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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 networks 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.
We present a method for conditional time series forecasting based on an adaptation of the recent deep convolutional WaveNet architecture. The proposed network contains stacks of dilated convolutions that allow it to access a broad range of history wh
Many applications require the ability to judge uncertainty of time-series forecasts. Uncertainty is often specified as point-wise error bars around a mean or median forecast. Due to temporal dependencies, such a method obscures some information. We w
This paper addresses the problem of time series forecasting for non-stationary signals and multiple future steps prediction. To handle this challenging task, we introduce DILATE (DIstortion Loss including shApe and TimE), a new objective function for
Due to the dynamic nature, chaotic time series are difficult predict. In conventional signal processing approaches signals are treated either in time or in space domain only. Spatio-temporal analysis of signal provides more advantages over convention
Forecasting high-dimensional time series plays a crucial role in many applications such as demand forecasting and financial predictions. Modern datasets can have millions of correlated time-series that evolve together, i.e they are extremely high dim