  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.
