In smart applications, such as smart medical devices, in order to prevent privacy leaks, more data needs to be processed and trained locally or near the local end. However, the storage and computing capabilities of smart devices are limited, so some computing tasks need to be outsourced; concurrently, the prevention of malicious nodes from accessing user data during outsourcing computing is required. Therefore, this paper proposes EVPP (efficient, verifiable, and privacy-preserving), a machine learning method based on a collaboration of edge computing devices. In this solution, the computationally intensive part of the model training process is outsourced. Meanwhile, a random encryption perturbation is performed on the outsourced training matrix, and verification factors are introduced to ensure the verifiability of the results. In addition, when a malicious service node is found, verifiable evidence can be generated to build a trust mechanism. Through the analysis of theoretical and experimental data, it can be shown that the scheme proposed in this paper can effectively use the computing power of the equipment. Keywords: Machine learning • Edge computing • Privacy-preserving • Mobile devices • Outsourced computingWe would like to thank the anonymous reviewers for their careful reading and useful comments.