High-dimensional autoregressive point processes model how current events trigger or inhibit future events, such as activity by one member of a social network can affect the future activity of his or her neighbors. While past work has focused on estimating the underlying network structure based solely on the times at which events occur on each node of the network, this paper examines the more nuanced problem of estimating context-dependent networks that reflect how features associated with an event (such as the content of a social media post) modulate the strength of influences among nodes. Specifically, we leverage ideas from compositional time series and regularization methods in machine learning to conduct network estimation for high-dimensional marked point processes. Two models and corresponding estimators are considered in detail: an autoregressive multinomial model suited to categorical marks and a logistic-normal model suited to marks with mixed membership in different categories. Importantly, the logistic-normal model leads to a convex negative log-likelihood objective and captures dependence across categories. We provide theoretical guarantees for both estimators, which we validate by simulations and a synthetic data-generating model. We further validate our methods through two real data examples and demonstrate the advantages and disadvantages of both approaches.

中文翻译：

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上下文相关的自激点过程：高维模型、方法和风险界限

高维自回归点过程模拟当前事件如何触发或抑制未来事件，例如社交网络的一个成员的活动会影响他或她的邻居的未来活动。虽然过去的工作侧重于仅根据网络每个节点上发生事件的时间来估计底层网络结构，但本文研究了估计上下文相关网络的更细微问题，这些问题反映了与事件相关的特征（例如作为社交媒体帖子的内容）调节节点之间的影响强度。具体来说，我们利用机器学习中的组合时间序列和正则化方法的思想来对高维标记点过程进行网络估计。详细考虑了两个模型和相应的估计量：适用于分类标记的自回归多项式模型和适用于具有不同类别混合成员资格的标记的逻辑正态模型。重要的是，逻辑正态模型导致凸负对数似然目标并捕获跨类别的依赖性。我们为两个估计器提供理论保证，我们通过模拟和合成数据生成模型对其进行验证。我们通过两个真实数据示例进一步验证了我们的方法，并展示了两种方法的优缺点。我们为两个估计器提供理论保证，我们通过模拟和合成数据生成模型对其进行验证。我们通过两个真实数据示例进一步验证了我们的方法，并展示了两种方法的优缺点。我们为两个估计器提供理论保证，我们通过模拟和合成数据生成模型对其进行验证。我们通过两个真实数据示例进一步验证了我们的方法，并展示了两种方法的优缺点。