This lecture will provide an introduction to Wasserstein Information Geometry for learning from data. This is an active area that combines Information Geometry and Wasserstein Geometry in order to capture two important aspects of learning: the geometry of the learning model and the geometry of the data under consideration. First we introduce Information Geometry, which emphasises the geometry of the learning model, based on natural notions of invariance with respect to transformations of the hypotheses and their parametrisation. Then we introduce Wasserstein Geometry, which departs from the geometry of the data space. We discuss consequences, computation, applications, and topics of current research.
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