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原文連結
論文資訊
- 類型：已發表論文
- 日期：2023-01-03
摘要
Predictive equivalence in discrete 隨機 processes has been applied with great success to identify randomness and structure in 統計 physics and chaotic dynamical systems and to inferring hidden 馬可夫 models. We examine the conditions under which predictive states can be reliably reconstructed from time-series data, showing that convergence of predictive states can be achieved from empirical samples in the weak topology of measures. Moreover, predictive states may be represented in Hilbert spaces that replicate the weak topology. We 數學ly explain how these representations are particularly beneficial when reconstructing high-memory processes and connect them to reproducing kernel Hilbert spaces.
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