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We present a method for fitting monotone curves using cubic B-splines, whichis equivalent to putting a monotonicity constraint on the coefficients. Weexplore different ways of enforcing this constraint and analyze theirtheoretical and empirical properties. We propose two algorithms for solving thespline fitting problem: one that uses standard optimization techniques and onethat trains a Multi-Layer Perceptrons (MLP) generator to approximate thesolutions under various settings and perturbations. The generator approach canspeed up the fitting process when we need to solve the problem repeatedly, suchas when constructing confidence bands using bootstrap. We evaluate our methodagainst several existing methods, some of which do not use the monotonicityconstraint, on some monotone curves with varying noise levels. We demonstratethat our method outperforms the other methods, especially in high-noisescenarios. We also apply our method to analyze the polarization-hole phenomenonduring star formation in astrophysics. The source code is accessible at\texttt{\url{https://github.com/szcf-weiya/MonotoneSplines.jl}}.

Monotone Cubic B-Splines with a Neural-Network Generator