We propose an alternating minimization heuristic for regression over the space of
tropical rational functions with fixed exponents. The method alternates between
fitting the numerator and denominator terms via tropical polynomial regression,
which is known to admit a closed form solution. We demonstrate the behavior of the
alternating minimization method experimentally. Experiments demonstrate that the
heuristic provides a reasonable approximation of the input data. Our work is
motivated by applications to ReLU neural networks, a popular class of network
architectures in the machine learning community which are closely related to tropical
rational functions.
