提出新型多变量评分规则，提升回归模型精度与相关性敏感度。
Scoring rule nets: beyond mean target prediction in multivariate regression
- 引入条件CRPS，扩展单变量CRPS至多变量场景
- 对常见分布可求闭式解，且对变量相关性敏感
- 实测性能超越MLE，媲美先进非参数模型
以最大似然估计（MLE）训练的概率回归模型在多变量情形下常过度估计方差。尽管单变量场景广泛使用连续排名概率得分（CRPS），但多变量领域尚无被广泛接受的替代方案。现有最深入研究的能源得分（Energy Score）缺乏闭式表达，且对目标变量间相关性不敏感。本文提出条件CRPS：一种扩展自CRPS的严格恰当多变量评分规则。我们证明了其对常见分布存在闭式表达，并展示了其对相关性的敏感性。在合成与真实数据上的多种实验表明，条件CRPS通常优于MLE，且性能可媲美最先进的非参数模型，如分布随机森林（DRF）。
原文摘要 · Abstract (English)
Probabilistic regression models trained with maximum likelihood estimation (MLE), can sometimes overestimate variance to an unacceptable degree. This is mostly problematic in the multivariate domain. While univariate models often optimize the popular Continuous Ranked Probability Score (CRPS), in the multivariate domain, no such alternative to MLE has yet been widely accepted. The Energy Score - the most investigated alternative - notoriously lacks closed-form expressions and sensitivity to the correlation between target variables. In this paper, we propose Conditional CRPS: a multivariate strictly proper scoring rule that extends CRPS. We show that closed-form expressions exist for popular distributions and illustrate their sensitivity to correlation. We then show in a variety of experiments on both synthetic and real data, that Conditional CRPS often outperforms MLE, and produces results comparable to state-of-the-art non-parametric models, such as Distributional Random Forest (DRF).
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