论文标题
有限混合模型：具有随机几何学和choquet理论的桥梁
Finite admixture models: a bridge with stochastic geometry and Choquet theory
论文作者
论文摘要
在有限混合模型的背景下，其组件和权重是未知的，如果可识别组件的数量是收集的数据量的函数，我们使用随机凸几何形状中的技术来找到其预期值的增长率。此外，当已知组件但权重时，我们提供了经典的Glivenko-Cantelli定理的应用，使我们能够检索可识别的混合物组件支持的Choquet度量。反过来，这为我们提供了可识别的混合权重。最后，我们提出了一种新型算法，该算法仅使用严格必要数量的组件估算捕获数据复杂性的模型。
In the context of a finite admixture model whose components and weights are unknown, if the number of identifiable components is a function of the amount of data collected, we use techniques from stochastic convex geometry to find the growth rate of its expected value. In addition, when the components are known but the weights are not, we provide an application of the classic Glivenko-Cantelli's theorem that allows us to retrieve the Choquet measure supported on the identifiable admixture components. In turn, this gives us the identifiable admixture weights. Finally, we propose a novel algorithm that estimates the model capturing the complexity of the data using only the strictly necessary number of components.
