On the Convergence of Semi Unsupervised Calibration through Prior Adaptation Algorithm

Calibration is an essential key in machine leaning. Semi Unsupervised Calibration through Prior Adaptation (SUCPA) is a calibration algorithm used in (but not limited to) large-scale language models defined by a {system of first-order difference equation. The map derived by this system} has the peculiarity of being non-hyperbolic {with a non-bounded set of non-isolated fixed points}. In this work, we prove several convergence properties of this algorithm from the perspective of dynamical systems. For a binary classification problem, it can be shown that the algorithm always converges, {more precisely, the map is globally asymptotically stable, and the orbits converge} to a single line of fixed points. Finally, we perform numerical experiments on real-world application to support the presented results. Experiment codes are available online.