A simple randomized algorithm for sequential prediction of ergodic time series
A simple randomized algorithm for sequential prediction of ergodic time series
复制标题
遍历时间序列顺序预测的简单随机算法
DOI：
10.1109/18.796420
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
G. Morvai
中科院分区：
文献类型：
--
作者：
L. Györfi;G. Lugosi;G. Morvai
我们提出了一个简单的随机过程的预测的二进制序列。该算法使用的思想，从以前的发展理论的预测个别序列。我们证明，如果序列是平稳且各态历经的随机过程的实现，那么平均错误数几乎肯定会收敛到贝叶斯预测器给出的最优值。期望的有限样本性质的预测器说明其性能的马尔可夫过程。在这种情况下，即使不知道马尔可夫过程的顺序，预测器也会表现出接近最优的行为。还考虑了边信息的预测。
We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from previous developments of the theory of the prediction of individual sequences. We show that if the sequence is a realization of a stationary and ergodic random process then the average number of mistakes converges, almost surely, to that of the optimum, given by the Bayes predictor. The desirable finite-sample properties of the predictor are illustrated by its performance for Markov processes. In such cases the predictor exhibits near-optimal behavior even without knowing the order of the Markov process. Prediction with side information is also considered.