Divergence, Optimization and Geometry

作者: Shun-ichi Amari

DOI: 10.1007/978-3-642-10677-4_21

关键词:

摘要: Measures of divergence are used in many engineering problems such as statistics, mathematical programming, computational vision, and neural networks. The Kullback-Leibler is its typical example which defined between two probability distributions, invariant under information transformations. Bregman another type divergence, often optimization signal processing. This a class divergences having dually flat geometrical structure. Divergence for minimizing discrepancy observed evidences an underlying model. Projection to the model subspace plays fundamental role. Here, geometry important geodesic structure useful, because generalized Pythagorean theorem projection hold.

参考文章(24)
S. M. Ali, S. D. Silvey, A General Class of Coefficients of Divergence of One Distribution from Another Journal of the Royal Statistical Society: Series B (Methodological). ,vol. 28, pp. 131- 142 ,(1966) , 10.1111/J.2517-6161.1966.TB00626.X
Shun-ichi Amari, Information Geometry and Its Applications: Convex Function and Dually Flat Manifold Emerging Trends in Visual Computing. pp. 75- 102 ,(2009) , 10.1007/978-3-642-00826-9_4
Shun-ichi Amari, Hiroshi Nagaoka, Methods of information geometry ,(2000)
Emerging Trends in Visual Computing Lecture Notes in Computer Science. ,vol. 5416, ,(2009) , 10.1007/978-3-642-00826-9
M. R. GRASSELLI, DUALITY, MONOTONICITY AND THE WIGNER YANASE DYSON METRICS Infinite Dimensional Analysis, Quantum Probability and Related Topics. ,vol. 07, pp. 215- 232 ,(2004) , 10.1142/S021902570400161X
Dénes Petz, Monotone metrics on matrix spaces Linear Algebra and its Applications. ,vol. 244, pp. 81- 96 ,(1996) , 10.1016/0024-3795(94)00211-8
Inderjit S. Dhillon, Joel A. Tropp, Matrix Nearness Problems with Bregman Divergences SIAM Journal on Matrix Analysis and Applications. ,vol. 29, pp. 1120- 1146 ,(2007) , 10.1137/060649021
Shun-ichi Amari, Integration of Stochastic Models by Minimizing α-Divergence Neural Computation. ,vol. 19, pp. 2780- 2796 ,(2007) , 10.1162/NECO.2007.19.10.2780
Hiroshi Hasegawa, α-Divergence of the non-commutative information geometry Reports on Mathematical Physics. ,vol. 33, pp. 87- 93 ,(1993) , 10.1016/0034-4877(93)90043-E