提出递归状态推断算法，高效恢复慢特征表示。
Recursive State Inference for Linear PASFA
- 基于ARMA过程构建递归估计框架，实现最优均方误差推断。
- 在合成数据集上验证算法正确性，状态恢复精度高。
- 适合需要稳定慢特征提取的信号分析与分类任务。
慢特征分析（SFA）作为一种学习分类与信号分析中缓慢变化特征的方法，近年来受到广泛关注。最近的概率扩展方法在分类任务中学习到有效表征。值得注意的是，概率自适应慢特征分析（PASFA）将慢特征建模为自回归移动平均（ARMA）过程中的状态，并从观测数据中估计模型。然而，如何高效地从观测数据和模型中推断出状态（即慢特征）仍存在挑战。本文提出了线性PASFA的递归扩展算法，该算法针对遵循ARMA过程的状态，在给定观测数据和模型的情况下，执行最小均方误差（MMSE）状态估计。尽管现有方法通过将ARMA过程转换为状态空间模型并使用卡尔曼滤波器来解决此问题，但原始状态（或慢特征）难以准确恢复。所提方法在合成数据集上进行了评估，结果证明其正确性。
原文摘要 · Abstract (English)
Slow feature analysis (SFA), as a method for learning slowly varying features in classification and signal analysis, has attracted increasing attention in recent years. Recent probabilistic extensions to SFA learn effective representations for classification tasks. Notably, the Probabilistic Adaptive Slow Feature Analysis models the slow features as states in an ARMA process and estimate the model from the observations. However, there is a need to develop efficient methods to infer the states (slow features) from the observations and the model. In this paper, a recursive extension to the linear PASFA has been proposed. The proposed algorithm performs MMSE estimation of states evolving according to an ARMA process, given the observations and the model. Although current methods tackle this problem using Kalman filters after transforming the ARMA process into a state space model, the original states (or slow features) that form useful representations cannot be easily recovered. The proposed technique is evaluated on a synthetic dataset to demonstrate its correctness.
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