贝叶斯不确定性估计随机特征回归的贝叶斯不确定性估计的非对称性.
Youngsoo Baek1, Samuel I Berchuck2, Sayan Mukherjee3
1Department of Statistical Science, Duke University, Durham, NC 27705.
Advances in neural information processing systems
|December 15, 2025
概括
这项研究比较了后置预测分布和最大后置 (MAP) 估计器在过度参数化的随机特征回归中. 这些贝叶斯式和频率主义方法之间的非对称协议取决于信号噪声比和数据尺寸.
科学领域:
- 统计 统计 统计 统计
- 机器学习 机器学习
- 计算科学 计算科学
背景情况:
- 在过度参数化的模型中,贝叶斯和频率估计器的行为是研究的一个关键领域.
- 了解后期预测分布和最大后期 (MAP) 估计器之间的关系对于模型评估至关重要.
研究的目的:
- 在随机特征回归中,将后置预测分布 (贝叶斯模型平均值) 与最大后置 (MAP) 估计器的风险进行比较.
- 在过度参数化状态下分析它们的非对称行为,重点关注信号噪声比率和维度的作用.
主要方法:
- 对后预测分布的方差和MAP估计器风险的理论分析.
- 在两个模式下进行非对称分析:模型尺寸增长速度快于样本,样本增长速度快于尺寸.
- 数字模拟用于研究有限维性质和分布特征.
主要成果:
- 后预测分布和MAP估计器风险之间的非对称一致性是由信号对噪声比率的相位过渡决定的,当尺寸比样本增长更快时.
- 当样本数量比模型尺寸增长得更快时,这些数量也在异常一致.
- 数字模拟揭示了有限维度的更细微的分布性质.
结论:
- 这项研究建立了贝叶斯和频率主义估计器在过度参数化的随机特征回归中的非对称协议的条件.
- 关于高斯波动和与高斯序列模型发现的相似性提出了一个猜想,这表明了更广泛的理论含义.
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