Human activity recognition (HAR) is a key challenge in pervasive computing and its solutions have been presented based on various disciplines. Specifically, for HAR in a smart space without privacy and accessibility issues, data streams generated by deployed pervasive sensors are leveraged. In this paper, we focus on a group activity by which a group of users perform a collaborative task without user identification and propose an efficient group activity recognition scheme which extracts causality patterns from pervasive sensor event sequences generated by a group of users to support as good recognition accuracy as the state-of-the-art graphical model. To filter out irrelevant noise events from a given data stream, a set of rules is leveraged to highlight causally related events. Then, a pattern-tree algorithm extracts frequent causal patterns by means of a growing tree structure. Based on the extracted patterns, a weighted sum-based pattern matching algorithm computes the likelihoods of stored group activities to the given test event sequence by means of matched event pattern counts for group activity recognition. We evaluate the proposed scheme using the data collected from our testbed and CASAS datasets where users perform their tasks on a daily basis and validate its effectiveness in a real environment. Experiment results show that the proposed scheme performs higher recognition accuracy and with a small amount of runtime overhead than the existing schemes.