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With the emerging Internet of Things (IoT) paradigm, more than a billion sensing devices will be collecting an unprecedented amount of data. Simultaneously, the field of data analytics is being revolutionized by modern machine learning (ML) techniques that enable sophisticated processing of massive datasets. Many researchers are envisioning a combination of these two technologies to support exciting applications such as environmental monitoring, Industry 4.0, and vehicular communications. However, traditional wireless communication protocols are inefficient in supporting distributed ML services, where data and computations are distributed over wireless networks. This motivates the need for new wireless communication methods. One such method, over-the-air computation (AirComp), promises to communicate with massive gains in terms of energy, latency, and spectrum efficiency compared to traditional methods.

The expected efficiency of AirComp is due to the complete spectrum sharing for all participating devices. Unlike in traditional physical-layer communications, where interference is avoided by allocating orthogonal communication channels, AirComp promotes interference to compute a function of the individually transmitted messages. However, AirComp can not reconstruct functions perfectly but introduces errors in the process, which harms the convergence rate and region of optimality of ML algorithms. The main objective of this thesis is to develop methods that reduce these errors and analyze their effects on ML performance.