论文标题
改进的系统建模的错误自相关目标函数
Error Autocorrelation Objective Function for Improved System Modeling
论文作者
论文摘要
对深度学习模型进行了训练，以最大程度地减少模型的输出与实际值之间的误差。典型的成本函数，平方误差（MSE），是由于最大化添加剂独立，相同分布的高斯噪声的对数可能性而产生的。但是，最大程度地减少MSE并不能最大程度地减少残差的互相关，从而导致模型过度拟合和较差的训练集（概括）之外的模型外推。在本文中，我们引入了“美白”成本函数，即Ljung-box统计量，该统计量不仅可以最大程度地减少误差，还可以最大程度地减少错误之间的相关性，从而确保拟合与独立和相同分布和相同分布式（I.I.D）高斯高斯噪声模型的强制兼容性。结果表明，复发性神经网络（RNN）（1D）和图像自动编码器（2D）的概括显着改善。具体而言，我们研究模拟和实际机械系统中系统ID的时间相关性。我们还研究视觉自动编码器中的空间相关性，以证明美白目标功能会导致更好的外推 - 这是对可靠的控制系统非常理想的属性。
Deep learning models are trained to minimize the error between the model's output and the actual values. The typical cost function, the Mean Squared Error (MSE), arises from maximizing the log-likelihood of additive independent, identically distributed Gaussian noise. However, minimizing MSE fails to minimize the residuals' cross-correlations, leading to over-fitting and poor extrapolation of the model outside the training set (generalization). In this paper, we introduce a "whitening" cost function, the Ljung-Box statistic, which not only minimizes the error but also minimizes the correlations between errors, ensuring that the fits enforce compatibility with an independent and identically distributed (i.i.d) gaussian noise model. The results show significant improvement in generalization for recurrent neural networks (RNNs) (1d) and image autoencoders (2d). Specifically, we look at both temporal correlations for system-id in simulated and actual mechanical systems. We also look at spatial correlation in vision autoencoders to demonstrate that the whitening objective functions lead to much better extrapolation--a property very desirable for reliable control systems.
