噪声清理短时间序列的精度矩阵
Miguel Ibáñez-Berganza1, Carlo Lucibello2, Francesca Santucci3
1Networks Unit, IMT School for Advanced Studies Lucca, Piazza San Francesco 19, 50100 Lucca, Italy and Istituto Italiano di Tecnologia. Largo Barsanti e Matteucci, 53, 80125 Napoli, Italy.
Physical review. E
|September 19, 2023
概括
我们对功能磁共振成像 (fMRI) 数据的矩阵估计算法进行了比较. 一个最佳的旋转不变估计器提高了精度矩阵准确度和功能性大脑活动数据分析.
科学领域:
- 神经科学是一个神经科学.
- 统计 统计 统计 统计
- 机器学习 机器学习
背景情况:
- 估计协变率和精度矩阵对于从功能磁共振成像 (fMRI) 数据中分析神经活动至关重要.
- 在fMRI中典型的具有高维度的小型数据集,对准确的矩阵估计构成挑战.
- 对于神经活动,高斯模型经常被假定,因此需要否定经验矩阵.
研究的目的:
- 从小型fMRI数据集中推断共变率和精度矩阵的各种算法进行比较.
- 确定最可靠的噪声清理算法,用于消除经验矩阵的噪声.
- 改进从人类大脑活动时间序列中估计真精度和协差矩阵.
主要方法:
- 在合成和真实fMRI数据集上比较标准的噪声清理算法.
- 来自高斯模型生成的合成数据,具有可控维度 (q) 和相关性.
- 来自休息状态的人类实体的真实数据,使用功能磁共振成像 (fMRI) 进行分析.
主要成果:
- 在合成数据中,最佳旋转不变估计器 (ORIE) 与真精度矩阵的距离明显较小.
- 与其他估计器相比,ORIE在自然fMRI数据上实现了更高的测试组概率.
- ORIE的交叉验证优化的变体在严格的样本下采样制度 (大q) 中表现优于其他方法.
结论:
- 最佳旋转不变估计器是分析fMRI数据的可靠方法,特别是在样本不足的条件下.
- 交叉验证方法提高了fMRI时间序列的ORIE性能.
- 一个代的概率梯度上升算法显示了对弱相关合成数据的承诺.
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