Variational Inference of Parameters in Opinion Dynamics Models

TL;DR

The paper tackles the challenge of estimating parameters in agent-based opinion dynamics models by turning ABMs into Probabilistic Generative ABMs (PGABMs) and performing Variational Inference (VI) with differentiable relaxations and normalizing flows. It assesses four BCM-b extensions (BCM-S, BCM-I, BCM-U, BCM-G) and demonstrates that VI-based methods outperform simulation-based approaches (ABC) and MCMC both in accuracy and speed, even enabling recovery of up to 400 microscopic agent attributes. The work provides a principled, data-driven framework for tuning ABMs to real observations and offers insights into human behavior in social systems, while discussing limitations and future directions for broader applicability. Overall, the approach integrates probabilistic modeling with differentiable ABMs to enable scalable, data-informed calibration of complex social dynamics.

Abstract

Despite the frequent use of agent-based models (ABMs) for studying social phenomena, parameter estimation remains a challenge, often relying on costly simulation-based heuristics. This work uses variational inference to estimate the parameters of an opinion dynamics ABM, by transforming the estimation problem into an optimization task that can be solved directly. Our proposal relies on probabilistic generative ABMs (PGABMs): we start by synthesizing a probabilistic generative model from the ABM rules. Then, we transform the inference process into an optimization problem suitable for automatic differentiation. In particular, we use the Gumbel-Softmax reparameterization for categorical agent attributes and stochastic variational inference for parameter estimation. Furthermore, we explore the trade-offs of using variational distributions with different complexity: normal distributions and normalizing flows. We validate our method on a bounded confidence model with agent roles (leaders and followers). Our approach estimates both macroscopic (bounded confidence intervals and backfire thresholds) and microscopic ($200$ categorical, agent-level roles) more accurately than simulation-based and MCMC methods. Consequently, our technique enables experts to tune and validate their ABMs against real-world observations, thus providing insights into human behavior in social systems via data-driven analysis.

Figures (8)

• Figure 1: The proposed parameter estimation pipeline. First, we translate the agent-based model into a probabilistic generative agent-based model. Then, we apply variational inference to get an approximate posterior of the target parameters within a given dataset.
• Figure 2: Probabilistic Graphical Model associated with the Bounded Confidence model with backfire effect. Circles represent stochastic variables, diamonds deterministic variables, and letters without enclosures are given PGM parameters. Shaded variables are observed and white ones are latent. $\pmb{X_t}$ is the opinion vector at time $\pmb{t}$, $\pmb{e}$ is the vector of the interacting agents, $\pmb{s}$ encodes the interactions outcomes, and $\pmb{\varepsilon}$ is the latent vector ($\pmb{\varepsilon^+}$, $\pmb{\varepsilon^-}$) of ABM parameters.
• Figure 3: BCM-S. Comparison between actual values $\varepsilon$ (x-axis) and estimates $\pmb{\hat{\varepsilon\xspace}}$ (y-axis) for each macroscopic parameter (rows) and method (columns). Each experiment samples $\varepsilon^+_F$ and $\varepsilon^+_L$ in $\pmb{\{0.05, 0.15, 0.25, 0.35, 0.45\}}$, such that $\varepsilon^+_F$$\pmb{\geq}$$\varepsilon^+_L$, $\varepsilon^-_F$ and $\varepsilon^-_L$ in $\pmb{\{0.55, 0.65, 0.75, 0.85, 0.95\}}$, and $\varepsilon^+_F$$\pmb{\leq}$$\varepsilon^+_L$. Points on the diagonals represent exact estimates.
• Figure 4: BCM-S. Specific errors on $\varepsilon^+_F$, $\varepsilon^+_L$, $\varepsilon^-_F$, $\varepsilon^-_L$, and $\mathbf{r}$ as functions of $\pmb{T}$ (left), $\pmb{N}$ (center), and proportion of leaders (right). The error bars represent the standard errors.
• Figure 5: BCM-I. Specific errors on $\pmb{\varepsilon\xspace^+}$, $\pmb{\varepsilon\xspace^-}$, and $\pmb{K}$, as functions of $\pmb{T}$ (left), $\pmb{F}$ (right). The error bars represent the standard errors. The relative error on $K$ is computed as $\lvert \hat{K} - K \rvert / F$.