Information Geometry of α-Projection in Mean Field Approximation
Information Geometry of α-Projection in Mean Field Approximation
复制标题
平均场近似中α投影的信息几何
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
H. Shimokawa
中科院分区：
文献类型：
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作者：
S. Amari;Shiro Ikeda;H. Shimokawa
将信息几何应用于平均场近似，以阐明其在自旋玻璃模型或玻尔兹曼机中的性质。α-散度用于逼近，其中α-测地线投影起重要作用。从信息几何的角度研究了概率分布族的朴素平均场近似和TAP近似。研究了α-投影的分支，在分支处α-逼近的唯一性被破坏.
Information geometry is applied to mean field approximation for elucidating its properties in the spin glass model or the Boltzmann machine. The α-divergence is used for approximation, where α-geodesic projection plays an important role. The naive mean field approximation and TAP approximation are studied from the point of view of information geometry, which treats the intrinsic geometric structures of a family of probability distributions. The bifurcation of the α-projection is studied, at which the uniqueness of the α-approximation is broken.