时间序列插补模型相关工作

• 一些早期的研究通过空间关系或相邻序列来填充缺失值，如KNN [12]，[13]和Kriging [32]。
  [12] H. Trevor, T. Robert, and F. Jerome, “The elements of statistical learning:
  data mining, inference, and prediction,” 2009.
  [13] L. Beretta and A. Santaniello, “Nearest neighbor imputation algorithms:
  a critical evaluation,” BMC medical informatics and decision making,
  vol. 16, no. 3, pp. 197–208, 2016.
  [32] M. L. Stein, Interpolation of spatial data: some theory for kriging.
  Springer Science & Business Media, 1999.
• MICE使用链式方程来填充缺失值。
  Ian R White, Patrick Royston, and Angela MWood. 2011. Multiple imputation
  using chained equations: issues and guidance for practice. Statistics in medicine
  30, 4 (2011), 377–399.
• 一些代表性的自回归模型，如ARIMA和VAR，可用于插补缺失值。
  George EP Box, Gwilym M Jenkins, Gregory C Reinsel, and Greta M Ljung. 2015.
  Time series analysis: forecasting and control. John Wiley & Sons.
  Eric Zivot and Jiahui Wang. 2006. Vector autoregressive models for multivariate
  time series. Modeling financial time series with S-PLUS® (2006), 385–429.
• 选择最接近的邻居，并使用邻居值的平均值来填充缺失值。
  Andrew T Hudak, Nicholas L Crookston, Jeffrey S Evans, David E Hall, and
  Michael J Falkowski. 2008. Nearest neighbor imputation of species-level, plot-
  scale forest structure attributes from LiDAR data. Remote Sensing ofEnvironment
  112, 5 (2008), 2232–2245.
• MF将不完整的数据集分解为低秩矩阵，并采用这两个矩阵的乘积来估算缺失值。
  Morten Morup, Daniel M Dunlavy, Evrim Acar, and Tamara Gibson Kolda. 2010.
  Scalable tensor factorizations with missing data. Technical Report. Sandia National
  Laboratories (SNL), Albuquerque, NM, and Livermore, CA . . . .

以上这些方法难以拟合大型数据集，并且其插补精度有限。

• 为了提高代表能力，[12]将自我训练机制应用于多元插补。
  Tae-Min Choi, Ji-Su Kang, and Jong-Hwan Kim. 2020. RDIS: Random drop
  imputation with self-training for incomplete time series data. arXiv preprint
  arXiv:2010.10075 (2020).

• [31，35]提出了基于注意力的多变量插补模型。
  *[31] Satya Narayan Shukla and Benjamin M Marlin. 2021. Multi-time attention
  networks for irregularly sampled time series. arXiv preprint arXiv:2101.10318
  (2021).

  [35] Qiuling Suo, Weida Zhong, Guangxu Xun, Jian