Probabilistic modelling provides a frame-work for understanding what learning is, and has therefore emerged as one of the principal theoretical and practical approaches for designing machines that learn from data acquired through experience. The probabilistic framework, which describes how to represent and manipulate uncertainty about models and predictions, plays a central role in scientific data analysis, machine learning, robotics, cognitive science, and artificial intelligence. This article provides an introduction to this probabilistic framework, and reviews some state-of-the-art advances in the field, namely, probabilistic programming, Bayesian optimisation, data compression, and automatic model discovery.

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