Outlier-Robust Linear System Identification Under Heavy-Tailed Noise
How to estimate the state transition matrix of a linear time-invariant system from noisy trajectories when the process noise has heavy tails or adversarial outliers, assuming only a finite fourth moment. The learner sees why standard least-squares estimators fail under heavy tails, how forming many weakly-concentrated estimators and boosting them with robust-statistics tools recovers nearly the sub-Gaussian sample complexity, and how the noise kurtosis sets the number of trajectories required.
2501.00421
This paper gives the first finite-sample (PAC) guarantees for estimating the unknown state transition matrix A of a linear time-invariant system x_{t+1}=A x_t + w_t from multiple independent trajecto…