Reformulating Strict Monotonic Probabilities with a Generative Cost Model
Keywords: monotonic model, variational inference, generative model
TL;DR: We propose a generative method that solves the monotonic modeling task.
Abstract: In numerous machine learning contexts, the relationship between input variables and predicted outputs is not only statistically significant but also strictly monotonic. Conventional approaches to ensuring monotonicity focus primarily on construction or regularization methods. This paper establishes that the problem of strict monotonic probability can be interpreted as a comparison between an observable revenue variable and a latent cost variable. This insight allows us to reformulate the original monotonicity challenge into modeling the latent cost variable and estimating its distribution. To address this issue, we introduce a generative model for the latent cost variable, called the Generative Cost Model (\textbf{GCM}), and derive a corresponding loss function. We further enhance the estimation of latent variables using variational inference, which reformulate our loss function accordingly. Lastly, we validate our approach through a numerical simulation of quantile regression and several experiments on public datasets, demonstrating that our method significantly outperforms traditional techniques. The code of GCM is available in https://github.com/iclr-2025-4464/GCM.
Primary Area: generative models
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Submission Number: 4464
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