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. For this reason, 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：过去五十年来，美国发生了数百起大规模公共枪击事件，导致数千名受害者。此类事件以其频繁发生和破坏性为特征，已成为严重危害公共健康的问题，深刻影响个人与社区的安全与福祉。鉴于该现象的流行病学特征，学界为理解导致公共枪击事件的根源并制定有效预防策略做出了协同努力。为此，我们提出一种分位数混合图模型，用于探究这一复杂现象在不同领域内及跨领域关系中的内在关联。该模型利用Parzen中分位数的定义，在无需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。为提取图结构并仅保留最相关的连接，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。我们提出两步估计过程：第一步通过半参数方法获得条件中概率，第二步通过求解带LASSO惩罚的隐式方程来估计模型参数。