Classifying streams of data, for instance financial transactions or emails, is an essential element in applications such as online advertising and spam or fraud detection. The data stream is often large or even unbounded; furthermore, the stream is in many instances non-stationary. Therefore, an adaptive approach is required that can manage concept drift in an online fashion. This paper presents a probabilistic non-parametric generative model for stream classification that can handle concept drift efficiently and adjust its complexity over time. Unlike recent methods, the proposed model handles concept drift by adapting data-concept association without unnecessary i.i.d. assumption among the data of a batch. This allows the model to efficiently classify data using fewer and simpler base classifiers. Moreover, an online algorithm for making inference on the proposed non-conjugate time-dependent non-parametric model is proposed. Extensive experimental results on several stream datasets demonstrate the effectiveness of the proposed model.