Ultimate limit on learning non-Markovian behavior: Fisher information rate and excess information
学习非马尔可夫行为的极限：费舍尔信息率与超额信息
We address the fundamental limits of learning unknown parameters of any stochastic process from time-series data, and discover exact closed-form expressions for how optimal inference scales with observation length. Given a parametrized class of candidate models, the Fisher information of observed sequence probabilities lower-bounds the variance in model estimation from finite data. As sequence-length increases, the minimal variance scales as the square inverse of the length…