SLIP: Learning to Predict in Unknown Dynamical Systems with Long-Term Memory

• URL: http://arxiv.org/abs/2010.05899v1
• Date: Mon, 12 Oct 2020 17:50:21 GMT
• Title: SLIP: Learning to Predict in Unknown Dynamical Systems with Long-Term Memory
• Authors: Paria Rashidinejad, Jiantao Jiao, Stuart Russell
• Abstract summary: We present an efficient and practical (polynomial time) algorithm for online prediction in unknown and partially observed linear dynamical systems. Our algorithm competes with Kalman filter in hindsight with only logarithmic regret. Our theoretical and experimental results shed light on the conditions required for efficient probably approximately correct (PAC) learning of the Kalman filter from partially observed data.
• Score: 21.09861411069719
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present an efficient and practical (polynomial time) algorithm for online prediction in unknown and partially observed linear dynamical systems (LDS) under stochastic noise. When the system parameters are known, the optimal linear predictor is the Kalman filter. However, the performance of existing predictive models is poor in important classes of LDS that are only marginally stable and exhibit long-term forecast memory. We tackle this problem through bounding the generalized Kolmogorov width of the Kalman filter model by spectral methods and conducting tight convex relaxation. We provide a finite-sample analysis, showing that our algorithm competes with Kalman filter in hindsight with only logarithmic regret. Our regret analysis relies on Mendelson's small-ball method, providing sharp error bounds without concentration, boundedness, or exponential forgetting assumptions. We also give experimental results demonstrating that our algorithm outperforms state-of-the-art methods. Our theoretical and experimental results shed light on the conditions required for efficient probably approximately correct (PAC) learning of the Kalman filter from partially observed data.

Related papers

• System Identification for Continuous-time Linear Dynamical Systems [0.7510165488300368]
  Generalizing the learning of latent linear dynamical systems to continuous-time may extend the use of the hybrid Kalman filter. We apply the method by learning the parameters of a latent, multivariate Fokker-Planck SDE representing a toggle-switch genetic circuit.
  arXiv  Detail & Related papers  (2023-08-23T05:53:13Z)
• Low-rank extended Kalman filtering for online learning of neural networks from streaming data [71.97861600347959]
  We propose an efficient online approximate Bayesian inference algorithm for estimating the parameters of a nonlinear function from a potentially non-stationary data stream. The method is based on the extended Kalman filter (EKF), but uses a novel low-rank plus diagonal decomposition of the posterior matrix. In contrast to methods based on variational inference, our method is fully deterministic, and does not require step-size tuning.
  arXiv  Detail & Related papers  (2023-05-31T03:48:49Z)
• Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation [59.45669299295436]
  We propose a Monte Carlo PDE solver for training unsupervised neural solvers. We use the PDEs' probabilistic representation, which regards macroscopic phenomena as ensembles of random particles. Our experiments on convection-diffusion, Allen-Cahn, and Navier-Stokes equations demonstrate significant improvements in accuracy and efficiency.
  arXiv  Detail & Related papers  (2023-02-10T08:05:19Z)
• Deep Learning for the Benes Filter [91.3755431537592]
  We present a new numerical method based on the mesh-free neural network representation of the density of the solution of the Benes model. We discuss the role of nonlinearity in the filtering model equations for the choice of the domain of the neural network.
  arXiv  Detail & Related papers  (2022-03-09T14:08:38Z)
• On the Benefits of Large Learning Rates for Kernel Methods [110.03020563291788]
  We show that a phenomenon can be precisely characterized in the context of kernel methods. We consider the minimization of a quadratic objective in a separable Hilbert space, and show that with early stopping, the choice of learning rate influences the spectral decomposition of the obtained solution.
  arXiv  Detail & Related papers  (2022-02-28T13:01:04Z)
• Predicting Flat-Fading Channels via Meta-Learned Closed-Form Linear Filters and Equilibrium Propagation [38.42468500092177]
  Predicting fading channels is a classical problem with a vast array of applications. In practice, the Doppler spectrum is unknown, and the predictor has only access to a limited time series of estimated channels. This paper proposes to leverage meta-learning in order to mitigate the requirements in terms of training data for channel fading prediction.
  arXiv  Detail & Related papers  (2021-10-01T14:00:23Z)
• KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics [84.18625250574853]
  We present KalmanNet, a real-time state estimator that learns from data to carry out Kalman filtering under non-linear dynamics. We numerically demonstrate that KalmanNet overcomes nonlinearities and model mismatch, outperforming classic filtering methods.
  arXiv  Detail & Related papers  (2021-07-21T12:26:46Z)
• Deep learning: a statistical viewpoint [120.94133818355645]
  Deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-perfect solutions to non-optimal training problems. We conjecture that specific principles underlie these phenomena.
  arXiv  Detail & Related papers  (2021-03-16T16:26:36Z)
• Online Learning of the Kalman Filter with Logarithmic Regret [2.0305676256390934]
  We show that it is possible to achieve a regret of the order of $mathrmpolylog(N)$ with high probability, where $N$ is the number of observations collected. This is achieved using an online least-squares algorithm, which exploits the approximately linear relation between future observations and past observations.
  arXiv  Detail & Related papers  (2020-02-12T18:31:31Z)

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.