| 最大熵原理及改进方法的研究现状 |
| Research Status of Maximum Entropy Principle and Improved Methods |
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| 中文摘要: |
| 熵作为信息论中的一个基本概念受到了广泛的关注与研究。以熵为基础的最大熵原理也在众多学者的研究与应用中不断发展，逐渐形成了自有的理论体系并得到了广泛应用，例如在使用贝叶斯方法进行测量不确定度评定时，最大熵原理可以估计先验分布。本文以Shannon熵为主要对象，对目前研究中涉及的不同约束下最大熵原理进行了归纳，并整理为形式较为统一的模型。论述了利用转换函数法、密度核估计法等改善传统最大熵原理不足的方法，具体介绍了它们的改进思路、理论模型及应用特点。最后结合实践，从约束选择、评价指标和优化算法等方面对最大熵原理改进方法进行总结，为最大熵原理的进一步研究及应用起到推动作用。 |
| 英文摘要: |
| Entropy as a basic concept in information theory has been widely concerned and studied. The principle of maximum entropy based on entropy has been developing in the research and application of many scholars and has gradually formed its own theoretical system, and has been widely used. For example, when the Bayesian method is used to evaluate the measurement uncertainty, the principle of maximum entropy can estimate the prior distribution. In this paper, Shannon entropy is taken as the main object, and the maximum entropy principle under different constraints involved in the current research is summarized, and sorted out into a relatively unified model. This paper discusses some methods to improve the traditional maximum entropy principle by using transformation function method and density kernel estimation method, and introduces their improvement ideas, theoretical models and application characteristics in detail. Finally, combined with practice, the improved methods of maximum entropy principle are summarized from the aspects of constraint selection, evaluation index and optimization algorithm, which will promote the further research and application of maximum entropy principle. |
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| 中文关键词: 最大熵原理 优化求解 矩约束 秩约束 转换函数 密度核估计 |
| 英文关键词:maximum entropy principle optimization solution moment constraints rank constraints conversion function density kernel estimation |
| 基金项目: |
| DOI：10.11823/j.issn.1674-5795.2022.01.02 |
| 引用本文：黄乾坤，吴娅辉.最大熵原理及改进方法的研究现状[J].计测技术,2022,(1):. |
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