基于交叉验证特征值的图维数估计
Estimating Graph Dimension with Cross-validated Eigenvalues
AI总结：
本文提出了一种基于交叉验证特征值的方法，用于估计图的潜在维度数量，适用于不同统计检测需求的场景，并在模拟和实际数据中表现出良好的性能。
摘要：
在应用多变量统计学中，估计潜在维度数量或聚类数量k是一个基础且反复出现的问题。我们研究了一种称为“交叉验证特征值”的统计序列。在包含泊松和伯努利边的广泛随机图模型下，无需参数假设，我们为每个交叉验证特征值提供p值。该方法测试了样本特征向量与真实潜在维度正交（即不相关）的原假设。这种做法自然适应于某些维度无法统计检测的情况。在所有k维度均可估计的情况下，我们证明我们的程序能够一致地估计k。在模拟和数据示例中，所提出的估计器在计算和统计性能上均优于其他方法。
英文摘要：
In applied multivariate statistics, estimating the number of latent dimensions or the number of clusters, $k$, is a fundamental and recurring problem. We study a sequence of statistics called "cross-validated eigenvalues." Under a large class of random graph models, including both Poisson and Bernoulli edges, without parametric assumptions, we provide a $p$-value for each cross-validated eigenvalue. It tests the null hypothesis that the sample eigenvector is orthogonal to (i.e., uncorrelated with) the true latent dimensions. This approach naturally adapts to problems where some dimensions are not statistically detectable. In scenarios where all $k$ dimensions can be estimated, we show that our procedure consistently estimates $k$. In simulations and data example, the proposed estimator compares favorably to alternative approaches in both computational and statistical performance.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
