Summary Markov Models for Event Sequences

TL;DR

This paper introduces summary Markov models for event sequences without timestamps, capturing dependencies based on summaries of past events, and demonstrates their effectiveness through theoretical analysis and case studies.

Contribution

It proposes a new family of summary Markov models, establishes their theoretical properties, and develops algorithms for learning them from data.

Findings

Unique minimal influencing sets exist for event types.

The models outperform relevant baselines in experiments.

Case studies show effective knowledge discovery.

Abstract

Datasets involving sequences of different types of events without meaningful time stamps are prevalent in many applications, for instance when extracted from textual corpora. We propose a family of models for such event sequences -- summary Markov models -- where the probability of observing an event type depends only on a summary of historical occurrences of its influencing set of event types. This Markov model family is motivated by Granger causal models for time series, with the important distinction that only one event can occur in a position in an event sequence. We show that a unique minimal influencing set exists for any set of event types of interest and choice of summary function, formulate two novel models from the general family that represent specific sequence dynamics, and propose a greedy search algorithm for learning them from event sequence data. We conduct an experimental investigation comparing the proposed models with relevant baselines, and illustrate their knowledge acquisition and discovery capabilities through case studies involving sequences from text.