Data, in its many forms and across various disciplines, is becoming anessential source for research in the 21st century. In fact, data driven knowledge extraction nowadays constitutes one of the core paradigms for scientific discovery. This paradigm is supported by the many successes with universal architectures andalgorithms, such as deep neural networks, which can explain observed data and, at the same time, generalise extremely well to unobserved new data. Thus, such systems are capable of revealing the intrinsic structure of the data, as an important step within thep rocess of knowledge extraction. Structure is coupled with geometry at various levels. Traditionally, information geometry has been concerned with the identification of natural geometric structures of statistical models. These structures turn out to be crucial within statistical methods and learning algorithms.
One instance of this is given by the natural gradient method, which improves the learning simply by utilising the natural geometry induced by the Fisher-Rao metric. The talk will outline the general perspective of information
geometry and highlight its geometric structures. This perspective had already a greatinfluence on machine learning and is expected to further influence the general field of data science.
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