Distributed Machine Learning in the Context of Function Computation over Wireless Networks

Due to strict limitations on the capacity of wireless links, applications of machine learning to various problems in wireless networks require the development of novel distributed solutions that facilitate an efficient evaluation of linear and nonlinear functions over the wireless channel. In this paper, we focus on selected machine learning-based approaches to the problem of detecting anomalies in applications such as condition monitoring, fault diagnosis and in general industrial environments. In particular, we study the possibility of exploiting the broadcast property of the wireless channel to efficiently compute discriminant functions over the channel. Our contribution includes quantitative (exponential) bounds on probabilities of mislabeling in binary linear classification and error in distributed linear function approximation. The problem of exploiting the broadcast property of the wireless channel to compute nonlinear functions might be difficult because the nomographic representation of general pornographic functions is not known. Therefore, we consider two approaches to this problem. First we combine computation coding for combating the impact of noise with a transmitter side nonlinear pre-processing, whose goal is to approximate nomographic representations by general additive models. Our second approach is to extend the principle of computation coding to embed data in higher dimensions where data sets are linearly separable.