论文标题
基于Bregman Divergence EM算法及其在经典和量子损坏理论中的应用
Bregman divergence based em algorithm and its application to classical and quantum rate distortion theory
论文作者
论文摘要
我们在Bregman Divergence的框架中制定EM算法，这是信息几何形状的一般问题设置。也就是说，我们解决了Bregman Divergence系统中的指数亚家族与混合物中的Bregman差异的最小化问题。然后，我们在几个条件下显示了收敛及其速度。我们将此算法应用于量子及其变形（包括量子设置）的变形，并显示我们一般算法的有用性。实际上，Arimoto-blahut算法在评估失真理论上的现有应用使使用Lagrange乘数优化了相互信息的加权总和和成本函数。但是，在速率失真理论中，需要在成本函数的恒定限制下最小化互信息。我们的算法直接解决了这种最小化。此外，我们在经典的速率失真问题情况下，数值检查了算法的收敛速度。
We formulate em algorithm in the framework of Bregman divergence, which is a general problem setting of information geometry. That is, we address the minimization problem of the Bregman divergence between an exponential subfamily and a mixture subfamily in a Bregman divergence system. Then, we show the convergence and its speed under several conditions. We apply this algorithm to rate distortion and its variants including the quantum setting, and show the usefulness of our general algorithm. In fact, existing applications of Arimoto-Blahut algorithm to rate distortion theory make the optimization of the weighted sum of the mutual information and the cost function by using the Lagrange multiplier. However, in the rate distortion theory, it is needed to minimize the mutual information under the constant constraint for the cost function. Our algorithm directly solves this minimization. In addition, we have numerically checked the convergence speed of our algorithm in the classical case of rate distortion problem.
