LEADER 04117nam 22006735 450 001 9910254078503321 005 20250609110124.0 010 $a4-431-55978-7 024 7 $a10.1007/978-4-431-55978-8 035 $a(CKB)3710000000588341 035 $a(EBL)4387676 035 $a(SSID)ssj0001653543 035 $a(PQKBManifestationID)16433868 035 $a(PQKBTitleCode)TC0001653543 035 $a(PQKBWorkID)14982931 035 $a(PQKB)10186908 035 $a(DE-He213)978-4-431-55978-8 035 $a(MiAaPQ)EBC4387676 035 $a(PPN)192222139 035 $a(MiAaPQ)EBC6242282 035 $a(EXLCZ)993710000000588341 100 $a20160201d2016 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aInformation Geometry and Its Applications /$fby Shun-ichi Amari 205 $a1st ed. 2016. 210 1$aTokyo :$cSpringer Japan :$cImprint: Springer,$d2016. 215 $a1 online resource (376 p.) 225 1 $aApplied Mathematical Sciences,$x2196-968X ;$v194 300 $aDescription based upon print version of record. 311 08$a4-431-55977-9 320 $aIncludes bibliographical references and index. 327 $a1 Manifold, Divergence and Dually Flat Structure -- 2 Exponential Families and Mixture Families of Probability -- 3 Invariant Geometry of Manifold of Probability -- 4 ?-Geometry, Tsallis q-Entropy and Positive-Definite -- 5 Elements of Differential Geometry -- 6 Dual Affine Connections and Dually Flat Manifold -- 7 Asymptotic Theory of Statistical Inference -- 8 Estimation in the Presence of Hidden Variables -- 9 Neyman?Scott Problem -- 10 Linear Systems and Time Series -- 11 Machine Learning -- 12 Natural Gradient Learning and its Dynamics in Singular -- 13 Signal Processing and Optimization -- Index. 330 $aThis is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman?Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields. 410 0$aApplied Mathematical Sciences,$x2196-968X ;$v194 606 $aGeometry, Differential 606 $aComputer science$xMathematics 606 $aStatistics 606 $aDifferential Geometry 606 $aMathematical Applications in Computer Science 606 $aStatistical Theory and Methods 615 0$aGeometry, Differential. 615 0$aComputer science$xMathematics. 615 0$aStatistics. 615 14$aDifferential Geometry. 615 24$aMathematical Applications in Computer Science. 615 24$aStatistical Theory and Methods. 676 $a516 700 $aAmari$b Shun-ichi$4aut$4http://id.loc.gov/vocabulary/relators/aut$052369 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254078503321 996 $aInformation geometry and its applications$91523395 997 $aUNINA