Novel Methods for High-Dimensional Output Analysis for Agent-Based Models

Summary

We are looking for strong candidates to work on this exciting multidisciplinary project described below!

The challenge:

Agent-based models (ABMs) is a powerful computational approach for understanding complex systems. It focuses on modelling individual agents and their interactions, allowing emergent phenomena to arise from the bottom up (i.e. there are no equilibrium conditions to constrain the model outcomes, which are dynamic and evolving). In ABMs, agents are autonomous entities with defined behaviours and decision-making processes. These agents interact with each other and their environment according to specified rules, leading to complex system-level behaviours that often cannot be predicted from the individual components alone. This approach is particularly useful for studying social, economic, and environmental systems where heterogeneity, spatial and temporal aspects, and non-linear dynamics play crucial roles.

The outputs of agent-based models are often high-dimensional due to the inherent complexity and richness of the systems they simulate. Each agent in the model can have multiple attributes that change over time, and the model typically tracks numerous variables at both the individual and aggregate levels. For instance, in our urban transition model (1,2), we might track each household's income, employment status, housing situation, and location, as well as neighbourhood-level variables like average property values and employment rates. Additionally, the model may generate time series data for multiple scenarios, further increasing the dimensionality. In our global trade model (3), we track multiple variables for each country agent, including import and export volumes for 91 different food commodities, as well as the consumption and nutritional intake of 15 different macro and micronutrients. This results in thousands of output variables for each simulation run. This high-dimensionality allows for a comprehensive analysis of the system but also presents challenges in terms of data visualisation, interpretation, and communication of results to stakeholders, but also presents significant challenges insensitivity analysis, calibration, and validation of the model.

The high-dimensional outputs of agent-based models present significant challenges in several key areas of model development and analysis. Sensitivity analysis, which aims to understand how changes in input parameters affect model outcomes, becomes particularly complex with high-dimensional outputs. Traditional methods like one-at-a-time sensitivity analysis can be inadequate. Calibration and validation of agent-based models with high-dimensional outputs are particularly challenging. The process of fitting model parameters to match empirical data becomes increasingly difficult as the number of output variables grows. This is compounded by the fact that not all output variables may have corresponding empirical data for comparison. Lee et al. (2015)(4) discuss these challenges in the context of urban models, highlighting the need for advanced calibration techniques such as Bayesian inference and machine learning approaches. Validation faces similar hurdles, as assessing model performance across multiple dimensions simultaneously can be complex. Windrum et al. (2007)(5) propose various validation approaches for agent-based models, but note that the field still lacks standardised methods for dealing with high-dimensional outputs. These challenges underscore the need for innovative approaches in handling and interpreting the rich, but complex, data generated by agent-based models.

Proposed approach:

Since the outputs of ABMs are high dimensional variables, which make the sensitivity analysis, calibration and validation very complicated. A natural proposal is to cluster the outputs with high similarity, pick a few variables in each cluster and then perform sensitivity analysis, calibration and validation on these variables.

The spatial and temporal property of the outputs of ABMs imply traditional multivariate clustering analysis methods might be inappropriate. Therefore, time series clustering and functional data clustering methods (6) will be utlised. Our proposed nonparametric clustering (7) designed for functional data can be implemented, however different distance (similarity measures) might have different performance for outputs of ABMs. So the clustering methods and similarity measures should be selected carefully, say by conducting extensive simulations. Notice that for high-dimensional variables with different units and domains, pre-processing such as registration and standardisation usually needs to be designed before implementing clustering methods.

If sensitivity analysis based on selected variables is different from that based on original variables, sensitivity analysis methods should be adapted.

Since we have to conduct sensitivity analysis, calibration and validation using selected variables. Then the following questions arise. How do we know we have selected the right ones? Is there any benchmark to measure against? These questions are to be explored in this project.

References:

1. Ge J, Furtado BA. Modelling urban transition with coupled housing and labour markets. Environment and Planning B:Urban Analytics and City Science. 2023 Jul 4;23998083231186623.

2. Ge J, Furtado BA. Simulating urban transition in major socio-economic shocks. In IEEE; 2021. p. 1–10.

3. Ge J, Polhill JG, Macdiarmid JI, Fitton N, Smith P, Clark H, et al. Food and nutrition security under global trade: arelation-driven agent-based global trade model. Royal Society open science. 2021;8(1):201587.

4. Lee JS, Filatova T, Ligmann-Zielinska A, Hassani-Mahmooei B, Stonedahl F, Lorscheid I, et al. The complexities ofagent-based modeling output analysis. Journal of Artificial Societies and Social Simulation [Internet]. 2015 [cited 2024 Jul22];18(4). Available from: https://www.econstor.eu/handle/10419/230635

5. Windrum P, Fagiolo G, Moneta A. Empirical Validation of Agent-Based Models: Alternatives and Prospects. Journal ofArtificial Societies and Social Simulation [Internet]. 2007;10(2). Available from: http://jasss.soc.surrey.ac.uk/10/2/8.html

6. Zhang, M., & Parnell, A. (2023). Review of clustering methods for functional data. ACM Transactions on KnowledgeDiscovery from Data, 17(7), 1-34.

7. Xie, M., Liu, H., & Houwing-Duistermaat, J. Nonparametric clustering for longitudinal functional data with the applicationto H-NMR spectra of kidney transplant patients. In Longitudinal functional data clustering. Theor Biol Forum 2021; 114 (1-2):15 (Vol. 28).

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