Dirichlet process mixture models with pairwise constraints for data clustering

The Dirichlet process mixture (DPM) model, a typical Bayesian nonparametric model, can infer the number of clusters automatically, and thus performing priority in data clustering. This paper investigates the influence of pairwise constraints in the DPM model. The pairwise constraint, known as two types: must-link (ML) and cannot-link (CL) constraints, indicates the relationship between two data points. We have proposed two relevant models which incorporate pairwise constraints: the constrained DPM (C-DPM) and the constrained DPM with selected constraints (SC-DPM). In C-DPM, the concept of chunklet is introduced. ML constraints are compiled into chunklets and CL constraints exist between chunklets. We derive the Gibbs sampling of the C-DPM based on chunklets. We further propose a principled approach to select the most useful constraints, which will be incorporated into the SC-DPM. We evaluate the proposed models based on three real datasets: 20 Newsgroups dataset, NUS-WIDE image dataset and Facebook comments datasets we collected by ourselves. Our SC-DPM performs priority in data clustering. In addition, our SC-DPM can be potentially used for short-text clustering.

SECC: simultaneous extraction of context and community from pervasive signals

Understanding user contexts and group structures plays a central role in pervasive computing. These contexts and community structures are complex to mine from data collected in the wild due to the unprecedented growth of data, noise, uncertainties and complexities. Typical existing approaches would first extract the latent patterns to explain the human dynamics or behaviors and then use them as the way to consistently formulate numerical representations for community detection, often via a clustering method. While being able to capture high-order and complex representations, these two steps are performed separately. More importantly, they face a fundamental difficulty in determining the correct number of latent patterns and communities. This paper presents an approach that seamlessly addresses these challenges to simultaneously discover latent patterns and communities in a unified Bayesian nonparametric framework. Our Simultaneous Extraction of Context and Community (SECC) model roots in the nested Dirichlet process theory which allows nested structure to be built to explain data at multiple levels. We demonstrate our framework on three public datasets where the advantages of the proposed approach are validated.

Learning latent activities from social signals with hierarchical dirichlet processes

Understanding human activities is an important research topic, most noticeably in assisted-living and healthcare monitoring environments. Beyond simple forms of activity (e.g., an RFID event of entering a building), learning latent activities that are more semantically interpretable, such as sitting at a desk, meeting with people, or gathering with friends, remains a challenging problem. Supervised learning has been the typical modeling choice in the past. However, this requires labeled training data, is unable to predict never-seen-before activity, and fails to adapt to the continuing growth of data over time. In this chapter, we explore the use of a Bayesian nonparametric method, in particular the hierarchical Dirichlet process, to infer latent activities from sensor data acquired in a pervasive setting. Our framework is unsupervised, requires no labeled data, and is able to discover new activities as data grows. We present experiments on extracting movement and interaction activities from sociometric badge signals and show how to use them for detecting of subcommunities. Using the popular Reality Mining dataset, we further demonstrate the extraction of colocation activities and use them to automatically infer the structure of social subgroups. © 2014 Elsevier Inc. All rights reserved.

Bayesian nonparametric multilevel clustering with group-level contexts

We present a Bayesian nonparametric framework for multilevel clustering which utilizes group- level context information to simultaneously discover low-dimensional structures of the group contents and partitions groups into clusters. Using the Dirichlet process as the building block, our model constructs a product base-measure with a nested structure to accommodate content and context observations at multiple levels. The proposed model possesses properties that link the nested Dinchiet processes (nDP) and the Dirichlet process mixture models (DPM) in an interesting way: integrating out all contents results in the DPM over contexts, whereas integrating out group-specific contexts results in the nDP mixture over content variables. We provide a Polyaurn view of the model and an efficient collapsed Gibbs inference procedure. Extensive experiments on real-world datasets demonstrate the advantage of utilizing context information via our model in both text and image domains.

A Bayesian nonparametric approach to multilevel regression

Regression is at the cornerstone of statistical analysis. Multilevel regression, on the other hand, receives little research attention, though it is prevalent in economics, biostatistics and healthcare to name a few. We present a Bayesian nonparametric framework for multilevel regression where individuals including observations and outcomes are organized into groups. Furthermore, our approach exploits additional group-specific context observations, we use Dirichlet Process with product-space base measure in a nested structure to model group-level context distribution and the regression distribution to accommodate the multilevel structure of the data. The proposed model simultaneously partitions groups into cluster and perform regression. We provide collapsed Gibbs sampler for posterior inference. We perform extensive experiments on econometric panel data and healthcare longitudinal data to demonstrate the effectiveness of the proposed model

Simple approximate MAP inference for Dirichlet processes mixtures

The Dirichlet process mixture model (DPMM) is a ubiquitous, flexible Bayesian nonparametric statistical model. However, full probabilistic inference in this model is analytically intractable, so that computationally intensive techniques such as Gibbs sampling are required. As a result, DPMM-based methods, which have considerable potential, are restricted to applications in which computational resources and time for inference is plentiful. For example, they would not be practical for digital signal processing on embedded hardware, where computational resources are at a serious premium. Here, we develop a simplified yet statistically rigorous approximate maximum a-posteriori (MAP) inference algorithm for DPMMs. This algorithm is as simple as DP-means clustering, solves the MAP problem as well as Gibbs sampling, while requiring only a fraction of the computational effort. (For freely available code that implements the MAP-DP algorithm for Gaussian mixtures see http://www.maxlittle.net/.) Unlike related small variance asymptotics (SVA), our method is non-degenerate and so inherits the “rich get richer” property of the Dirichlet process. It also retains a non-degenerate closed-form likelihood which enables out-of-sample calculations and the use of standard tools such as cross-validation. We illustrate the benefits of our algorithm on a range of examples and contrast it to variational, SVA and sampling approaches from both a computational complexity perspective as well as in terms of clustering performance. We demonstrate the wide applicabiity of our approach by presenting an approximate MAP inference method for the infinite hidden Markov model whose performance contrasts favorably with a recently proposed hybrid SVA approach. Similarly, we show how our algorithm can applied to a semiparametric mixed-effects regression model where the random effects distribution is modelled using an infinite mixture model, as used in longitudinal progression modelling in population health science. Finally, we propose directions for future research on approximate MAP inference in Bayesian nonparametrics.

Bayesian mixtures for modelling complex medical data : a case study in Parkinson’s disease

Mixture models are a flexible tool for unsupervised clustering that have found popularity in a vast array of research areas. In studies of medicine, the use of mixtures holds the potential to greatly enhance our understanding of patient responses through the identification of clinically meaningful clusters that, given the complexity of many data sources, may otherwise by intangible. Furthermore, when developed in the Bayesian framework, mixture models provide a natural means for capturing and propagating uncertainty in different aspects of a clustering solution, arguably resulting in richer analyses of the population under study. This thesis aims to investigate the use of Bayesian mixture models in analysing varied and detailed sources of patient information collected in the study of complex disease. The first aim of this thesis is to showcase the flexibility of mixture models in modelling markedly different types of data. In particular, we examine three common variants on the mixture model, namely, finite mixtures, Dirichlet Process mixtures and hidden Markov models. Beyond the development and application of these models to different sources of data, this thesis also focuses on modelling different aspects relating to uncertainty in clustering. Examples of clustering uncertainty considered are uncertainty in a patient’s true cluster membership and accounting for uncertainty in the true number of clusters present. Finally, this thesis aims to address and propose solutions to the task of comparing clustering solutions, whether this be comparing patients or observations assigned to different subgroups or comparing clustering solutions over multiple datasets. To address these aims, we consider a case study in Parkinson’s disease (PD), a complex and commonly diagnosed neurodegenerative disorder. In particular, two commonly collected sources of patient information are considered. The first source of data are on symptoms associated with PD, recorded using the Unified Parkinson’s Disease Rating Scale (UPDRS) and constitutes the first half of this thesis. The second half of this thesis is dedicated to the analysis of microelectrode recordings collected during Deep Brain Stimulation (DBS), a popular palliative treatment for advanced PD. Analysis of this second source of data centers on the problems of unsupervised detection and sorting of action potentials or "spikes" in recordings of multiple cell activity, providing valuable information on real time neural activity in the brain.

Identifying Meaningful Places

Place identification refers to the process of analyzing sensor data in order to detect places, i.e., spatial areas that are linked with activities and associated with meanings. Place information can be used, e.g., to provide awareness cues in applications that support social interactions, to provide personalized and location-sensitive information to the user, and to support mobile user studies by providing cues about the situations the study participant has encountered. Regularities in human movement patterns make it possible to detect personally meaningful places by analyzing location traces of a user. This thesis focuses on providing system level support for place identification, as well as on algorithmic issues related to the place identification process. The move from location to place requires interactions between location sensing technologies (e.g., GPS or GSM positioning), algorithms that identify places from location data and applications and services that utilize place information. These interactions can be facilitated using a mobile platform, i.e., an application or framework that runs on a mobile phone. For the purposes of this thesis, mobile platforms automate data capture and processing and provide means for disseminating data to applications and other system components. The first contribution of the thesis is BeTelGeuse, a freely available, open source mobile platform that supports multiple runtime environments. The actual place identification process can be understood as a data analysis task where the goal is to analyze (location) measurements and to identify areas that are meaningful to the user. The second contribution of the thesis is the Dirichlet Process Clustering (DPCluster) algorithm, a novel place identification algorithm. The performance of the DPCluster algorithm is evaluated using twelve different datasets that have been collected by different users, at different locations and over different periods of time. As part of the evaluation we compare the DPCluster algorithm against other state-of-the-art place identification algorithms. The results indicate that the DPCluster algorithm provides improved generalization performance against spatial and temporal variations in location measurements.

Discovering transcriptional modules by Bayesian data integration.

MOTIVATION: We present a method for directly inferring transcriptional modules (TMs) by integrating gene expression and transcription factor binding (ChIP-chip) data. Our model extends a hierarchical Dirichlet process mixture model to allow data fusion on a gene-by-gene basis. This encodes the intuition that co-expression and co-regulation are not necessarily equivalent and hence we do not expect all genes to group similarly in both datasets. In particular, it allows us to identify the subset of genes that share the same structure of transcriptional modules in both datasets. RESULTS: We find that by working on a gene-by-gene basis, our model is able to extract clusters with greater functional coherence than existing methods. By combining gene expression and transcription factor binding (ChIP-chip) data in this way, we are better able to determine the groups of genes that are most likely to represent underlying TMs. AVAILABILITY: If interested in the code for the work presented in this article, please contact the authors. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Bayesian two-sample tests

In this paper, we present two classes of Bayesian approaches to the two-sample problem. Our first class of methods extends the Bayesian t-test to include all parametric models in the exponential family and their conjugate priors. Our second class of methods uses Dirichlet process mixtures (DPM) of such conjugate-exponential distributions as flexible nonparametric priors over the unknown distributions.

Projective Limit Random Probabilities on Polish Spaces

A pivotal problem in Bayesian nonparametrics is the construction of prior distributions on the space M(V) of probability measures on a given domain V. In principle, such distributions on the infinite-dimensional space M(V) can be constructed from their finite-dimensional marginals---the most prominent example being the construction of the Dirichlet process from finite-dimensional Dirichlet distributions. This approach is both intuitive and applicable to the construction of arbitrary distributions on M(V), but also hamstrung by a number of technical difficulties. We show how these difficulties can be resolved if the domain V is a Polish topological space, and give a representation theorem directly applicable to the construction of any probability distribution on M(V) whose first moment measure is well-defined. The proof draws on a projective limit theorem of Bochner, and on properties of set functions on Polish spaces to establish countable additivity of the resulting random probabilities.

Nonparametric mixtures of factor analyzers

The mixtures of factor analyzers (MFA) model allows data to be modeled as a mixture of Gaussians with a reduced parametrization. We present the formulation of a nonparametric form of the MFA model, the Dirichlet process MFA (DPMFA). The proposed model can be used for density estimation or clustering of high dimensiona data. We utilize the DPMFA for clustering the action potentials of different neurons from extracellular recordings, a problem known as spike sorting. DPMFA model is compared to Dirichlet process mixtures of Gaussians model (DPGMM) which has a higher computational complexity. We show that DPMFA has similar modeling performance in lower dimensions when compared to DPGMM, and is able to work in higher dimensions. ©2009 IEEE.

Determinantal Clustering Processes - A Nonparametric Bayesian Approach to Kernel Based Semi-Supervised Clustering

Semi-supervised clustering is the task of clustering data points into clusters where only a fraction of the points are labelled. The true number of clusters in the data is often unknown and most models require this parameter as an input. Dirichlet process mixture models are appealing as they can infer the number of clusters from the data. However, these models do not deal with high dimensional data well and can encounter difficulties in inference. We present a novel nonparameteric Bayesian kernel based method to cluster data points without the need to prespecify the number of clusters or to model complicated densities from which data points are assumed to be generated from. The key insight is to use determinants of submatrices of a kernel matrix as a measure of how close together a set of points are. We explore some theoretical properties of the model and derive a natural Gibbs based algorithm with MCMC hyperparameter learning. The model is implemented on a variety of synthetic and real world data sets.

A reversible infinite HMM using normalised random measures

Copyright 2014 by the author(s). We present a nonparametric prior over reversible Markov chains. We use completely random measures, specifically gamma processes, to construct a countably infinite graph with weighted edges. By enforcing symmetry to make the edges undirected we define a prior over random walks on graphs that results in a reversible Markov chain. The resulting prior over infinite transition matrices is closely related to the hierarchical Dirichlet process but enforces reversibility. A reinforcement scheme has recently been proposed with similar properties, but the de Finetti measure is not well characterised. We take the alternative approach of explicitly constructing the mixing measure, which allows more straightforward and efficient inference at the cost of no longer having a closed form predictive distribution. We use our process to construct a reversible infinite HMM which we apply to two real datasets, one from epigenomics and one ion channel recording.

BPEL流程监视的可视化实现

When a BPEL process is executed,it is necessary to dynamically monitor the process.BPEL is a executable language,which is not suitable for visual monitoring.On the other hand,BPMN is designed to visually describe business process and is more intuitive for monitoring.To visually monitor a BPEL process, transformation from BPEL to BPMN is necessary.However,current study of transformation from BPEL to BPMN does not support the transformation of"link"activity.Besides,no work has been done to add supplementary information into BPMN during transformation.In this paper,we transform nested BPEL process into a flat BPMN process graph without hierarchy through applying a flattening strategy.Especially, we analyze various scenarios of the transformation of link activity,and provide a method to deal with it. Besides,we analyze the mapping between BPEL activities and BPMN graph,through which we found out that some supplementary information cannot automatically obtained from BPEL process.These supplementary information need to be added during transformation.At the end of this paper,we present the structure of our monitoring tool which is based on our transformation algorithm.