arXiv:2511.11983stat.MLcs.LG2025-11

融合贝叶斯与AI,实现精准风险预测与智能调参。

Bayesian--AI Fusion for Epidemiological Decision Making: Calibrated Risk, Honest Uncertainty, and Hyperparameter Intelligence

  • 用贝叶斯逻辑回归做个体风险预测,输出可信区间。
  • 通过高斯过程优化提升生存模型性能,AUC和对数损失均改善。
  • 适合需可靠不确定性和自动化调参的流行病学决策场景。

现代流行病学分析广泛使用机器学习模型,虽预测能力强但不确定性常未校准。贝叶斯方法能提供严谨的不确定性量化,却难融入现代AI工作流。本文提出统一的贝叶斯与AI框架,结合贝叶斯预测与贝叶斯超参数优化。在皮马印第安人糖尿病数据集上,采用贝叶斯逻辑回归获得个体疾病风险及可信区间;在GBSG2乳腺癌队列中,利用高斯过程贝叶斯优化调整惩罚型Cox生存模型。构建双层系统:贝叶斯预测层以后验分布表示风险,贝叶斯优化层将模型选择视为对黑箱目标的推断。低维与高维模拟显示,贝叶斯层具有可靠覆盖率与更好校准性,贝叶斯收缩提升AUC、Brier得分与对数损失;贝叶斯优化持续推动生存模型逼近近似最优一致性。整体而言,贝叶斯推理同时增强了推断质量与搜索效率,为流行病学决策提供校准风险与原则化超参数智能。

原文摘要 · Abstract (English)

Modern epidemiological analytics increasingly use machine learning models that offer strong prediction but often lack calibrated uncertainty. Bayesian methods provide principled uncertainty quantification, yet are viewed as difficult to integrate with contemporary AI workflows. This paper proposes a unified Bayesian and AI framework that combines Bayesian prediction with Bayesian hyperparameter optimization. We use Bayesian logistic regression to obtain calibrated individual-level disease risk and credible intervals on the Pima Indians Diabetes dataset. In parallel, we use Gaussian-process Bayesian optimization to tune penalized Cox survival models on the GBSG2 breast cancer cohort. This yields a two-layer system: a Bayesian predictive layer that represents risk as a posterior distribution, and a Bayesian optimization layer that treats model selection as inference over a black-box objective. Simulation studies in low- and high-dimensional regimes show that the Bayesian layer provides reliable coverage and improved calibration, while Bayesian shrinkage improves AUC, Brier score, and log-loss. Bayesian optimization consistently pushes survival models toward near-oracle concordance. Overall, Bayesian reasoning enhances both what we infer and how we search, enabling calibrated risk and principled hyperparameter intelligence for epidemiological decision making.

贝叶斯方法风险预测生存分析超参数优化

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