Alternating Minimization for Regression with Tropical Rational Functions
This work addresses regression problems, particularly motivated by applications to ReLU neural networks, but it is incremental as it builds on existing tropical polynomial regression methods.
The authors tackled regression using tropical rational functions with fixed exponents by proposing an alternating minimization heuristic that alternates between fitting numerator and denominator terms via tropical polynomial regression, and experiments showed it provides a reasonable approximation of input data.
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.