论文标题
使用进化算法探索最大的熵分布
Exploring Maximum Entropy Distributions with Evolutionary Algorithms
论文作者
论文摘要
本文展示了如何以一组约束的数值方式进化的最大熵概率分布，这是一个变异的演算问题。进化算法可以获得一些众所周知的分析结果的近似值，但更灵活，并且可以找到无法轻易说明封闭公式的分布。数值方法在有限间隔内处理分布。我们表明，有两种操作方法的方法：通过直接优化受约束问题的拉格朗日，或通过优化满足约束的分布子集中的熵。一旦用两种方法解决了约束问题，一种增量进化策略很容易获得统一，指数，高斯，对数正态，拉普拉斯等分布。还可以找到混合（“嵌合”）分布的解决方案。我们解释了为什么许多分布是对称和连续的，但有些不是。
This paper shows how to evolve numerically the maximum entropy probability distributions for a given set of constraints, which is a variational calculus problem. An evolutionary algorithm can obtain approximations to some well-known analytical results, but is even more flexible and can find distributions for which a closed formula cannot be readily stated. The numerical approach handles distributions over finite intervals. We show that there are two ways of conducting the procedure: by direct optimization of the Lagrangian of the constrained problem, or by optimizing the entropy among the subset of distributions which fulfill the constraints. An incremental evolutionary strategy easily obtains the uniform, the exponential, the Gaussian, the log-normal, the Laplace, among other distributions, once the constrained problem is solved with any of the two methods. Solutions for mixed ("chimera") distributions can be also found. We explain why many of the distributions are symmetrical and continuous, but some are not.
