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Here we propose a new machine learning algorithm for classification of human activities by means of accelerometer and gyroscope signals. Based on a novel hierarchical system of logistic regression classifiers and a relatively small set of features extracted from the filtered signals, the proposed algorithm outperformed previous work on the DaLiAc (Daily Life Activity) and mHealth datasets. The algorithm also represents a significant improvement in terms of computational costs and requires no feature selection and hyper-parameter tuning. The algorithm still showed a robust performance with only two (ankle and wrist) out of the four devices (chest, wrist, hip and ankle) placed on the body (96.8% vs. 97.3% mean accuracy for the DaLiAc dataset). The present work shows that low-complexity models can compete with heavy, inefficient models in classification of advanced activities when designed with a careful upstream inspection of the data.