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Updated: Sep 15, 2025

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关于生物序列空间上的学习函数:关联高斯过程先验,规范化和尺度固定.
Samantha Petti1, Carlos Martí-Gómez2, Justin B Kinney2
1Department of Mathematics, Tufts University, Medford, MA, 02155.
ArXiv
|July 17, 2025
概括
这项研究将使用权重空间中的规范回归与函数空间中的高斯过程的序列到函数地图推理连接起来. 它阐明了调节器如何定义序列函数表示,并使序列函数统计数据的有效计算成为可能.
科学领域:
- 计算生物学 计算生物学
- 机器学习 机器学习
- 基因组学就是基因组学.
背景情况:
- 生物序列到功能地图对于理解DNA,RNA和蛋白质功能至关重要.
- 推断这些地图并分解它们以了解后续贡献是关键的挑战.
- 解释序列函数地图需要"尺度固定"来定义独特的表示.
研究的目的:
- 在过度参数化的权重空间中建立规范回归与函数空间中的高斯过程方法之间的关系.
- 解开重量空间调节器如何影响隐性先验并将最佳重量限制在特定尺寸上.
- 为了使任意高斯过程先验和各种尺度的调节器的构建.
主要方法:
- 在过度参数化的权重空间中连接L2规则化的回归与函数空间中的高斯过程.
- 分析重量空间调节器如何强加隐性先验并定义尺度.
- 开发用于特定高斯过程先验和尺度的调节器的方法.
主要成果:
- 建立了权重空间规范回归和函数空间高斯过程之间的正式联系.
- 对于普通重量空间调节器的隐式函数空间先验的特征.
- 衍生了序列到函数统计的高效计算方法,包括尺寸固定权重和表态系数,使用产品内核先验的内核技巧.
结论:
- 该研究提供了一个统一的框架,用于理解序列到函数地图推断和分解.
- 它提供了一种构建调节器的方法,这些调节器与所需的高斯过程先验和测量器保持一致.
- 现在可以有效计算复杂的序列函数统计数据,从而推进生物序列分析.
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