Information Geometry? Exercises de Styles: Review
Indeed, information geometry, IG is an ever-growing area with a great scope of applications ranging from Probability & Statistics, Machine Learning (ML), Artificial Intelligence (AI), Signal Processing, Mathematical Programming, etc.,. There is always a great race to distil information from data to models. Since its inception, IG as a concept has been known under a variety of guises and been used in numerous contexts, establishing an almost rock-star status in both sciences and popular culture. The three most prominent “styles” which IG has been (re)told in and which have determined its popularity are Deep Learning, Statistical learning and Machine Learning. Following the footsteps of the relentless hunt for the core of the concept that kindled this underlying development, connections with emergence of time combined with irreversibility, the elegant nature of probability and the generated information which add to its illusiveness as much as simulating its cross-contextual adoption and proliferation. In this review, we search and retrace through the five main perspectives from which IG has been regarded, emphasizing the motivations behind each application, their ramifications as well as the bridges that have been constructed to justify them. Consequently, this analysis of the foundations provides a beautiful panorama of several characteristic traits of the concept that underline its significance and exceptionality as an engine of conceptual progress.
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