发表机构
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出凹过程先验与潜变量模型，联合建模NBA球员多项表现指标的老化轨迹，提升预测性能并揭示不同指标的巅峰年龄差异。
AI 中文摘要
NBA运动员的表现通常随着职业生涯早期的发展和对联盟的适应而提升，随后因年龄相关的运动能力衰退而下降。尽管这一总体模式持续存在，但轨迹的具体形状因运动员和不同表现指标而异。为了对表现的提升和下降进行建模，我们引入了凹过程先验，这是一种新颖的、基于凹函数的非参数先验。随后，我们使用潜变量模型来刻画跨球员-指标的老化特征之间的依赖性，将每位球员嵌入到一个共享的低维潜空间中，使得具有相似老化特征的球员能够学习到相似的轨迹形状、巅峰年龄和巅峰值。对学习到的嵌入的后验分析支持基于潜空间最近邻检索的职业生涯可比球员，以及对年轻球员的知情预测。我们将模型应用于1997年至2026年赛季中超过两千名球员的十余项表现指标数据。结果表明，联合建模所有指标相比单一指标替代方案提高了留出数据的预测性能，且凹性约束本身也改善了预测。我们发现，以运动能力驱动的指标（如盖帽和进攻篮板）在球员二十岁出头时达到巅峰，而基于技能的投篮指标则在二十五岁或更晚达到巅峰。
英文摘要
NBA athlete performance tends to increase through early career as athletes develop and acclimate to the league, followed by decline due to age-related deterioration in athleticism. While this general pattern persists, the precise shape of this trajectory varies by athlete and across different measures of performance. To model performance increase and decline, we introduce the concave process prior, a novel nonparametric prior over concave functions. We then use a latent variable model to characterize dependence in aging profiles across player-metrics, embedding each player in a shared low-dimensional latent space so that players with similar profiles learn similar trajectory shapes, peak ages, and peak values. Posterior analysis of the learned embedding supports latent-space nearest-neighbor retrieval of career-comparable players and informed projections of young players. We apply our model to data across over a dozen performance metrics for over two thousand players in seasons ranging from 1997 to 2026. Our results show that jointly modeling all metrics improves held-out predictive performance over single-metric alternatives, and that the concavity constraint itself improves prediction. We find that athleticism-driven metrics such as blocks and offensive rebounds peak in a player's early twenties, while skill-based shooting metrics peak in the mid-twenties or later.
