论文标题
相互作用标记过程的凸参数恢复
Convex Parameter Recovery for Interacting Marked Processes
论文作者
论文摘要
我们介绍了一种具有分类交互标记的多元离散事件数据的新的通用建模方法，我们称之为标记的Bernoulli过程。在提议的模型中，特定类别发生在某个位置的事件的可能性可能会受到该地点和其他位置的过去事件的影响。我们不限于随着时间的流逝而限制相互作用是积极的或衰减的，因此我们可以从不同类别的历史事件，位置和事件中捕获任意影响的影响形状。在我们的建模中，通过允许对模型参数的一般凸约限制来纳入先验知识。我们使用约束的最小二乘（LS）和最大似然（ML）估计来开发两个参数估计程序，这些估计是使用单调操作员的变异不平等解决的。我们讨论了我们方法的不同应用，并说明了在合成示例和现实世界警察数据集上提出的恢复程序的性能。
We introduce a new general modeling approach for multivariate discrete event data with categorical interacting marks, which we refer to as marked Bernoulli processes. In the proposed model, the probability of an event of a specific category to occur in a location may be influenced by past events at this and other locations. We do not restrict interactions to be positive or decaying over time as it is commonly adopted, allowing us to capture an arbitrary shape of influence from historical events, locations, and events of different categories. In our modeling, prior knowledge is incorporated by allowing general convex constraints on model parameters. We develop two parameter estimation procedures utilizing the constrained Least Squares (LS) and Maximum Likelihood (ML) estimation, which are solved using variational inequalities with monotone operators. We discuss different applications of our approach and illustrate the performance of proposed recovery routines on synthetic examples and a real-world police dataset.
