分位数混合图模型及其在美国大规模公共枪击案中的应用
Quantile mixed graphical models with an application to mass public shootings in the United States
AI总结：
针对美国大规模公共枪击案的成因探究需求，提出一种基于Parzen中分位数定义的分位数混合图模型，采用邻域选择与带LASSO惩罚的两步估计法提取变量关联结构，为研究该复杂现象的多领域关联提供无严格分布假设的建模工具。
摘要：
过去五十年间，美国发生了数百起大规模公共枪击案，造成数千名受害者。大规模枪击案因发生频率高、破坏性强的特点，已成为重大公共健康危害，极大影响着个人与社区的安全和福祉。鉴于这一现象的流行特征，各方已协同开展工作，探究导致公共大规模枪击案的根本原因，以制定有效的预防策略。我们提出一种分位数混合图模型，用于研究这一复杂现象跨领域及领域内关联的内在机制，该模型采用Parzen的中分位数定义，在无严格分布假设的条件下，对离散变量与连续变量之间的条件关系进行建模。为提取图结构并仅恢复最相关的关联，我们采用邻域选择方法，将网络中每个变量的条件中分位数建模为其余所有变量的稀疏函数。我们提出一种两步流程来估计该图：第一步以半参数方式得到条件中概率，第二步通过求解带LASSO惩罚项的隐式方程来估计模型参数。
英文摘要：
Over the last fifty years, the United States have experienced hundreds of mass public shootings that resulted in thousands of victims. Characterized by their frequent occurrence and devastating nature, mass shootings have become a major public health hazard that dramatically impact safety and well-being of individuals and communities. Given the epidemic traits of this phenomenon, there have been concerted efforts to understand the root causes that lead to public mass shootings in order to implement effective prevention strategies. We propose a quantile mixed graphical model for investigating the intricacies of inter- and infra-domain relationships of this complex phenomenon, where conditional relations between discrete and continuous variables are modeled without stringent distributional assumptions using Parzen's definition of mid-quantile. To retrieve the graph structure and recover only the most relevant connections, we consider the neighborhood selection approach in which conditional mid-quantiles of each variable in the network are modeled as a sparse function of all others. We propose a two-step procedure to estimate the graph where, in the first step, conditional mid-probabilities are obtained semi-parametrically and, in the second step, the model parameters are estimated by solving an implicit equation with a LASSO penalty.
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