Machine learning (automated processes that learn by example in order to classify, predict, discover or generate new data) and artificial intelligence (methods by which a computer makes decisions or discoveries that would usually require human intelligence) are now firmly established in astronomy. Every week, new applications of machine learning and artificial intelligence are added to a growing corpus of work. Random forests, support vector machines, and neural networks (artificial, deep, and convolutional) are now having a genuine impact for applications as diverse as discovering extrasolar planets, transient objects, quasars, and gravitationally-lensed systems, forecasting solar activity, and distinguishing between signals and instrumental effects in gravitational wave astronomy. This review surveys contemporary, published literature on machine learning and artificial intelligence in astronomy and astrophysics. Applications span seven main categories of activity: classification, regression, clustering, forecasting, generation, discovery, and the development of new scientific insight. These categories form the basis of a hierarchy of maturity, as the use of machine learning and artificial intelligence emerges, progresses or becomes established.
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