000			a
999			_c30743 _d30743
008			220223b xxu||||| |||| 00| 0 eng d
020			_a9784431567431
082			_a510.1154 _bAMA
100			_aAmari, Shun-ichi
245			_aInformation geometry and its applications
260			_bSpringer, _c2016 _aJapan :
300			_axiii, 374 p. ; _bill., _c24 cm
365			_b84.99 _cEUR _d88.10
490			_aApplied mathematical sciences, 0066-5452 ; _vvol. 194
504			_aIncludes bibliographical references and index.
520			_aThis is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman-Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields.
650			_aGeometry, Differential
650			_aMathematical statistics
650			_aInformation theory
650			_aInformation theory in mathematics
650			_aStatistics
650			_aComputer science, Mathematics
650			_aGlobal differential geometry
942			_2ddc _cBK