Chebyshev center computation problem, i.e. finding the point which is at minimum distance to a set of given points, on the probability simplex with $\alpha$-divergence distance measure is studied. The proposed solution generalizes the Arimoto-Blahut (AB) algorithm utilizing Kullback-Leibler divergence to $\alpha$-divergence, and reduces to the AB method as $\alpha \rightarrow 1$. Similar to the AB algorithm, the method is an ascent method with a guarantee on the objective value ($\alpha$-mutual information or Chebyshev radius) improvement at every iteration. A practical application area for the method is the fusion of probability mass functions lacking a joint probability description. Another application area is the error exponent calculation.

中文翻译：

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具有 $\alpha$-散度测度的概率单纯形的切比雪夫中心计算

Chebyshev 中心计算问题，即在概率单纯形上找到与一组给定点距离最小的点 $\alpha$- 研究散度距离度量。所提出的解决方案将利用 Kullback-Leibler 散度的 Arimoto-Blahut (AB) 算法推广到$\alpha$-divergence，并简化为 AB 方法为 $\alpha \rightarrow 1$. 与AB算法类似，该方法是一种保证目标值（$\alpha$-相互信息或切比雪夫半径）在每次迭代中的改进。该方法的一个实际应用领域是缺乏联合概率描述的概率质量函数的融合。另一个应用领域是误差指数计算。