aiqbench analysis
This research introduces generalized engression models, a unified deep generative framework capable of modeling the joint conditional distributions for mixed-type multivariate outcomes including continuous, binary, and categorical variables. By integrating data-type-specific link functions with stochastic perturbation, the method enables gradient-based training on discontinuous losses while outperforming purpose-built state-of-the-art models in ecological and health benchmarks. The work advances nonparametric distributional regression by establishing universal representation results across diverse outcome types within a single architecture.
Generalized Engression Models
arXiv:2610.01823v1 Announce Type: cross Abstract: We consider estimating the conditional distribution of a multivariate outcome given covariates when its coordinates may be continuous, binary, categorical, ordinal or rankings, and are conditionally dependent on one another. Different statistical methods have been developed for each outcome type, and most of them target a summary of the conditional distribution, such as the mean of each coordinate, rather than the joint distribution of the outcome vector. We develop generalized engression models, a unified nonparametric distributional regression framework for outcomes of any type. The proposed method builds upon engression, a scoring-rule-based deep generative model, and introduces a data-type-specific link function and a stochastic perturbation that smooths the loss, enabling gradient-based training even with discontinuous links. We establish universal representation results for continuous, discrete and mixed outcomes. In simulations and in two applications, 242 species in a community ecology benchmark and a 17-dimensional mixed-type health outcome, the method matches type-specific models on marginal scores, improves on them on the joint distribution, and matches or exceeds purpose-built state-of-the-art joint species distribution models. Software is available in Python.
Abstract:We consider estimating the conditional distribution of a multivariate outcome given covariates when its coordinates may be continuous, binary, categorical, ordinal or rankings, and are conditionally dependent on one another. Different statistical methods have been developed for each outcome type, and most of them target a summary of the conditional distribution, such as the mean of each coordinate, rather than the joint distribution of the outcome vector. We develop generalized engression models, a unified nonparametric distributional regression framework for outcomes of any type. The proposed method builds upon engression, a scoring-rule-based deep generative model, and introduces a data-type-specific link function and a stochastic perturbation that smooths the loss, enabling gradient-based training even with discontinuous links. We establish universal representation results for continuous, discrete and mixed outcomes. In simulations and in two applications, 242 species in a community ecology benchmark and a 17-dimensional mixed-type health outcome, the method matches type-specific models on marginal scores, improves on them on the joint distribution, and matches or exceeds purpose-built state-of-the-art joint species distribution models. Software is available in Python.
Methodology (stat.ME); Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2610.01823 [stat.ME]
(or arXiv:2610.01823v1 [stat.ME] for this version)
https://doi.org/10.48550/arXiv.2610.01823 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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