• 1 Manifold, Divergence and Dually Flat Structure.- 2 Exponential Families and Mixture Families of Probability.- 3 Invariant Geometry of Manifold of Probability.- 4 α-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.

“This book gives a reasonably accessible introduction to the subject and then considers various applications. … The book provides a nice introduction to the subject. … the book provides a nice introduction to a difficult subject that has many important applications.” (Marvin H. J. Gruber, Technometrics, Vol. 58 (4), April, 2016)

• 1 Manifold, Divergence and Dually Flat Structure.- 2 Exponential Families and Mixture Families of Probability.- 3 Invariant Geometry of Manifold of Probability.- 4 α-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.

“This book gives a reasonably accessible introduction to the subject and then considers various applications. … The book provides a nice introduction to the subject. … the book provides a nice introduction to a difficult subject that has many important applications.” (Marvin H. J. Gruber, Technometrics, Vol. 58 (4), April, 2016)

• 1 Manifold, Divergence and Dually Flat Structure.- 2 Exponential Families and Mixture Families of Probability.- 3 Invariant Geometry of Manifold of Probability.- 4 α-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.

“This book gives a reasonably accessible introduction to the subject and then considers various applications. … The book provides a nice introduction to the subject. … the book provides a nice introduction to a difficult subject that has many important applications.” (Marvin H. J. Gruber, Technometrics, Vol. 58 (4), April, 2016)