Learning Monotonic Probabilities with a Generative Cost Model
This addresses the need for reliable monotonic modeling in tasks like quantile regression, offering a novel approach that improves performance over traditional methods.
The paper tackles the problem of ensuring monotonic relationships between input and output variables in machine learning by reformulating it as modeling a latent cost variable, and introduces Generative Cost Models (GCM and IGCM) that significantly outperform existing techniques in experiments on public datasets.
In many machine learning tasks, it is often necessary for the relationship between input and output variables to be monotonic, including both strictly monotonic and implicitly monotonic relationships. Traditional methods for maintaining monotonicity mainly rely on construction or regularization techniques, whereas this paper shows that the issue of strict monotonic probability can be viewed as a partial order between an observable revenue variable and a latent cost variable. This perspective enables us to reformulate the monotonicity challenge into modeling the latent cost variable. To tackle this, we introduce a generative network for the latent cost variable, termed the Generative Cost Model (GCM), which inherently addresses the strict monotonic problem, and propose the Implicit Generative Cost Model (IGCM) to address the implicit monotonic problem. We further validate our approach with a numerical simulation of quantile regression and conduct multiple experiments on public datasets, showing that our method significantly outperforms existing monotonic modeling techniques. The code for our experiments can be found at https://github.com/tyxaaron/GCM.