The Dependent Random Measures with Independent Increments in Mixture Models

When observations are organized into groups where commonalties exist amongst them, the dependent random measures can be an ideal choice for modeling. One of the propositions of the dependent random measures is that the atoms of the posterior distribution are shared amongst groups, and hence groups can borrow information from each other. When normalized dependent random measures prior with independent increments are applied, we can derive appropriate exchangeable probability partition function (EPPF), and subsequently also deduce its inference algorithm given any mixture model likelihood. We provide all necessary derivation and solution to this framework. For demonstration, we used mixture of Gaussians likelihood in combination with a dependent structure constructed by linear combinations of CRMs. Our experiments show superior performance when using this framework, where the inferred values including the mixing weights and the number of clusters both respond appropriately to the number of completely random measure used

A non-parametric conditional factor regression model for high-dimensional input and response

In this paper, we propose a non-parametric conditional factor regression (NCFR)model for domains with high-dimensional input and response. NCFR enhances linear regression in two ways: a) introducing low-dimensional latent factors leading to dimensionality reduction and b) integrating an Indian Buffet Process as a prior for the latent factors to derive unlimited sparse dimensions. Experimental results comparing NCRF to several alternatives give evidence to remarkable prediction performance.Comment: 9 pages, 3 figures, NIPS submissio

An Adaptive Online HDP-HMM for Segmentation and Classification of Sequential Data

In the recent years, the desire and need to understand sequential data has been increasing, with particular interest in sequential contexts such as patient monitoring, understanding daily activities, video surveillance, stock market and the like. Along with the constant flow of data, it is critical to classify and segment the observations on-the-fly, without being limited to a rigid number of classes. In addition, the model needs to be capable of updating its parameters to comply with possible evolutions. This interesting problem, however, is not adequately addressed in the literature since many studies focus on offline classification over a pre-defined class set. In this paper, we propose a principled solution to this gap by introducing an adaptive online system based on Markov switching models with hierarchical Dirichlet process priors. This infinite adaptive online approach is capable of segmenting and classifying the sequential data over unlimited number of classes, while meeting the memory and delay constraints of streaming contexts. The model is further enhanced by introducing a learning rate, responsible for balancing the extent to which the model sustains its previous learning (parameters) or adapts to the new streaming observations. Experimental results on several variants of stationary and evolving synthetic data and two video datasets, TUM Assistive Kitchen and collatedWeizmann, show remarkable performance in segmentation and classification, particularly for evolutionary sequences with changing distributions and/or containing new, unseen classes.Comment: 23 pages, 9 figures and 4 table

Bayesian nonparametric image segmentation using a generalized Swendsen-Wang algorithm

Unsupervised image segmentation aims at clustering the set of pixels of an image into spatially homogeneous regions. We introduce here a class of Bayesian nonparametric models to address this problem. These models are based on a combination of a Potts-like spatial smoothness component and a prior on partitions which is used to control both the number and size of clusters. This class of models is flexible enough to include the standard Potts model and the more recent Potts-Dirichlet Process model \cite{Orbanz2008}. More importantly, any prior on partitions can be introduced to control the global clustering structure so that it is possible to penalize small or large clusters if necessary. Bayesian computation is carried out using an original generalized Swendsen-Wang algorithm. Experiments demonstrate that our method is competitive in terms of RAND\ index compared to popular image segmentation methods, such as mean-shift, and recent alternative Bayesian nonparametric models

Smoothed Hierarchical Dirichlet Process: A Non-Parametric Approach to Constraint Measures

Time-varying mixture densities occur in many scenarios, for example, the distributions of keywords that appear in publications may evolve from year to year, video frame features associated with multiple targets may evolve in a sequence. Any models that realistically cater to this phenomenon must exhibit two important properties: the underlying mixture densities must have an unknown number of mixtures, and there must be some "smoothness" constraints in place for the adjacent mixture densities. The traditional Hierarchical Dirichlet Process (HDP) may be suited to the first property, but certainly not the second. This is due to how each random measure in the lower hierarchies is sampled independent of each other and hence does not facilitate any temporal correlations. To overcome such shortcomings, we proposed a new Smoothed Hierarchical Dirichlet Process (sHDP). The key novelty of this model is that we place a temporal constraint amongst the nearby discrete measures $\{G_j\}$ in the form of symmetric Kullback-Leibler (KL) Divergence with a fixed bound $B$. Although the constraint we place only involves a single scalar value, it nonetheless allows for flexibility in the corresponding successive measures. Remarkably, it also led us to infer the model within the stick-breaking process where the traditional Beta distribution used in stick-breaking is now replaced by a new constraint calculated from $B$. We present the inference algorithm and elaborate on its solutions. Our experiment using NIPS keywords has shown the desirable effect of the model

Cooperative Hierarchical Dirichlet Processes: Superposition vs. Maximization

The cooperative hierarchical structure is a common and significant data structure observed in, or adopted by, many research areas, such as: text mining (author-paper-word) and multi-label classification (label-instance-feature). Renowned Bayesian approaches for cooperative hierarchical structure modeling are mostly based on topic models. However, these approaches suffer from a serious issue in that the number of hidden topics/factors needs to be fixed in advance and an inappropriate number may lead to overfitting or underfitting. One elegant way to resolve this issue is Bayesian nonparametric learning, but existing work in this area still cannot be applied to cooperative hierarchical structure modeling. In this paper, we propose a cooperative hierarchical Dirichlet process (CHDP) to fill this gap. Each node in a cooperative hierarchical structure is assigned a Dirichlet process to model its weights on the infinite hidden factors/topics. Together with measure inheritance from hierarchical Dirichlet process, two kinds of measure cooperation, i.e., superposition and maximization, are defined to capture the many-to-many relationships in the cooperative hierarchical structure. Furthermore, two constructive representations for CHDP, i.e., stick-breaking and international restaurant process, are designed to facilitate the model inference. Experiments on synthetic and real-world data with cooperative hierarchical structures demonstrate the properties and the ability of CHDP for cooperative hierarchical structure modeling and its potential for practical application scenarios

Learning Hidden Structures with Relational Models by Adequately Involving Rich Information in A Network

Effectively modelling hidden structures in a network is very practical but theoretically challenging. Existing relational models only involve very limited information, namely the binary directional link data, embedded in a network to learn hidden networking structures. There is other rich and meaningful information (e.g., various attributes of entities and more granular information than binary elements such as "like" or "dislike") missed, which play a critical role in forming and understanding relations in a network. In this work, we propose an informative relational model (InfRM) framework to adequately involve rich information and its granularity in a network, including metadata information about each entity and various forms of link data. Firstly, an effective metadata information incorporation method is employed on the prior information from relational models MMSB and LFRM. This is to encourage the entities with similar metadata information to have similar hidden structures. Secondly, we propose various solutions to cater for alternative forms of link data. Substantial efforts have been made towards modelling appropriateness and efficiency, for example, using conjugate priors. We evaluate our framework and its inference algorithms in different datasets, which shows the generality and effectiveness of our models in capturing implicit structures in networks

Diverse Online Feature Selection

Online feature selection has been an active research area in recent years. We propose a novel diverse online feature selection method based on Determinantal Point Processes (DPP). Our model aims to provide diverse features which can be composed in either a supervised or unsupervised framework. The framework aims to promote diversity based on the kernel produced on a feature level, through at most three stages: feature sampling, local criteria and global criteria for feature selection. In the feature sampling, we sample incoming stream of features using conditional DPP. The local criteria is used to assess and select streamed features (i.e. only when they arrive), we use unsupervised scale invariant methods to remove redundant features and optionally supervised methods to introduce label information to assess relevant features. Lastly, the global criteria uses regularization methods to select a global optimal subset of features. This three stage procedure continues until there are no more features arriving or some predefined stopping condition is met. We demonstrate based on experiments conducted on that this approach yields better compactness, is comparable and in some instances outperforms other state-of-the-art online feature selection methods

Dependent Indian Buffet Process-based Sparse Nonparametric Nonnegative Matrix Factorization

Nonnegative Matrix Factorization (NMF) aims to factorize a matrix into two optimized nonnegative matrices appropriate for the intended applications. The method has been widely used for unsupervised learning tasks, including recommender systems (rating matrix of users by items) and document clustering (weighting matrix of papers by keywords). However, traditional NMF methods typically assume the number of latent factors (i.e., dimensionality of the loading matrices) to be fixed. This assumption makes them inflexible for many applications. In this paper, we propose a nonparametric NMF framework to mitigate this issue by using dependent Indian Buffet Processes (dIBP). In a nutshell, we apply a correlation function for the generation of two stick weights associated with each pair of columns of loading matrices, while still maintaining their respective marginal distribution specified by IBP. As a consequence, the generation of two loading matrices will be column-wise (indirectly) correlated. Under this same framework, two classes of correlation function are proposed (1) using Bivariate beta distribution and (2) using Copula function. Both methods allow us to adopt our work for various applications by flexibly choosing an appropriate parameter settings. Compared with the other state-of-the art approaches in this area, such as using Gaussian Process (GP)-based dIBP, our work is seen to be much more flexible in terms of allowing the two corresponding binary matrix columns to have greater variations in their non-zero entries. Our experiments on the real-world and synthetic datasets show that three proposed models perform well on the document clustering task comparing standard NMF without predefining the dimension for the factor matrices, and the Bivariate beta distribution-based and Copula-based models have better flexibility than the GP-based model.Comment: 14 pages, 10 figure

Nonparametric Relational Topic Models through Dependent Gamma Processes

Traditional Relational Topic Models provide a way to discover the hidden topics from a document network. Many theoretical and practical tasks, such as dimensional reduction, document clustering, link prediction, benefit from this revealed knowledge. However, existing relational topic models are based on an assumption that the number of hidden topics is known in advance, and this is impractical in many real-world applications. Therefore, in order to relax this assumption, we propose a nonparametric relational topic model in this paper. Instead of using fixed-dimensional probability distributions in its generative model, we use stochastic processes. Specifically, a gamma process is assigned to each document, which represents the topic interest of this document. Although this method provides an elegant solution, it brings additional challenges when mathematically modeling the inherent network structure of typical document network, i.e., two spatially closer documents tend to have more similar topics. Furthermore, we require that the topics are shared by all the documents. In order to resolve these challenges, we use a subsampling strategy to assign each document a different gamma process from the global gamma process, and the subsampling probabilities of documents are assigned with a Markov Random Field constraint that inherits the document network structure. Through the designed posterior inference algorithm, we can discover the hidden topics and its number simultaneously. Experimental results on both synthetic and real-world network datasets demonstrate the capabilities of learning the hidden topics and, more importantly, the number of topics