用于密度估计和分类的噪声独立因子分析模型
Noisy Independent Factor Analysis Model for Density Estimation and Classification
摘要：
我们考虑的问题，多变量密度估计时，假设未知密度遵循一个特定形式的降维，噪声独立因子分析（IFA）模型。在该模型中，数据由具有未知分布的多个潜在独立分量生成，并在高斯噪声中观察。我们并不假设组分的数量或混合组分的矩阵是已知的。我们表明，这种形式的密度可以估计一个快速的速度。使用镜像平均聚集算法，我们构造了一个密度估计器，当样本量$n$趋于无穷大时，该密度估计器实现了与数据维数无关的近似参数率log^（1/4）n/sqrt（n）。该估计器是自适应的分量的数量，它们的分布和混合矩阵。然后，我们应用此密度估计构建非参数插件分类器，并表明它们实现了最佳的超额贝叶斯风险率，在一个对数因子独立的维度的数据。该分类器的模拟数据集和遥感实验的实际数据的应用程序显示出可喜的结果。
英文摘要：
We consider the problem of multivariate density estimation when the unknown density is assumed to follow a particular form of dimensionality reduction, a noisy independent factor analysis (IFA) model. In this model the data are generated by a number of latent independent components having unknown distributions and are observed in Gaussian noise. We do not assume that either the number of components or the matrix mixing the components are known. We show that the densities of this form can be estimated with a fast rate. Using the mirror averaging aggregation algorithm, we construct a density estimator which achieves a nearly parametric rate log^(1/4)n/sqrt(n), independent of the dimensionality of the data, as the sample size $n$ tends to infinity. This estimator is adaptive to the number of components, their distributions and the mixing matrix. We then apply this density estimator to construct nonparametric plug-in classifiers and show that they achieve the best obtainable rate of the excess Bayes risk, to within a logarithmic factor independent of the dimension of the data. Applications of this classifier to simulated data sets and to real data from a remote sensing experiment show promising results.
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