Exact Recovery for System Identification with More Corrupt Data than Clean Data

• URL: http://arxiv.org/abs/2305.10506v3
• Date: Wed, 24 Apr 2024 18:45:27 GMT
• Title: Exact Recovery for System Identification with More Corrupt Data than Clean Data
• Authors: Baturalp Yalcin, Haixiang Zhang, Javad Lavaei, Murat Arcak,
• Abstract summary: This paper investigates the system identification problem for linear discrete-time systems under adversaries. We show that when the system is stable and attacks are injected periodically, the sample complexity for exact recovery of the system dynamics is linear. As a by-product, our estimators still learn the system correctly even when more than half of the data is compromised.
• Score: 17.310966086344777
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: This paper investigates the system identification problem for linear discrete-time systems under adversaries and analyzes two lasso-type estimators. We examine both asymptotic and non-asymptotic properties of these estimators in two separate scenarios, corresponding to deterministic and stochastic models for the attack times. Since the samples collected from the system are correlated, the existing results on lasso are not applicable. We prove that when the system is stable and attacks are injected periodically, the sample complexity for exact recovery of the system dynamics is linear in terms of the dimension of the states. When adversarial attacks occur at each time instance with probability p, the required sample complexity for exact recovery scales polynomially in the dimension of the states and the probability p. This result implies almost sure convergence to the true system dynamics under the asymptotic regime. As a by-product, our estimators still learn the system correctly even when more than half of the data is compromised. We highlight that the attack vectors are allowed to be correlated with each other in this work, whereas we make some assumptions about the times at which the attacks happen. This paper provides the first mathematical guarantee in the literature on learning from correlated data for dynamical systems in the case when there is less clean data than corrupt data.

Related papers

• Learning Controlled Stochastic Differential Equations [61.82896036131116]
  This work proposes a novel method for estimating both drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled differential equations with non-uniform diffusion. We provide strong theoretical guarantees, including finite-sample bounds for (L2), (Linfty), and risk metrics, with learning rates adaptive to coefficients' regularity. Our method is available as an open-source Python library.
  arXiv  Detail & Related papers  (2024-11-04T11:09:58Z)
• Exact Recovery Guarantees for Parameterized Nonlinear System Identification Problem under Sparse Disturbances or Semi-Oblivious Attacks [16.705631360131886]
  We study the problem of learning a nonlinear dynamical system by parameterizing its dynamics using basis functions. We show that finite-time exact recovery is achieved with high probability, even when $p$ approaches 1.
  arXiv  Detail & Related papers  (2024-08-30T22:12:57Z)
• A least-square method for non-asymptotic identification in linear switching control [17.938732931331064]
  It is known that the underlying partially-observed linear dynamical system lies within a finite collection of known candidate models. We characterize the finite-time sample complexity of this problem by leveraging recent advances in the non-asymptotic analysis of linear least-square methods. We propose a data-driven switching strategy that identifies the unknown parameters of the underlying system.
  arXiv  Detail & Related papers  (2024-04-11T20:55:38Z)
• Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations [114.17826109037048]
  Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning. theoretical aspects, e.g., identifiability and properties of statistical estimation are still obscure. This paper derives a sufficient condition for the identifiability of homogeneous linear ODE systems from a sequence of equally-spaced error-free observations sampled from a single trajectory.
  arXiv  Detail & Related papers  (2022-10-12T06:46:38Z)
• Finite Sample Identification of Bilinear Dynamical Systems [29.973598501311233]
  We show how to estimate the unknown bilinear system up to a desired accuracy with high probability. Our sample complexity and statistical error rates are optimal in terms of the trajectory length, the dimensionality of the system and the input size.
  arXiv  Detail & Related papers  (2022-08-29T22:34:22Z)
• Causality-Based Multivariate Time Series Anomaly Detection [63.799474860969156]
  We formulate the anomaly detection problem from a causal perspective and view anomalies as instances that do not follow the regular causal mechanism to generate the multivariate data. We then propose a causality-based anomaly detection approach, which first learns the causal structure from data and then infers whether an instance is an anomaly relative to the local causal mechanism. We evaluate our approach with both simulated and public datasets as well as a case study on real-world AIOps applications.
  arXiv  Detail & Related papers  (2022-06-30T06:00:13Z)
• Identifying the Dynamics of a System by Leveraging Data from Similar Systems [1.9813182042770605]
  We study the problem of identifying the dynamics of a linear system when one has access to samples generated by a similar system. We use a weighted least squares approach and provide finite sample performance guarantees on the quality of the identified dynamics.
  arXiv  Detail & Related papers  (2022-04-11T23:47:06Z)
• A Priori Denoising Strategies for Sparse Identification of Nonlinear Dynamical Systems: A Comparative Study [68.8204255655161]
  We investigate and compare the performance of several local and global smoothing techniques to a priori denoise the state measurements. We show that, in general, global methods, which use the entire measurement data set, outperform local methods, which employ a neighboring data subset around a local point.
  arXiv  Detail & Related papers  (2022-01-29T23:31:25Z)
• Causal Discovery from Sparse Time-Series Data Using Echo State Network [0.0]
  Causal discovery between collections of time-series data can help diagnose causes of symptoms and hopefully prevent faults before they occur. We propose a new system comprised of two parts, the first part fills missing data with a Gaussian Process Regression, and the second part leverages an Echo State Network. We report on their corresponding Matthews Correlation Coefficient(MCC) and Receiver Operating Characteristic curves (ROC) and show that the proposed system outperforms existing algorithms.
  arXiv  Detail & Related papers  (2022-01-09T05:55:47Z)
• Consistency of mechanistic causal discovery in continuous-time using Neural ODEs [85.7910042199734]
  We consider causal discovery in continuous-time for the study of dynamical systems. We propose a causal discovery algorithm based on penalized Neural ODEs.
  arXiv  Detail & Related papers  (2021-05-06T08:48:02Z)
• Active Learning for Nonlinear System Identification with Guarantees [102.43355665393067]
  We study a class of nonlinear dynamical systems whose state transitions depend linearly on a known feature embedding of state-action pairs. We propose an active learning approach that achieves this by repeating three steps: trajectory planning, trajectory tracking, and re-estimation of the system from all available data. We show that our method estimates nonlinear dynamical systems at a parametric rate, similar to the statistical rate of standard linear regression.
  arXiv  Detail & Related papers  (2020-06-18T04:54:11Z)
• Data-Driven Verification under Signal Temporal Logic Constraints [0.0]
  We consider systems under uncertainty whose dynamics are partially unknown. Our aim is to study satisfaction of temporal logic properties by trajectories of such systems. We employ Bayesian inference techniques to associate a confidence value to the satisfaction of the property.
  arXiv  Detail & Related papers  (2020-05-08T08:32:30Z)

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.