Statistical properties of large data sets with linear latent features
Statistical properties of large data sets with linear latent features
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具有线性潜在特征的大数据集的统计特性
DOI：
10.1103/physreve.106.014102
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发表时间：
2022
影响因子：
2.4
通讯作者：
Nemenman, Ilya
中科院分区：
文献类型：
--
作者：
Fleig, Philipp;Nemenman, Ilya
对于低维潜在特征如何在高维数据中显露出来，目前还缺乏分析上的理解。我们通过定义一个带有加性噪声的概率线性潜在特征模型，通过解析和数值计算数据相关矩阵的成对相关性和特征值的统计分布来研究这一点。这使我们能够解析由记录的变量、观测、潜在特征和信噪比设置的广泛的数据区域中的潜在特征结构。我们在相关性和本征值的分布中找到了潜在特征的特征印记，并对信号和噪声之间的边界提供了一个解析估计，即使在没有谱间隙的情况下也是如此。
Analytical understanding of how low-dimensional latent features reveal themselves in large-dimensional data is still lacking. We study this by defining a probabilistic linear latent features model with additive noise and by analytically and numerically computing the statistical distributions of pairwise correlations and eigenvalues of the data correlation matrix. This allows us to resolve the latent feature structure across a wide range of data regimes set by the number of recorded variables, observations, latent features, and the signal-to-noise ratio. We find a characteristic imprint of latent features in the distribution of correlations and eigenvalues and provide an analytic estimate for the boundary between signal and noise, even in the absence of a spectral gap.