Where you model timing effect Training and Prediction Steps
They are targeting “multi” on type of interaction, Node respectively:
Marked: Multi- types of interaction (usually represent as $k$) MTPP: Multi- number of Node One easy way to differntiate them is by the likelihood function:
Zhang, Yunhao, and Junchi Yan. 2021. “Neural Relation Inference for Multi-Dimensional Temporal Point Processes via Message Passing Graph.” In , 3:3406–12. https://doi.org/10.24963/ijcai.2021/469.
A multidimentional(D nodes) marked(M types of possible events) TPP($N_m$ length of sequence) modeling
Researcher Junchi Yan
Graph with MTPP explicit graph structures
Shang and Sun, 2019 Wu et al., 2020 Liu et al., 2018 use MTPP to model topological evolution of dynamic graphs
Shchur, Oleksandr, Ali Caner Türkmen, Tim Januschowski, and Stephan Günnemann. 2021. “Neural Temporal Point Processes: A Review.” ArXiv:2104.03528 [Cs], August. http://arxiv.org/abs/2104.03528.
Neural TPP = TPP + Deep Learning
Model Sequence Events: any sequential model(RNN, transfomer) + TPP
The timing modeling is not embedded in the complex structure of RNN, so the pdf of $t$ could be solved analytically
Modeling of timing is embedded into the LSTM structure. so the hidden state $h(t)$ is a function of $t$(continuous)
Hawkes Process is a special kind of point process with 1. postive 2. additive 3. exponentail decay self-exiciting factor 2.
Point Process is widely used in modeling sequence of events that: 1. timing is important 2.rare to happen