时间序列的非参数密度估计、在线预测、回归和分类的压缩方法
Compression-based methods for nonparametric density estimation, on-line prediction, regression and classification for time series
摘要：
我们解决平稳和遍历时间序列的特征的非参数估计问题。我们考虑有限字母表时间序列和实值时间序列以及以下四个问题：i）（极限）概率的估计（或实值时间序列密度的估计），ii）在线预测，iii）回归和iv）分类（或所谓的边信息问题）。我们表明，所谓的存档（或数据压缩器）可以用作解决这些问题的工具。特别是，首先，它被证明，任何所谓的通用代码（或通用数据压缩器）可以被用来作为一个基础，为上述问题构造渐近最优方法。(By定义，通用码可以渐近地“压缩”由平稳和遍历源生成的任何序列，直到源的香农熵。其次，我们通过实验表明，基于实际使用的数据压缩方法的估计具有合理的精度。
英文摘要：
We address the problem of nonparametric estimation of characteristics for stationary and ergodic time series. We consider finite-alphabet time series and real-valued ones and the following four problems: i) estimation of the (limiting) probability (or estimation of the density for real-valued time series), ii) on-line prediction, iii) regression and iv) classification (or so-called problems with side information). We show that so-called archivers (or data compressors) can be used as a tool for solving these problems. In particular, firstly, it is proven that any so-called universal code (or universal data compressor) can be used as a basis for constructing asymptotically optimal methods for the above problems. (By definition, a universal code can "compress" any sequence generated by a stationary and ergodic source asymptotically till the Shannon entropy of the source.) And, secondly, we show experimentally that estimates, which are based on practically used methods of data compression, have a reasonable precision.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
