treatment as input for classification methods. In this approach, we investigated two aspects: determine an appropriate distance between documents by studying the relevance of Probabilistic-Based and Vector-Based Measurements and effect groupings according to several criteria using a pseudo-distance defined from pretopology. The second work introduces a general framework for modeling Complex Networks by developing a reformulation of stochastic pretopology and proposes Pretopology Cascade Model as a general model for information diffusion. In addition, we proposed an agent-based model, Textual-ABM, to analyze complex dynamic networks associated with textual information using author-topic model and introduced Textual-Homo-IC, an independent cascade model of the resemblance, in which homophily is measured based on textual content obtained by utilizing Topic Modeling