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October 3, 2025Open Access

Error-In-Variables Methods for Efficient System Identification with Finite-Sample Guarantees

Key Points

The proposed algorithms achieve superior sample complexities compared to traditional methods, facilitating better learning of linear dynamical systems.
In the context of noisy observations, the methods significantly reduce bias in parameter estimates, enhancing model accuracy and reliability.
The instrumental variable and bias compensation methods are effectively adapted for error-in-variables models, leading to refined non-asymptotic analyses.
The findings indicate that these algorithms achieve the optimal sample complexity known for learning systems without observation noise, addressing common challenges.

Abstract

This paper addresses the problem of learning linear dynamical systems from noisy observations. In this setting, existing algorithms either yield biased parameter estimates or have large sample complexities. We resolve these issues by adapting the instrumental variable method and the bias compensation method, originally proposed for error-in-variables models, to our setting. We provide refined non-asymptotic analysis for both methods. Under mild conditions, our algorithms achieve superior sample complexities that match the best-known sample complexity for learning a fully observable system without observation noise.

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