Prime-Time: Symbolic Regression Takes Its Place in the Real World 249
contemporaneous and (2) when the relationships are dynamic due to lags, is shown
in Kordon ( 2014 ). In the first case, a simple nonlinear transform, generated by GP
and used as exogenous input in the ARIMAX model, has shown the best ex-ante
performance. In the second case, GP has generated a dynamic model with accurate
lags.
This model has been compared to another contemporaneous nonlinear model,
generated by GP, and the best linear ARIMAX model. The ex-ante performance
of the dynamic model is the best for the tested period of time. These encouraging
results based on real world applications with high economic impact demonstrate the
big potential of GP in business forecasting.
4 Modern Complex Systems Analysis and Policy Making
For many years already we have been proposing to use symbolic regression for
simulation-based optimization, with its claim to fame being an white-box model
which can be built to model the behaviors of a complex simulator and a built-in
variable selection capability, which will only be producing models using variables
impacting simulator responses. The more robust are the symbolic regression
features—the more complicated simulators we can consider to understand and
meta-model. The process of building models of simulation models is referred to
as meta-modeling, and the process of optimizing and understanding the models
(as well as the underlying simulators and complex systems they are mimicking)
is referred to as simulation-based optimization, derivative-free optimization.
In this section we share the results of an exciting project to understand an truly
complex system—the state of the art simulator of the spread of infectious diseases
in a large population of humans, based on probabilistic individual-based models.
This inter-disciplinary project took place in Belgium by several groups and led
to a publication on Active Learning to Understand Infectious Disease Models and
Improve Policy Making at PLOS Computational Biology by Lander Willem, Sean
Stijven, Ekaterina Vladislavleva, Jan Broeckhove, Philippe Beutels, and Niel Hens.
Results presented in this section appeared in Active Learning to Understand
Infectious Disease Models and Improve Policy Making at PLOS Computational
Biology by Lander Willem, Sean Stijven, Ekaterina Vladislavleva, Jan Broeck-
hove, Philippe Beutels, and Niel Hens (DOI:10.1371/journal.pcbi.1003563) and
are presented here for the audience interested in complex systems analysis and
simulation-based optimization.
By large population we mean demographies of 0.5–300 million people in known
geographies (cities, counties, countries) and known probabilistic contact networks.
Population is decided into age groups from the known distribution, into families,
“children” go to school and kindergarten, adults travel to work by cars and public
transportation, communicate with their colleagues at work during the day and with
their families in the evening. In the presence of an infections disease with a certain
infectious rate R0, each individual can be in one of the four states—healthy, infected
and being infectious without symptoms, infectious while displaying symptoms, and
recovered.