Boosting-Enabled Robust System Identification of Partially Observed LTI Systems Under Heavy-Tailed Noise

• URL: http://arxiv.org/abs/2504.18444v1
• Date: Fri, 25 Apr 2025 15:57:13 GMT
• Title: Boosting-Enabled Robust System Identification of Partially Observed LTI Systems Under Heavy-Tailed Noise
• Authors: Vinay Kanakeri, Aritra Mitra,
• Abstract summary: We consider the problem of system identification of partially observed linear time-invariant (LTI) systems.<n>We provide non-asymptotic guarantees for identifying the system parameters under general heavy-tailed noise processes.<n>We show that our proposed algorithm achieves sample complexity bounds that nearly match those derived under sub-Gaussian noise.
• Score: 2.07180164747172
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Efficient learning and optimizing non-Gaussian correlated noise in digitally controlled qubit systems [0.6138671548064356]
  We show how to achieve higher-order spectral estimation for noise-optimized circuit design.<n>Remarkably, we find that the digitally driven qubit dynamics can be solely determined by the complexity of the applied control.
  arXiv  Detail & Related papers  (2025-02-08T02:09:40Z)
• Outlier-Robust Linear System Identification Under Heavy-tailed Noise [2.07180164747172]
  We consider the problem of estimating the state transition matrix of a linear time-invariant (LTI) system.<n>We develop a novel robust system identification algorithm that relies on constructing multiple weakly-concentrated estimators.<n>We show that our algorithm and analysis technique can be easily extended to account for scenarios where an adversary can arbitrarily corrupt a small fraction of the collected trajectory data.
  arXiv  Detail & Related papers  (2024-12-31T12:53:02Z)
• Robust Control for Dynamical Systems With Non-Gaussian Noise via Formal Abstractions [59.605246463200736]
  We present a novel controller synthesis method that does not rely on any explicit representation of the noise distributions. First, we abstract the continuous control system into a finite-state model that captures noise by probabilistic transitions between discrete states. We use state-of-the-art verification techniques to provide guarantees on the interval Markov decision process and compute a controller for which these guarantees carry over to the original control system.
  arXiv  Detail & Related papers  (2023-01-04T10:40:30Z)
• The Optimal Noise in Noise-Contrastive Learning Is Not What You Think [80.07065346699005]
  We show that deviating from this assumption can actually lead to better statistical estimators. In particular, the optimal noise distribution is different from the data's and even from a different family.
  arXiv  Detail & Related papers  (2022-03-02T13:59:20Z)
• Sampling-Based Robust Control of Autonomous Systems with Non-Gaussian Noise [59.47042225257565]
  We present a novel planning method that does not rely on any explicit representation of the noise distributions. First, we abstract the continuous system into a discrete-state model that captures noise by probabilistic transitions between states. We capture these bounds in the transition probability intervals of a so-called interval Markov decision process (iMDP)
  arXiv  Detail & Related papers  (2021-10-25T06:18:55Z)
• Analyzing and Improving the Optimization Landscape of Noise-Contrastive Estimation [50.85788484752612]
  Noise-contrastive estimation (NCE) is a statistically consistent method for learning unnormalized probabilistic models. It has been empirically observed that the choice of the noise distribution is crucial for NCE's performance. In this work, we formally pinpoint reasons for NCE's poor performance when an inappropriate noise distribution is used.
  arXiv  Detail & Related papers  (2021-10-21T16:57:45Z)
• Learning Numeric Optimal Differentially Private Truncated Additive Mechanisms [5.079561894598125]
  We introduce a tool to learn truncated noise for additive mechanisms with strong utility bounds. We show that it is sufficient to consider symmetric and thatnew, for from the mean monotonically falling noise. For sensitivity bounded mechanisms, we show that it is sufficient to consider symmetric and thatnew, for from the mean monotonically falling noise.
  arXiv  Detail & Related papers  (2021-07-27T17:22:57Z)
• Learning based signal detection for MIMO systems with unknown noise statistics [84.02122699723536]
  This paper aims to devise a generalized maximum likelihood (ML) estimator to robustly detect signals with unknown noise statistics. In practice, there is little or even no statistical knowledge on the system noise, which in many cases is non-Gaussian, impulsive and not analyzable. Our framework is driven by an unsupervised learning approach, where only the noise samples are required.
  arXiv  Detail & Related papers  (2021-01-21T04:48:15Z)
• Contextual Linear Bandits under Noisy Features: Towards Bayesian Oracles [65.9694455739978]
  We study contextual linear bandit problems under feature uncertainty, where the features are noisy and have missing entries. Our analysis reveals that the optimal hypothesis can significantly deviate from the underlying realizability function, depending on the noise characteristics. This implies that classical approaches cannot guarantee a non-trivial regret bound.
  arXiv  Detail & Related papers  (2017-03-03T21:39:56Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.