Latent state estimation for agent-based models using data assimilation

Scientists have recognized the need to build bottom-up models for socio-economic systems. Such models are often framed as heterogeneous agents interacting in a network following the rules of a dynamical system. However, the available data is often aggregated and incomplete, so even if we have a good model of reality, inferring the state of the individual agents remains a big open challenge. Moreover, these models are usually costly to simulate because one has to compute the individual interactions of all the agents in the system. We present a methodology to infer the latent states of agents embedded in a network when the data available is sparse, noisy, and low-dimensional. The methodology is based on the ensemble Kalman filter extended with a network localization technique that uses the system’s topology to improve the accuracy of the estimations. Our methodology has the following desired properties for bottom-up socioeconomic models: i) it treats the model as a black box, so it does not assume any closed-form mathematical form of the model a priori, ii) it requires a minimal number of simulations compared to state-of-the-art methods, iii) it exploits the underlying topology of the system to improve its predictions, iv) it works for nonlinear systems, v) it is well-justified from a Bayesian perspective, and vi) it is easy to implement. We validate our methodology in two informative examples: 1) a high-dimensional approximation of the Mackey-Glass chaotic system and 2) the Hegselmann-Krause bounded confidence (nonlinear) model of opinion dynamics embedded in a social network. While we do not use real-world data to showcase our methodology, we add noise and exogenous shocks to the observations, obtaining accurate predictions in both the observation and the latent state spaces. We aim to help bridge the gap between bottom-up modeling and data assimilation techniques in a computationally efficient way.