# Modeling Continuous Time Sequences with Intermittent Observations using Marked Temporal Point Processes

arXiv: https://arxiv.org/abs/2206.12414 · HTML: https://mlsanity.com/paper/2206.12414/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 68 references that are in the map.
- First posted on arXiv 23 Jun 2022.

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [VoxCeleb: a large-scale speaker identification dataset](https://mlsanity.com/paper/1706.08612/) (2017)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Predicting Dynamic Embedding Trajectory in Temporal Interaction Networks](https://mlsanity.com/paper/1908.01207/) (2019)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Intensity-Free Learning of Temporal Point Processes](https://mlsanity.com/paper/1909.12127/) (2019)
- [Fully Neural Network based Model for General Temporal Point Processes](https://mlsanity.com/paper/1905.09690/) (2019)
- [Neural Temporal Point Processes: A Review](https://mlsanity.com/paper/2104.03528/) (2021)
- [Modeling The Intensity Function Of Point Process Via Recurrent Neural Networks](https://mlsanity.com/paper/1705.08982/) (2017)
- [Estimating Missing Data in Temporal Data Streams Using Multi-directional Recurrent Neural Networks](https://mlsanity.com/paper/1711.08742/) (2017)
- [SEISMIC: A Self-Exciting Point Process Model for Predicting Tweet Popularity](https://mlsanity.com/paper/1506.02594/) (2015)
- [Wasserstein Learning of Deep Generative Point Process Models](https://mlsanity.com/paper/1705.08051/) (2017)
- [Imputing Missing Events in Continuous-Time Event Streams](https://mlsanity.com/paper/1905.05570/) (2019)
- [Learning Temporal Point Processes via Reinforcement Learning](https://mlsanity.com/paper/1811.05016/) (2018)
- [Processing of missing data by neural networks](https://mlsanity.com/paper/1805.07405/) (2018)
- [A Variational Auto-Encoder Model for Stochastic Point Processes](https://mlsanity.com/paper/1904.03273/) (2019)
- [Expecting to be HIP: Hawkes Intensity Processes for Social Media Popularity](https://mlsanity.com/paper/1602.06033/) (2016)
- [EA-LSTM: Evolutionary Attention-based LSTM for Time Series Prediction](https://mlsanity.com/paper/1811.03760/) (2018)
- [Fake News Mitigation via Point Process Based Intervention](https://mlsanity.com/paper/1703.07823/) (2017)
- [Self-Attentive Hawkes Processes](https://mlsanity.com/paper/1907.07561/) (2019)
- [Learning and Forecasting Opinion Dynamics in Social Networks](https://mlsanity.com/paper/1506.05474/) (2015)
- [Long Horizon Forecasting With Temporal Point Processes](https://mlsanity.com/paper/2101.02815/) (2021)
- [Training recurrent neural networks robust to incomplete data: application to Alzheimer's disease progression modeling](https://mlsanity.com/paper/1903.07173/) (2019)
- [Learning Temporal Point Processes for Efficient Retrieval of Continuous Time Event Sequences](https://mlsanity.com/paper/2202.11485/) (2022)
- [Region Invariant Normalizing Flows for Mobility Transfer](https://mlsanity.com/paper/2109.05738/) (2021)
- [ProActive: Self-Attentive Temporal Point Process Flows for Activity Sequences](https://mlsanity.com/paper/2206.05291/) (2022)

## Built on by (most cited first, 3 of 3)

- [Interacting Diffusion Processes for Event Sequence Forecasting](https://mlsanity.com/paper/2310.17800/) (2023)
- [Modeling Events and Interactions through Temporal Processes -- A Survey](https://mlsanity.com/paper/2303.06067/) (2023)
- [Proactive Resource Request for Disaster Response: A Deep Learning-based Optimization Model](https://mlsanity.com/paper/2307.16661/) (2023)

## Abstract (arXiv)

A large fraction of data generated via human activities such as online purchases, health records, spatial mobility etc. can be represented as a sequence of events over a continuous-time. Learning deep learning models over these continuous-time event sequences is a non-trivial task as it involves modeling the ever-increasing event timestamps, inter-event time gaps, event types, and the influences between different events within and across different sequences. In recent years neural enhancements to marked temporal point processes (MTPP) have emerged as a powerful framework to model the underlying generative mechanism of asynchronous events localized in continuous time. However, most existing models and inference methods in the MTPP framework consider only the complete observation scenario i.e. the event sequence being modeled is completely observed with no missing events -- an ideal setting that is rarely applicable in real-world applications. A recent line of work which considers missing events while training MTPP utilizes supervised learning techniques that require additional knowledge of missing or observed label for each event in a sequence, which further restricts its practicability as in several scenarios the details of missing events is not known apriori. In this work, we provide a novel unsupervised model and inference method for learning MTPP in presence of event sequences with missing events. Specifically, we first model the generative processes of observed events and missing events using two MTPP, where the missing events are represented as latent random variables. Then, we devise an unsupervised training method that jointly learns both the MTPP by means of variational inference. Such a formulation can effectively impute the missing data among the observed events and can identify the optimal position of missing events in a sequence.