Predicting when and where events will occur in cities, like taxi pick-ups,
crimes, and vehicle collisions, is a challenging and important problem with
many applications in fields such as urban planning, transportation optimization
and location-based marketing. Though many point processes have been proposed to
model events in a continuous spatio-temporal space, none of them allow for the
consideration of the rich contextual factors that affect event occurrence, such
as weather, social activities, geographical characteristics, and traffic. In
this paper, we propose \textsf{DMPP} (Deep Mixture Point Processes), a point
process model for predicting spatio-temporal events with the use of rich
contextual information; a key advance is its incorporation of the heterogeneous
and high-dimensional context available in image and text data. Specifically, we
design the intensity of our point process model as a mixture of kernels, where
the mixture weights are modeled by a deep neural network. This formulation
allows us to automatically learn the complex nonlinear effects of the
contextual factors on event occurrence. At the same time, this formulation
makes analytical integration over the intensity, which is required for point
process estimation, tractable. We use real-world data sets from different
domains to demonstrate that DMPP has better predictive performance than
existing methods.

本研究提出了基于深度混合点过程（DMPP）的点过程模型，用于利用丰富的上下文信息来预测时空事件。模型的密度函数被设计为核函数的混合，其中混合权重由深度神经网络建模，并且将复杂非线性上下文影响到事件发生的自动学习成为可能。与现有方法相比，DMPP 在真实世界数据集上具有更好的预测性能。

深度混合点过程：利用丰富的上下文信息进行时空事件预测

Deep Mixture Point Processes: Spatio-temporal Event Prediction with Rich  Contextual Information

We introduce a new type of point process model to describe the incidence of
contagious diseases. The model is a variant of the Hawkes self-exciting process
and exhibits similar clustering but without the restriction that the component
describing the contagion must remain static over time. Instead, our proposed
model prescribes that the degree of contagion (or productivity) changes as a
function of the conditional intensity; of particular interest is the special
case where the productivity is inversely proportional to the conditional
intensity. The model incorporates the premise that when the disease occurs at
very low frequency in the population, such as in the primary stages of an
outbreak, then anyone with the disease is likely to have a high rate of
transmission to others, whereas when the disease is prevalent in the
population, then the transmission rate is lower due to human mitigation actions
and prevention measures and a relatively high percentage of previous exposure
in the total population. The model is said to be recursive, in the sense that
the conditional intensity at any particular time depends on the productivity
associated with previous points, and this productivity in turn depends on the
conditional intensity at those points. Some basic properties of the model are
derived, estimation and simulation are discussed, and the recursive model is
shown to fit well to historic data on measles in Los Angeles, California, a
relevant example given the 2017 outbreak of this disease in the same region.

介绍了新型点过程模型，用于描述传染疾病的发生。该模型是 Hawkes 自励过程的变体，其聚类类似，但没有组成传染的组件在时间上保持静态的限制，传染度随条件强度变化而改变。

传染病的递归点过程模型

A recursive point process model for infectious diseases

A novel point process model continuous in space-time is proposed for
quantifying the transmission dynamics of the two most common meningococcal
antigenic sequence types observed in Germany 2002-2008. Modelling is based on
the conditional intensity function (CIF) which is described by a superposition
of additive and multiplicative components. As an epidemiological interesting
finding, spread behaviour was shown to depend on type in addition to age: basic
reproduction numbers were 0.25 (95% CI 0.19-0.34) and 0.11 (95% CI 0.07-0.17)
for types B:P1.7-2,4:F1-5 and C:P1.5,2:F3-3, respectively. Altogether, the
proposed methodology represents a comprehensive and universal regression
framework for the modelling, simulation and inference of self-exciting
spatio-temporal point processes based on the CIF. Usability of the modelling in
biometric practice is promoted by an implementation in the R package
surveillance.

研究了德国 2002-2008 年发生的两个最常见的脑膜炎球菌抗原序列类型的传输动力学， 提出一种新的连续时空点过程模型，通过条件强度函数描述和建模，发现传播行为除年龄外还与类型有关，基础再生数分别为 0.25 和 0.11，所提出的方法可用于自激励时空点过程的建模、模拟和推断。