标题： 非渐近拟合优度检验和价值随机块模型中的模型选择 显示英文标题

标题： Non-asymptotic goodness-of-fit tests and model selection in valued stochastic blockmodels

摘要： 有值的随机块模型（SBM）是一种查看网络数据的通用方法，其中节点被分组到块中，它们之间的链接通过计数或标签来衡量。 这一族模型允许不同的二元抽样方案，从而包括经典的、泊松的和带标签的SBM，以及某些边观测被删失的情况。 本文研究了此类非伯努利SBM的拟合优度检验问题，特别关注小样本检验。 我们推导了生成参考分布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程度的拟合优度统计量，这些统计量与相关模型族文献中的统计量相当。 对于带标签的SBM，其中包括特别的删失边模型，我们研究了这些统计量的渐近行为。 测试SBM拟合优度的主要目的之一是确定节点的块成员是否影响网络形成。 在模拟数据上验证了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使用渐近结果来选择块数的方法。 将为泊松SBM推导的方法应用于宿主-寄生相互作用的生态网络。 我们的数据分析结论在选择物种的块数方面与文献中的先前结果不同。 显示英文摘要

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.