# Time-Discounting Convolution for Event Sequences with Ambiguous Timestamps

## TL;DR

This paper introduces a novel time-discounting convolution method for modeling event sequences with ambiguous timestamps, achieving robustness against time-shifts and timestamp uncertainty while effectively handling infinite sequences.

## Contribution

The proposed method uniquely combines time-discounting convolution with dynamic pooling to address timestamp ambiguity and sequence length variability in event sequence modeling.

## Key findings

- Demonstrated robustness to timestamp uncertainty in real-world data
- Effectively handles infinite and variable-length sequences
- Outperformed traditional models in experiments

## Abstract

This paper proposes a method for modeling event sequences with ambiguous timestamps, a time-discounting convolution. Unlike in ordinary time series, time intervals are not constant, small time-shifts have no significant effect, and inputting timestamps or time durations into a model is not effective. The criteria that we require for the modeling are providing robustness against time-shifts or timestamps uncertainty as well as maintaining the essential capabilities of time-series models, i.e., forgetting meaningless past information and handling infinite sequences. The proposed method handles them with a convolutional mechanism across time with specific parameterizations, which efficiently represents the event dependencies in a time-shift invariant manner while discounting the effect of past events, and a dynamic pooling mechanism, which provides robustness against the uncertainty in timestamps and enhances the time-discounting capability by dynamically changing the pooling window size. In our learning algorithm, the decaying and dynamic pooling mechanisms play critical roles in handling infinite and variable length sequences. Numerical experiments on real-world event sequences with ambiguous timestamps and ordinary time series demonstrated the advantages of our method.