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摘要: 在针对控制和机器人的机器学习任务中, 高斯过程回归是一种常用方法, 具有无参数学习技术的优点. 然而, 它在面对大量训练数据时存在计算量大的缺点, 因此并不适用于实时更新模型的情况. 为了减少这种计算量, 使模型能够通过实时产生的大量数据不断更新, 本文提出了一种基于概率关联的局部高斯过程回归算法. 与其他局部回归模型相比, 该算法通过对多维局部空间模型边界的平滑处理, 使用紧凑支持的概率分布来划分局部模型中的数据, 得到了更好的预测精度. 另外, 还对更新预测矢量的计算方法进行了改进, 并使用k-d树最近邻搜索减少数据分配和预测的时间. 实验证明, 该算法在保持全局高斯过程回归预测精度的同时, 显著提升了计算效率, 并且预测精度远高于其他局部高斯过程回归模型. 该模型能够快速更新和预测, 满足工程中的在线学习的需求.Abstract: Gaussian regression is a common method in machine learning tasks for control and robotics, with the advantage of being a parametric learning technique. However, it has the disadvantage of being computationally intensive when faced with a large amount of training data, and thus is not suitable for the case of updating the model in real time. In order to reduce this amount of computation and realize the continuous updating of the model using a large amount of data generated in real time, this paper proposes a local regression algorithm based on probability correlation. Compared with other local regression models, the algorithm uses the tightly supported probability distribution to divide the data in the local model by smoothing the boundary of the multi-dimensional local space model and obtains better prediction accuracy. In addition, the calculation method of updating the prediction vector is improved, and the k-d tree nearest neighbor search is used to reduce the time of data allocation and prediction. Experiments show that the proposed algorithm improves the computational efficiency while maintaining the global regression prediction accuracy, and the prediction accuracy is much higher than other local regression models.
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Key words:
- Machine learning /
- probabilistic models /
- large data volumes /
- real-time update
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图 1 一维局部模型激活函数示意图
Fig. 1 Schematic diagram of one-dimensional local model activation function
图 3 局部模型参数对边界约束模型性能的影响
Fig. 3 Influence of local model parameters on performance of boundary constraint model
表 1 3种方法的性能对比
Table 1 Performance comparison of three methods
全局 GPR 硬边界 LGPR 边界约束 LGPR 预测误差 $ 1.281\times10^{-4}$ $ 97.775\times 10^{-4}$ $ 1.953\times10^{-4}$ 更新时间 (ms) 132.753 0.929 1.230 预测时间 (ms) 2.190 2.371 1.342 
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