On the Inability of Markov Models to Capture Criticality in Human Mobility

TL;DR

This paper demonstrates that Markov models are insufficient for capturing the long-range correlations in human mobility, and recurrent neural networks can surpass the traditional predictability bounds by accounting for these correlations.

Contribution

The study reveals the limitations of Markov models in human mobility prediction and introduces recurrent neural networks as a superior alternative that captures long-range dependencies.

Findings

Markov models underestimate human mobility predictability.

Recurrent neural networks outperform Markov models in prediction accuracy.

Human mobility exhibits scale-invariant long-range correlations.

Abstract

We examine the non-Markovian nature of human mobility by exposing the inability of Markov models to capture criticality in human mobility. In particular, the assumed Markovian nature of mobility was used to establish a theoretical upper bound on the predictability of human mobility (expressed as a minimum error probability limit), based on temporally correlated entropy. Since its inception, this bound has been widely used and empirically validated using Markov chains. We show that recurrent-neural architectures can achieve significantly higher predictability, surpassing this widely used upper bound. In order to explain this anomaly, we shed light on several underlying assumptions in previous research works that has resulted in this bias. By evaluating the mobility predictability on real-world datasets, we show that human mobility exhibits scale-invariant long-range correlations, bearing similarity to a power-law decay. This is in contrast to the initial assumption that human mobility follows an exponential decay. This assumption of exponential decay coupled with Lempel-Ziv compression in computing Fano's inequality has led to an inaccurate estimation of the predictability upper bound. We show that this approach inflates the entropy, consequently lowering the upper bound on human mobility predictability. We finally highlight that this approach tends to overlook long-range correlations in human mobility. This explains why recurrent-neural architectures that are designed to handle long-range structural correlations surpass the previously computed upper bound on mobility predictability.