在重尾噪声下实现高鲁棒性系统辨识，突破传统高斯假设限制。
Boosting-Enabled Robust System Identification of Partially Observed LTI Systems Under Heavy-Tailed Noise
- 基于鲁棒统计的增强方法，适用于仅二阶矩存在的噪声。
- 样本复杂度接近子高斯噪声下的最优水平，且对失败概率呈对数依赖。
- 只需输入信号四阶矩有限，适合真实工业场景中的异常数据建模。
研究部分可观测线性时不变（LTI）系统的系统辨识问题。给定输入输出数据，在一般重尾噪声过程中提供非渐近参数识别保证。不同于以往假设高斯或次高斯噪声的工作，本文考虑仅需存在二阶矩的更广泛噪声分布。利用鲁棒统计工具，提出一种基于增强思想的新算法。尽管噪声假设更弱，所提算法仍达到几乎与次高斯噪声下相当的样本复杂度界，且其界对指定失败概率保持对数依赖。有趣的是，该界仅需激励输入过程具有有限四阶矩即可实现。
原文摘要 · Abstract (English)
We consider the problem of system identification of partially observed linear time-invariant (LTI) systems. Given input-output data, we provide non-asymptotic guarantees for identifying the system parameters under general heavy-tailed noise processes. Unlike previous works that assume Gaussian or sub-Gaussian noise, we consider significantly broader noise distributions that are required to admit only up to the second moment. For this setting, we leverage tools from robust statistics to propose a novel system identification algorithm that exploits the idea of boosting. Despite the much weaker noise assumptions, we show that our proposed algorithm achieves sample complexity bounds that nearly match those derived under sub-Gaussian noise. In particular, we establish that our bounds retain a logarithmic dependence on the prescribed failure probability. Interestingly, we show that such bounds can be achieved by requiring just a finite fourth moment on the excitatory input process.
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