论文标题
部分可观测时空混沌系统的无模型预测
Hold-out estimates of prediction models for Markov processes
论文作者
论文摘要
我们考虑了马尔可夫时间序列的预测模型的选择。为此，我们研究了保留方法的理论特性。在《计量经济学文献》中，持有方法被称为样本外，是选择合适的时间序列模型的主要方法。该方法包括在学习集中估算模型，并在未来观察结果的验证集中以最小的经验误差来拾取模型。在独立案例中，对估算值进行了充分的研究，但是据我们所知，当验证集不独立于学习集时，情况并非如此。在本文中，假设马尔可夫链的统一性的牙齿性，我们对这种方法表示了概括和甲骨文的不平等。特别是，我们表明样本外选择方法适应噪声条件。
We consider the selection of prediction models for Markovian time series. For this purpose, we study the theoretical properties of the hold-out method. In the econometrics literature, the hold-out method is called out-of-sample and is the main method to select a suitable time series model. This method consists of estimating models on a learning set and picking up the model with minimal empirical error on a validation set of future observations. Hold-out estimates are well studied in the independent case, but, as far as we know, this is not the case when the validation set is not independent of the learning set. In this paper, assuming uniform ergodicity of the Markov chain, we state generalization bounds and oracle inequalities for such method; in particular, we show that the out-of-sample selection method is adaptative to noise condition.
