Traditional data mining techniques are designed to model a single type of heterogeneity, such as multi-task learning for modeling task heterogeneity, multi-view learning for modeling view heterogeneity, etc. Recently, a variety of real applications emerged, which exhibit dual heterogeneity, namely both task heterogeneity and view heterogeneity. Examples include insider threat detection across multiple organizations, web image classification in different domains, etc. Existing methods for addressing such problems typically assume that multiple tasks are equally related and multiple views are equally consistent, which limits their application in complex settings with varying task relatedness and view consistency. In this paper, we advance state-of-the-art techniques by adaptively modeling task relatedness and view consistency via a nonparametric Bayes model: we model task relatedness using normal penalty with sparse covariances, and view consistency using matrix Dirichlet process. Based on this model, we propose the NOBLE algorithm using an efficient Gibbs sampler. Experimental results on multiple real data sets demonstrate the effectiveness of the proposed algorithm.