贝叶斯的梯度流适应性重要性采样,让一个出口交叉验证,并应用于西格莫形分类模型.
Joshua C Chang1, Xiangting Li2, Shixin Xu3
1NIH Clinical Center, Rehabilitation Medicine, Epidemiology and Biostatistics Section, Bethesda MD, USA.
ArXiv
|May 7, 2024
概括
我们开发了梯度流导向的自适应重要性采样 (IS) 转换来稳定贝叶斯模型预测的蒙特卡洛近似. 这种方法通过调整后部和稳定重要性权重来提高离开一个失误 (LOO) 交叉验证的准确性.
科学领域:
- 贝叶斯的推理 贝叶斯的推理
- 计算统计的计算统计.
- 机器学习是机器学习.
背景情况:
- 在贝叶斯统计学中,交叉验证 Leave-one-out (LOO) 对模型评估至关重要.
- 对于LOO预测的蒙特卡洛近似值可能是不稳定的,特别是在重要性抽样 (IS) 中.
- 现有的方法在复杂的贝叶斯模型中难以稳定重要性权重.
研究的目的:
- 引入一种用于稳定LOO交叉验证预测的蒙特卡洛近似的新方法.
- 提高贝叶斯模型评估的可靠性和准确性.
- 为了解决LOO预测中的重要抽样权重的不稳定性.
主要方法:
- 开发了梯度流导向的适应性重要性采样 (IS) 转换.
- 定义的变量问题和使用梯度信息推导的非线性转换.
- 针对逻辑回归和浅层神经网络的Hessian模型计算了雅可比式决定因素.
- 提出了一个近似方法,以避免计算完整的黑塞矩阵.
主要成果:
- 拟议的转换有效地稳定了LOO预测的重要性权重.
- 对于特定的模型来说,对雅可比式决定者的封闭式公式得到了推导.
- 介绍了一种近似方法来绕过黑斯计算.
- 该方法在已知不稳定的LOO IS权重的数据集上证明了稳定性.
结论:
- 梯度流导向的自适应IS转换为稳定贝叶斯模型中LOO交叉验证提供了强大的解决方案.
- 该方法提高了蒙特卡洛集成用于预测分布的可靠性.
- 这种方法提供了一种计算可行的方法来改进贝叶斯模型评估.
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