Maximum likelihood estimation for randomized shortest paths with trajectory data

TL;DR

This paper develops maximum likelihood estimation methods for the randomized shortest paths model, enabling parameter inference from trajectory data in network analysis, demonstrated on artificial and real animal movement data.

Contribution

It introduces a principled approach to estimate the temperature parameter in RSP models from trajectory data, enhancing their applicability in real-world scenarios.

Findings

Effective MLE methods for RSP parameters demonstrated on artificial networks.

Application to wild reindeer movement data shows the model's practical utility.

RSP framework effectively models diverse movement and flow phenomena.

Abstract

Randomized shortest paths (RSP) are a tool developed in recent years for different graph and network analysis applications, such as modelling movement or flow in networks. In essence, the RSP framework considers the temperature-dependent Gibbs-Boltzmann distribution over paths in the network. At low temperatures, the distribution focuses solely on the shortest or least-cost paths, while with increasing temperature, the distribution spreads over random walks on the network. Many relevant quantities can be computed conveniently from this distribution, and these often generalize traditional network measures in a sensible way. However, when modelling real phenomena with RSPs, one needs a principled way of estimating the parameters from data. In this work, we develop methods for computing the maximum likelihood estimate of the model parameters, with focus on the temperature parameter, when modelling phenomena based on movement, flow, or spreading processes. We test the validity of the derived methods with trajectories generated on artificial networks as well as with real data on the movement of wild reindeer in a geographic landscape, used for estimating the degree of randomness in the movement of the animals. These examples demonstrate the attractiveness of the RSP framework as a generic model to be used in diverse applications.