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

Abstract

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 a priori. 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, which in turn enhances its predictive prowess, and can identify the optimal position of missing events in a sequence. Experiments with eight real-world datasets show that IMTPP outperforms the state-of-the-art MTPP frameworks for event prediction and missing data imputation, and provides stable optimization.