Monotonic Gaussian Process Flow
This work addresses the need for interpretable and uncertain monotonic functions in hierarchical probabilistic models, particularly for applications like temporal alignment of time-series data.
The authors tackled the problem of imposing monotonicity constraints in Bayesian nonparametric modeling by proposing a framework based on stochastic differential equations, resulting in competitive performance on benchmark functions compared to existing probabilistic monotonic models.
We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for interpretable priors and principled quantification of hierarchical uncertainty. We demonstrate the efficacy of the proposed model by providing competitive results to other probabilistic monotonic models on a number of benchmark functions. In addition, we consider the utility of a monotonic random process as a part of a hierarchical probabilistic model; we examine the task of temporal alignment of time-series data where it is beneficial to use a monotonic random process in order to preserve the uncertainty in the temporal warpings.