有值随机块模型中的非渐近拟合优度检验与模型选择
Non-asymptotic goodness-of-fit tests and model selection in valued stochastic blockmodels
AI总结：
本文针对有值随机块模型提出非渐近拟合优度检验方法，推导马尔可夫基移动并定义统计量，验证功效与错误率，并应用于生态网络以选择块数量，结论与文献不同。
摘要：
有值随机块模型（SBM）是一种观察网络数据的通用方式，其中节点被分组到块中，节点之间的链接通过计数或标签来衡量。该模型族允许不同的二元组采样方案，因此包括经典SBM、泊松SBM和带标签SBM，以及那些部分边观测被删失的模型。本文探讨了此类非伯努利SBM的拟合优度检验问题，特别关注有限样本检验。我们推导了从参考分布生成样本所需的显式马尔可夫基移动，并定义了用于确定模型拟合度的拟合优度统计量，这些统计量与文献中相关模型族的统计量相当。对于带标签的SBM（其中特别包括删失边模型），我们研究了这些统计量的渐近行为。检验SBM拟合优度的主要目的之一是确定节点的块成员身份是否影响网络形成。在模拟数据上验证了检验的功效和第一类错误率。此外，我们讨论了在潜在块建模假设下利用渐近结果选择块数量的方法。我们将为泊松SBM推导的方法应用于宿主-寄生虫相互作用的生态网络。我们的数据分析结论在选择物种块数量方面与文献中的先前结果不同。
英文摘要：
A valued stochastic blockmodel (SBM) is a general way to view networked data in which nodes are grouped into blocks and links between them are measured by counts or labels. This family allows for varying dyad sampling schemes, thereby including the classical, Poisson, and labeled SBMs, as well as those in which some edge observations are censored. This paper addresses the question of testing goodness-of-fit of such non-Bernoulli SBMs, focusing in particular on finite-sample tests. We derive explicit Markov bases moves necessary to generate samples from reference distributions and define goodness-of-fit statistics for determining model fit, comparable to those in the literature for related model families. For the labeled SBM, which includes in particular the censored-edge model, we study the asymptotic behavior of said statistics. One of the main purposes of testing goodness-of-fit of an SBM is to determine whether block membership of the nodes influences network formation. Power and Type 1 error rates are verified on simulated data. Additionally, we discuss the use of asymptotic results in selecting the number of blocks under the latent-block modeling assumption. The method derived for Poisson SBM is applied to ecological networks of host-parasite interactions. Our data analysis conclusions differ in selecting the number of blocks for the species from previous results in the literature.
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