  Agent-Based Models (ABMs) are used in several fields to study the evolution
of complex systems from micro-level assumptions. However, ABMs typically can
not estimate agent-specific (or "micro") variables: this is a major limitation
which prevents ABMs from harnessing micro-level data availability and which
greatly limits their predictive power. In this paper, we propose a protocol to
learn the latent micro-variables of an ABM from data. The first step of our
protocol is to reduce an ABM to a probabilistic model, characterized by a
computationally tractable likelihood. This reduction follows two general design
principles: balance of stochasticity and data availability, and replacement of
unobservable discrete choices with differentiable approximations. Then, our
protocol proceeds by maximizing the likelihood of the latent variables via a
gradient-based expectation maximization algorithm. We demonstrate our protocol
by applying it to an ABM of the housing market, in which agents with different
incomes bid higher prices to live in high-income neighborhoods. We demonstrate
that the obtained model allows accurate estimates of the latent variables,
while preserving the general behavior of the ABM. We also show that our
estimates can be used for out-of-sample forecasting. Our protocol can be seen
as an alternative to black-box data assimilation methods, that forces the
modeler to lay bare the assumptions of the model, to think about the
inferential process, and to spot potential identification problems.
