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.

翻译：过去五十年间，美国发生了数百起大规模公共枪击事件，导致数千人受害。此类事件以高发性和毁灭性为特征，已成为严重危害公众健康的风险因素，深刻影响个体与社区的安全福祉。鉴于这一现象的流行病学特征，学界已协同探究其根本诱因以制定有效预防策略。本文提出一种分位数混合图模型，用于解析这一复杂现象中域间与域内关系的精细结构，该模型基于Parzen中分位数定义，无需严格分布假设即可对离散变量与连续变量的条件关联建模。为提取图结构并保留最具相关性的连接，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他所有变量的稀疏函数。我们提出两阶段估计流程：第一阶段通过半参数方法获取条件中概率，第二阶段通过含LASSO惩罚的隐式方程求解模型参数。