• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Information Theory, IEEE Transactions on >The Bethe Permanent of a Nonnegative Matrix
【24h】

The Bethe Permanent of a Nonnegative Matrix

机译：非负矩阵的永久性

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

It has recently been observed that the permanent of a nonnegative square matrix, i.e., of a square matrix containing only nonnegative real entries, can very well be approximated by solving a certain Bethe free energy function minimization problem with the help of the sum–product algorithm. We call the resulting approximation of the permanent the Bethe permanent. In this paper, we give reasons why this approach to approximating the permanent works well. Namely, we show that the Bethe free energy function is convex and that the sum–product algorithm finds its minimum efficiently. We then discuss the fact that the permanent is lower bounded by the Bethe permanent, and we comment on potential upper bounds on the permanent based on the Bethe permanent. We also present a combinatorial characterization of the Bethe permanent in terms of permanents of so-called lifted versions of the matrix under consideration. Moreover, we comment on possibilities to modify the Bethe permanent so that it approximates the permanent even better, and we conclude the paper with some observations and conjectures about permanent-based pseudocodewords and permanent-based kernels.
机译：最近发现，非负方阵的永久性，即仅包含非负实项的方阵的永久性，可以通过求和积算法来解决某个Bethe自由能函数最小化问题而很好地近似。我们称永久物的近似结果为Bethe永久物。在本文中，我们给出了为什么这种近似永久性方法的效果很好的原因。即，我们表明Bethe自由能函数是凸的，并且求和积算法可以有效地找到其最小值。然后，我们讨论该永久物位于Bethe永久物下界的事实，并在基于Bethe永久物的基础上对该永久物的潜在上限进行评论。我们还根据所考虑的矩阵的所谓提升版本的永久性，提出了Bethe永久性的组合特征。此外，我们评论了修改Bethe永久性词的可能性，以使其更好地逼近该永久性词，并以一些关于基于永久性伪码字和基于永久性内核的观察和猜想来结束本文。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号