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Sensor-based activity recognition aims to predict users' activities from multi-dimensional streams of various sensor readings received from ubiquitous sensors. To use machine learning techniques for sensor-based activity recognition, previous approaches focused on composing a feature vector to represent sensor-reading streams received within a period of various lengths. With the constructed feature vectors, e.g., using predefined orders of moments in statistics, and their corresponding labels of activities, standard classification algorithms can be applied to train a predictive model, which will be used to make predictions online. However, we argue that in this way some important information, e.g., statistical information captured by higher-order moments, may be discarded when constructing features. Therefore, in this paper, we propose a new method, denoted by SMMAR, based on learning from distributions for sensor-based activity recognition. Specifically, we consider sensor readings received within a period as a sample, which can be represented by a feature vector of infinite dimensions in a Reproducing Kernel Hilbert Space (RKHS) using kernel embedding techniques. We then train a classifier in the RKHS. To scale-up the proposed method, we further offer an accelerated version by utilizing an explicit feature map instead of using a kernel function. We conduct experiments on four benchmark datasets to verify the effectiveness and scalability of our proposed method.