In this paper we derive a PAC-Bayesian-Like error bound for a class of stochastic dynamical systems with inputs, namely, for linear time-invariant stochastic state-space models (stochastic LTI systems for short). This class of systems is widely used in control engineering and econometrics, in particular, they represent a special case of recurrent neural networks. In this paper we 1) formalize the learning problem for stochastic LTI systems with inputs, 2) derive a PAC-Bayesian-Like error bound for such systems, 3) discuss various consequences of this error bound.
translated by 谷歌翻译
我们研究了评估基于微分方程（DE）网络的鲁棒性的问题和挑战，以防止合成分布转移。我们提出了一种新颖而简单的精度度量，可用于评估固有的鲁棒性并验证数据集损坏模拟器。我们还提出了方法论建议，注定要评估神经des'的鲁棒性的许多面孔，并将其与它们的离散对应物进行了严格的比较。然后，我们使用此标准来评估廉价数据增强技术，以证明神经ODE的自然鲁棒性，以防止多个数据集中的模拟图像损坏。
translated by 谷歌翻译
在本文中，我们表明，可以将复发性（ODE-RNN）和长短期内存（ODE-LSTM）网络的神经颂歌类似物嵌入到多项式系统的类别中。这种嵌入了固定的投入输出行为，并可以适当地扩展到其他神经DE架构。然后，我们使用多项式系统的实现理论为输入输出映射提供必要条件，以通过ODE-LSTM实现，并且有足够的条件以最小化此类系统。这些结果代表了实现复发性神经胶体系结构的第一步，这对于复发性神经ODE的模型还原和学习算法分析是有用的。
translated by 谷歌翻译
In this short article, we showcase the derivation of the optimal (minimum error variance) estimator, when one part of the stochastic LTI system output is not measured but is able to be predicted from the measured system outputs. Similar derivations have been done before but not using state-space representation.
translated by 谷歌翻译