论文标题
边际约束下最大熵的分类分布
Categorical Distributions of Maximum Entropy under Marginal Constraints
论文作者
论文摘要
在边际约束下的分类分布的估计以最高的方式总结了一些人群中的一些样本，这对于许多机器学习和数据驱动的方法是关键。我们提供了一个参数 - 不可思议的理论框架，该框架可以使此任务确保（i）在边缘约束下始终存在最大熵的分类分布，并且（ii）它是唯一的。迭代比例拟合（IPF）的过程自然估计，直接在概率空间中直接从任何一致的边缘约束组中分布，从而演绎了对种群的最小偏差表征。理论框架与IPF一起导致了整体工作流程，该工作流程可以仅使用提供的现象学信息来对任何类别的分类分布进行建模。
The estimation of categorical distributions under marginal constraints summarizing some sample from a population in the most-generalizable way is key for many machine-learning and data-driven approaches. We provide a parameter-agnostic theoretical framework that enables this task ensuring (i) that a categorical distribution of Maximum Entropy under marginal constraints always exists and (ii) that it is unique. The procedure of iterative proportional fitting (IPF) naturally estimates that distribution from any consistent set of marginal constraints directly in the space of probabilities, thus deductively identifying a least-biased characterization of the population. The theoretical framework together with IPF leads to a holistic workflow that enables modeling any class of categorical distributions solely using the phenomenological information provided.
