论文标题
超越黑匣子密度：偏差组件的参数学习
Beyond Black Box Densities: Parameter Learning for the Deviated Components
论文作者
论文摘要
当我们从以前通过黑匣子方法获得已知密度函数估计值的数据总体中收集其他样本时，数据集的复杂性的增加可能会导致通过混合分布从已知估计中偏离的真实密度。为了建模这种现象，我们考虑\ emph {偏差混合模型} $（1-λ^{*}）H_0 +λ^{*}（\ sum_ {i = 1}^{k}^{k} p_ {i}^{i}^{*}^{*}偏差比例$λ^{*} $和潜在混合度量$ g _ {*} = \ sum_ {i = 1}^{k} p_ {i}^{*}Δ__{θ_i^{*}}} $与混合物分布关联的是未知。通过一个新颖的概念，即已知的密度$ h_ {0} $与偏差混合物分布之间的区分性，我们建立了收敛速率的最大似然估计值为$λ^{*} $和$ g^{*} $。进行仿真研究以说明理论。
As we collect additional samples from a data population for which a known density function estimate may have been previously obtained by a black box method, the increased complexity of the data set may result in the true density being deviated from the known estimate by a mixture distribution. To model this phenomenon, we consider the \emph{deviating mixture model} $(1-λ^{*})h_0 + λ^{*} (\sum_{i = 1}^{k} p_{i}^{*} f(x|θ_{i}^{*}))$, where $h_0$ is a known density function, while the deviated proportion $λ^{*}$ and latent mixing measure $G_{*} = \sum_{i = 1}^{k} p_{i}^{*} δ_{θ_i^{*}}$ associated with the mixture distribution are unknown. Via a novel notion of distinguishability between the known density $h_{0}$ and the deviated mixture distribution, we establish rates of convergence for the maximum likelihood estimates of $λ^{*}$ and $G^{*}$ under Wasserstein metric. Simulation studies are carried out to illustrate the theory.
