A Gaussian process based technique for locating attractors from trajectories in time-varying fields.
This repository contains code used in the experiments of our paper: "Identifying Sources and Sinks in the Presence of Multiple Agents with Gaussian Process Vector Calculus" by Adam D. Cobb, Richard Everett, Andrew Markham, and Stephen J. Roberts.
In systems of multiple agents, identifying the cause of observed agent dynamics is challenging. Often, these agents operate in diverse, non-stationary environments, where models rely on handcrafted environment-specific features to infer influential regions in the system’s surroundings. To overcome the limitations of these inflexible models, we present GP-LAPLACE, a technique for locating sources and sinks from trajectories in time-varying fields. Using Gaussian processes, we jointly infer a spatio-temporal vector field, as well as canonical vector calculus operations on that field. Notably, we do this from only agent trajectories without requiring knowledge of the environment, and also obtain a metric for denoting the significance of inferred causal features in the environment by exploiting our probabilistic method. To evaluate our approach, we apply it to both synthetic and real-world GPS data, demonstrating the applicability of our technique in the presence of multiple agents, as well as its superiority over existing methods.
GP-LAPLACE applied to pelagic seabirds flying over the Mediterranean sea:
We have created a number of Jupyter notebooks to reproduce our results:
exp_synthetic_stationary.ipynb- Stationary attractors: Simulating agents in a non-stationary potential field.exp_synthetic_varying-strength.ipynb- Varying-strength attractors: Simulating agents in a potential field with attractors that vary their strength with time.exp_synthetic_rotating.ipynb- Rotating attractors: Simulating agents in a potential field with attractors that change location with time.
Each experiment should take no longer than 20 minutes from start to finish (with load_dict=False). Tested on:
- Ubuntu 16.04, 16GB memory, CPU @ 2.60GHz x 8
- Mac, 8GB memory, CPU @ 3.10GHz x 2
- Clone GP-LAPLACE and install requirements.
cd <installation_path_of_your_choice>
git clone https://github.com/AdamCobb/GP-LAPLACE
cd GP-LAPLACE
pip install -r requirements.txt
- Download and install GPFlow.
git clone https://github.com/GPflow/GPflow
cd GPflow
pip install .
- Run notebooks.
cd notebooks
jupyter notebook
Pollonara, E., Luschi, P., Guilford, T., Wikelski, M., Bonadonna, F. and Gagliardo, A., 2015. Olfaction and topography, but not magnetic cues, control navigation in a pelagic seabird: displacements with shearwaters in the Mediterranean Sea. Scientific reports, 5, p.16486.
Adam Cobb: acobb@robots.ox.ac.uk
Richard Everett: richard@robots.ox.ac.uk