随机时间序列的概率近似使用贝叶斯反复神经网络.
概括
这项研究分析了贝叶斯反复神经网络的时间序列预测. 我们表明,将序列转换为潜在变量模型,并使用Bayes by Backprop对更多样本进行预测,可以提高预测的准确性和收性.
科学领域:
- 机器学习 机器学习
- 时间序列分析时间序列分析
- 概率模型可能模型
背景情况:
- 随机时间序列具有累积依赖性,这对标准的循环神经网络具有挑战性.
- 贝叶斯反复神经网络 (BRNNs) 提供了一个概率方法,但它们的近似理论 (AT) 是复杂的.
- 现有的方法在循环架构中与时间序列数据的固有复杂性作斗争.
研究的目的:
- 为了研究贝叶斯反复神经网络 (BRNNs) 的近似理论 (AT),用于随机时间序列预测 (TSF).
- 开发一种方法来分析BRNN对时间序列数据的性能,解决数据依赖和网络结构之间的不兼容性.
- 在TSF的背景下,为BRNNs建立贝叶斯背向螺旋 (BBB) 训练算法,以确定贝叶斯背向螺旋 (BBB) 的融合特性.
主要方法:
- 随机时间序列的边缘化和转换成一个概率相当的潜变量模型 (LVM).
- 通过使用基于泰勒扩展的不确定性传播和分布参数化,评估BRNN输出平均值和LVM输出平均值之间的近似误差来分析AT.
- 通过Backprop (BBB) 算法研究贝叶斯概率的趋同,利用Khinchin的大数定律.
主要成果:
- 严格分析了BRNN和LVM输出平均值之间的近似误差.
- 已经证明,在贝叶斯的Backprop (BBB) 算法中增加蒙特卡洛样本可以提高趋同概率到1.
- 数字模拟证实了关于BRNN近似和BBB收的理论发现.
结论:
- 提出的方法有效地解决了将BRNN应用于随机时间序列预测的挑战.
- 这项研究为贝叶斯由Backprop训练算法的融合提供了理论保证.
- 这项工作有助于更深入地了解概率时间序列建模中BRNN的近似理论.
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