Conditionally Dependent Dirichlet Processes for Modelling Naturally Correlated Data Sources PDF Download

Author: Dinh Phung
Publisher:
ISBN:
Category : Correlation (Statistics)
Languages : en
Pages : 28

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Book Description
"We introduce a new class of conditionally dependent Dirichlet processes (CDP) for hierarchical mixture modelling of naturally correlated data sources. This class of models provides a Bayesian nonparametric approach for modelling a range of challenging datasets which typically consists of heterogeneous observations from multiple correlated data channels. Some typical examples include annotated social media, networks in community where information about friendship and relation coexist with user's pro les, medical records where patient's information exists in several dimension (demographic information, medical history, drug uses and so on). The proposed framework can easily be tailored to model multiple data sources which are correlated by some latent underlying processes, whereas most of existing topic models, notably hierarchical Dirichlet processes (HDP), is designed for only a single data observation channel. In these existing approaches, data are grouped into documents (e.g., text documents or they are grouped according to some covariates such as time or location). Our approach is di erent: we view context as distributions over some index space and model both topics and contexts jointly. Distributions over topic parameters are modelled according to the usual Dirichlet processes. Stick-breaking representation gives rise to explicit realizations of topic atoms which we use as an indexing mechanism to induce conditional random mixture distributions on the context observation spaces { loosely speaking, we use a stochastic process, being DP, to conditionally `index' other stochastic processes. The later can be designed on any suitable family of stochastic processes to suit modelling needs or data types of contexts (such as Beta or Gaussian processes). Dirichlet process is of course an obvious choice. Our model can be viewed as an integration of the hierarchical Dirichlet process (HDP) and the recent nested Dirichlet process (nDP) with shared mixture components. In fact, it provides an interesting interpretation whereas, under a suitable parameterization, integrating out the topic components results in a nested DP, whereas integrating out the context components results in a hierarchical DP. Di erent approaches for posterior inference exist. This paper focus on the development of an auxiliary conditional Gibbs sampling in which both topic and context atoms are marginalized out. We demonstrate the framework on synthesis datasets for temporal topic modelling and trajectory discovery in videos surveillance. We then demonstrate an application on a current visual category classi cation challenge in computer vision for which we signi cantly outperform the current reported state-of-the-art results. Finally, it is worthwide to note that our proposed approach can be easily twisted to accommodate di erent forms of supervision (weakly annotated data, semi-supervision) and to perform prediction." -- Abstract.