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Modeling Inter-Dependence Between Time and Mark in Multivariate Temporal Point Processes

Govind Waghmare, Ankur Debnath, Siddhartha Asthana, Aakarsh Malhotra

TL;DR

This work model the conditional inter-dependence of time and mark to overcome the limitations of conditionally independent models and construct a multivariate TPP conditioning the time distribution on the current event mark in addition to past events.

Abstract

Temporal Point Processes (TPP) are probabilistic generative frameworks. They model discrete event sequences localized in continuous time. Generally, real-life events reveal descriptive information, known as marks. Marked TPPs model time and marks of the event together for practical relevance. Conditioned on past events, marked TPPs aim to learn the joint distribution of the time and the mark of the next event. For simplicity, conditionally independent TPP models assume time and marks are independent given event history. They factorize the conditional joint distribution of time and mark into the product of individual conditional distributions. This structural limitation in the design of TPP models hurt the predictive performance on entangled time and mark interactions. In this work, we model the conditional inter-dependence of time and mark to overcome the limitations of conditionally independent models. We construct a multivariate TPP conditioning the time distribution on the current event mark in addition to past events. Besides the conventional intensity-based models for conditional joint distribution, we also draw on flexible intensity-free TPP models from the literature. The proposed TPP models outperform conditionally independent and dependent models in standard prediction tasks. Our experimentation on various datasets with multiple evaluation metrics highlights the merit of the proposed approach.

Modeling Inter-Dependence Between Time and Mark in Multivariate Temporal Point Processes

TL;DR

This work model the conditional inter-dependence of time and mark to overcome the limitations of conditionally independent models and construct a multivariate TPP conditioning the time distribution on the current event mark in addition to past events.

Abstract

Temporal Point Processes (TPP) are probabilistic generative frameworks. They model discrete event sequences localized in continuous time. Generally, real-life events reveal descriptive information, known as marks. Marked TPPs model time and marks of the event together for practical relevance. Conditioned on past events, marked TPPs aim to learn the joint distribution of the time and the mark of the next event. For simplicity, conditionally independent TPP models assume time and marks are independent given event history. They factorize the conditional joint distribution of time and mark into the product of individual conditional distributions. This structural limitation in the design of TPP models hurt the predictive performance on entangled time and mark interactions. In this work, we model the conditional inter-dependence of time and mark to overcome the limitations of conditionally independent models. We construct a multivariate TPP conditioning the time distribution on the current event mark in addition to past events. Besides the conventional intensity-based models for conditional joint distribution, we also draw on flexible intensity-free TPP models from the literature. The proposed TPP models outperform conditionally independent and dependent models in standard prediction tasks. Our experimentation on various datasets with multiple evaluation metrics highlights the merit of the proposed approach.
Paper Structure (16 sections, 26 equations, 5 figures, 6 tables)

This paper contains 16 sections, 26 equations, 5 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. Classical (non-neural) TPPs
  4. Neural TPPs
  5. Model Formulation
  6. Background and notations
  7. Proposed approach
  8. Likelihood estimation
  9. Experimental Evaluation
  10. Datasets
  11. Synthetic datasets
  12. Real-world datasets
  13. Baseline Algorithms
  14. Evaluation Protocols
  15. Training and Results
  16. ...and 1 more sections

Figures (5)

  • Figure 1: The proposed models are conditionally dependent, multivariate, and capable of employing both intensity-free and intensity-based formulations.
  • Figure 2: Overview of the proposed multivariate conditionally dependent model. The inter-event time distribution is learned either using an intensity-free or intensity-based approach. Input event sequence contains arrival time and mark for each event. Input representation contains inter-event time and mark embedding. RNN converts event history into a fixed dimension vector. In the end, we compute the conditional joint density of time and marks.
  • Figure 3: Sampling statistics for MIMIC-II dataset.
  • Figure 4: Sampling statistics for MOOC dataset.
  • Figure 5: Sampling statistics for Stack Overflow dataset.