arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~
arXiv 1802.09064cs.LGstat.ML
收藏

基于矩阵估计的模型无关时间序列分析

Model Agnostic Time Series Analysis via Matrix Estimation

Massachusetts Institute of Technology(麻省理工学院)

Anish Agarwal, Muhammad Jehangir Amjad, Devavrat Shah, Dennis Shen

摘要:

我们提出了一种算法来估算和预测的时间序列转换成一个矩阵,利用矩阵估计来恢复缺失值和去噪观测条目,并进行线性回归进行预测。我们分析的核心是一个表示结果,它指出对于一个大的模型类,变换后的时间序列矩阵是(近似)低秩的。实际上,这概括了时间序列文献中广泛使用的奇异谱分析(SSA),并使我们能够在时间序列分析和矩阵估计之间建立严格的联系。建立这种链接的关键是构建具有非重叠条目的Page矩阵,而不是如文献中通常所做的Hankel矩阵(例如,SSA)。这种特殊的矩阵结构使我们能够提供有限样本分析的填补和预测,并证明我们的方法的渐近一致性。我们的算法的另一个显着特点是,它是模型不可知论的基础时间动态和噪声分布的意见。我们的方法的噪声不可知属性允许我们在仅获得隐马尔可夫模型中的噪声和部分观测时恢复潜在状态;例如,恢复泊松过程的时变参数,而不知道底层过程是泊松。此外,由于我们的预测算法需要具有噪声特征的回归,因此我们的方法提出了一种基于矩阵估计的方法-再加上一种新的非标准矩阵估计误差度量-来解决变量回归问题中的误差,这可能是其本身的利益。通过合成和真实世界的数据集,我们证明了我们的算法优于标准的软件包(包括R库)的缺失数据的存在,以及高水平的噪音。

英文摘要:

We propose an algorithm to impute and forecast a time series by transforming the observed time series into a matrix, utilizing matrix estimation to recover missing values and de-noise observed entries, and performing linear regression to make predictions. At the core of our analysis is a representation result, which states that for a large model class, the transformed time series matrix is (approximately) low-rank. In effect, this generalizes the widely used Singular Spectrum Analysis (SSA) in time series literature, and allows us to establish a rigorous link between time series analysis and matrix estimation. The key to establishing this link is constructing a Page matrix with non-overlapping entries rather than a Hankel matrix as is commonly done in the literature (e.g., SSA). This particular matrix structure allows us to provide finite sample analysis for imputation and prediction, and prove the asymptotic consistency of our method. Another salient feature of our algorithm is that it is model agnostic with respect to both the underlying time dynamics and the noise distribution in the observations. The noise agnostic property of our approach allows us to recover the latent states when only given access to noisy and partial observations a la a Hidden Markov Model; e.g., recovering the time-varying parameter of a Poisson process without knowing that the underlying process is Poisson. Furthermore, since our forecasting algorithm requires regression with noisy features, our approach suggests a matrix estimation based method - coupled with a novel, non-standard matrix estimation error metric - to solve the error-in-variable regression problem, which could be of interest in its own right. Through synthetic and real-world datasets, we demonstrate that our algorithm outperforms standard software packages (including R libraries) in the presence of missing data as well as high levels of noise.

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。

↑