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Machine learning (ML) has disrupted a wide range of science and engineering disciplines in recent years. ML applications in optical communications and networking are also gaining more attention, particularly in the areas of nonlinear transmission systems, optical performance monitoring, and cross-layer network optimizations for software-defined networks. However, the extent to which ML techniques can benefit optical communications and networking is not clear and this is partly due to an insufficient understanding of the nature of ML concepts. This paper aims to describe the mathematical foundations of basic ML techniques from communication theory and signal processing perspectives, which in turn will shed light on the types of problems in optical communications and networking that naturally warrant ML use. This will be followed by an overview of ongoing ML research in optical communications and …