标题： 全连接神经网络在时间序列预测中的泛化能力 显示英文标题

标题： Generalisation in fully-connected neural networks for time series forecasting

摘要： 在本文中，我们研究了在时间序列预测背景下训练的全连接神经网络的泛化能力。时间序列不满足统计学习理论中数据是来自某种数据生成分布的独立同分布样本的典型假设。我们使用输入和权重的Hessian矩阵，即学习函数相对于输入的平滑性和权重空间中最小值的宽度，来量化网络对未见数据的泛化能力。虽然这种泛化指标在例如图像识别的独立同分布设置中已经被广泛研究，但在这里我们通过实证验证了它们在时间序列预测任务中的适用性。此外，我们讨论了如何通过训练过程控制网络的泛化能力，使用学习率、批次大小和训练迭代次数作为控制参数。利用这些超参数，可以在不施加显式约束的情况下有效控制输出函数的复杂度。 显示英文摘要

摘要： In this paper we study the generalization capabilities of fully-connected neural networks trained in the context of time series forecasting. Time series do not satisfy the typical assumption in statistical learning theory of the data being i.i.d. samples from some data-generating distribution. We use the input and weight Hessians, that is the smoothness of the learned function with respect to the input and the width of the minimum in weight space, to quantify a network's ability to generalize to unseen data. While such generalization metrics have been studied extensively in the i.i.d. setting of for example image recognition, here we empirically validate their use in the task of time series forecasting. Furthermore we discuss how one can control the generalization capability of the network by means of the training process using the learning rate, batch size and the number of training iterations as controls. Using these hyperparameters one can efficiently control the complexity of the output function without imposing explicit constraints.