关于高斯过程模型的可识别性和可解释性
Jiawen Chen1, Wancen Mu1, Yun Li1
1Department of Biostatistics, University of North Carolina at Chapel Hill.
Advances in neural information processing systems
|March 5, 2026
概括
在高斯过程 (GP) 模型中,马特恩核的添加剂混合物提供了有限的识别能力. 然而,乘法混合物非常适合多输出GP任务,共变矩阵可以识别到一个常数.
科学领域:
- 机器学习 机器学习
- 统计建模 统计建模
背景情况:
- 高斯过程 (GPs) 是用于概率模型的强大工具.
- 马特恩内核在GP模型中被广泛使用,因为它们在定义函数流性方面具有灵活性.
- 马特恩核的添加剂混合物在单一输出GP中很常见,但它们的特性尚未完全理解.
研究的目的:
- 在单个输出GP模型中批判性地检查Matérn核的添加剂混合物的特性.
- 探索多输出GP模型中Matérn核的倍增混合的潜力.
- 分析添加式和倍增式核混合物的参数的识别能力.
主要方法:
- 添加剂和乘法混合物的核性质的理论导出.
- 在单个和多输出GP模型中分析参数识别能力.
- 广泛的模拟和现实世界的应用来验证发现.
主要成果:
- 对于添加剂混合物,光滑度是由最不光滑的组件决定的,使单个组件参数无法识别.
- 对于多输出GP中的乘法混合物,共变矩阵可以识别到一个乘法常数.
- 这些发现适用于单输出和多输出GP设置.
结论:
- 在单个输出GP中添加Matérn核的混合物提供了有限的灵活性和识别能力.
- 多倍混合为多输出GP提供了一个有希望的方法,提高了模型的可解释性.
- 该研究强调了为特定的GP建模任务选择合适的内核结构的重要性.
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