  The adaptive immune system's T and B cells can be viewed as large populations
of simple, diverse classifiers. Artificial immune systems (AIS)
$\unicode{x2013}$ algorithmic models of T or B cell repertoires
$\unicode{x2013}$ are used in both computational biology and natural computing
to investigate how the immune system adapts to its changing environments.
However, researchers have struggled to build such systems at scale. For
string-based AISs, finite state machines (FSMs) can store cell repertoires in
compressed representations that are orders of magnitude smaller than explicitly
stored receptor sets. This strategy allows AISs with billions of receptors to
be generated in a matter of seconds. However, to date, these FSM-based AISs
have been unable to deal with multiplicity in input data. Here, we show how
weighted FSMs can be used to represent cell repertoires and model immunological
processes like negative and positive selection, while also taking into account
the multiplicity of input data. We use our method to build simple
immune-inspired classifier systems that solve various toy problems in anomaly
detection, showing how weights can be crucial for both performance and
robustness to parameters. Our approach can potentially be extended to increase
the scale of other population-based machine learning algorithms such as
learning classifier systems.

Neural and Evolutionary Computing