Dimensionality Collapse: Optimal Measurement Selection for Low-Error Infinite-Horizon Forecasting
维度坍缩:低误差无限期预测的最优测量选择
This work introduces a method to select linear functional measurements of a vector-valued time series optimized for forecasting distant time-horizons. By formulating and solving the problem of sequential linear measurement design as an infinite-horizon problem with the time-averaged trace of the Cramér-Rao lower bound (CRLB) for forecasting as the cost, the most informative data can be collected irrespective of the eventual forecasting algorithm. By introducing theoretical…