用有限宽的神经网络进行贝叶斯推理
1Department of Mathematics and Computer Science, Rutgers University, Newark, New Jersey 07102, USA.
Physical review. E
|August 16, 2023
概括
我们提出一种非高斯分布来建模有限神经网络输出,从而实现准确的贝叶斯回归. 这解决了有限宽度网络中高斯度的偏差,以改进机器学习推理.
科学领域:
- 机器学习 机器学习
- 贝叶斯的推理是贝叶斯的推理.
- 深度学习 (Deep Learning) 是一种深度学习.
背景情况:
- 机器学习从业者经常将神经网络模型为高斯过程,以获得分析效益.
- 有限网络宽度引入偏离理想高斯度的偏差,使推理复杂化.
- 现有的方法难以准确地建模这些有限宽度效应.
研究的目的:
- 开发一种非高斯分布,用于模拟有限宽的随机神经网络的输出.
- 通过导出非高斯后部分布来实现准确的贝叶斯回归.
- 在重量空间高斯过程框架内研究深度神经网络中的非高斯性.
主要方法:
- 使用多变量Edgeworth扩展来导出非高斯分布的微分形式.
- 导出拟议的非高斯分布的边际和条件性质.
- 在深度神经网络中使用边缘内核和小参数分析非高斯性.
主要成果:
- 为有限神经网络输出提出了一个新的非高斯分布.
- 该方法允许在贝叶斯回归中导出非高斯后分布.
- 深度高斯过程中的非高斯性通过特定的参数来表征.
结论:
- 拟议的非高斯方法增强了对于有限宽度神经网络的贝叶斯推理.
- 这项工作为超越高斯假设的神经网络输出提供了更现实的模型.
- 这些发现为复杂的深度学习模型提供了更好的分析处理能力.
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