Graph Kalman Filters

• URL: http://arxiv.org/abs/2303.12021v2
• Date: Tue, 20 Jun 2023 14:35:14 GMT
• Title: Graph Kalman Filters
• Authors: Cesare Alippi and Daniele Zambon
• Abstract summary: This paper generalizes Kalman filters to discrete-time settings where inputs, states, and outputs are represented as attributed graphs. Within the proposed theoretical framework, the unknown state-transition and the readout functions are learned end-to-end along with the downstream prediction task.
• Score: 19.407150082045636
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The well-known Kalman filters model dynamical systems by relying on state-space representations with the next state updated, and its uncertainty controlled, by fresh information associated with newly observed system outputs. This paper generalizes, for the first time in the literature, Kalman and extended Kalman filters to discrete-time settings where inputs, states, and outputs are represented as attributed graphs whose topology and attributes can change with time. The setup allows us to adapt the framework to cases where the output is a vector or a scalar too (node/graph level tasks). Within the proposed theoretical framework, the unknown state-transition and the readout functions are learned end-to-end along with the downstream prediction task.

Related papers

• Long-time accuracy of ensemble Kalman filters for chaotic and machine-learned dynamical systems [2.5245286741414663]
  This paper establishes long-time accuracy of ensemble Kalman filters. Our theory covers a wide class of partially-observed chaotic dynamical systems. We prove long-time accuracy of ensemble Kalman filters with surrogate dynamics.
  arXiv  Detail & Related papers  (2024-12-18T20:35:21Z)
• Uncertainty Representations in State-Space Layers for Deep Reinforcement Learning under Partial Observability [59.758009422067]
  We propose a standalone Kalman filter layer that performs closed-form Gaussian inference in linear state-space models. Similar to efficient linear recurrent layers, the Kalman filter layer processes sequential data using a parallel scan. Experiments show that Kalman filter layers excel in problems where uncertainty reasoning is key for decision-making, outperforming other stateful models.
  arXiv  Detail & Related papers  (2024-09-25T11:22:29Z)
• Online Graph Filtering Over Expanding Graphs [14.594691605523005]
  We propose an online graph filtering framework by relying on online learning principles. We design filters for scenarios where the topology is both known and unknown, including a learner adaptive to such evolution. We conduct a regret analysis to highlight the role played by the different components such as the online algorithm, the filter order, and the growing graph model.
  arXiv  Detail & Related papers  (2024-09-11T11:50:16Z)
• Port-Hamiltonian Architectural Bias for Long-Range Propagation in Deep Graph Networks [55.227976642410766]
  dynamics of information diffusion within graphs is a critical open issue that heavily influences graph representation learning. Motivated by this, we introduce (port-)Hamiltonian Deep Graph Networks. We reconcile under a single theoretical and practical framework both non-dissipative long-range propagation and non-conservative behaviors.
  arXiv  Detail & Related papers  (2024-05-27T13:36:50Z)
• Deep Manifold Graph Auto-Encoder for Attributed Graph Embedding [51.75091298017941]
  This paper proposes a novel Deep Manifold (Variational) Graph Auto-Encoder (DMVGAE/DMGAE) for attributed graph data. The proposed method surpasses state-of-the-art baseline algorithms by a significant margin on different downstream tasks across popular datasets.
  arXiv  Detail & Related papers  (2024-01-12T17:57:07Z)
• Deep Gaussian Markov Random Fields for Graph-Structured Dynamical Systems [0.0]
  We develop a principled approach to state estimation and learning in graph-structured state-space models. We reformulate graph-structured state-space models as Deep GMRFs defined by simple spatial and temporal graph layers.
  arXiv  Detail & Related papers  (2023-06-14T11:37:12Z)
• Asynchronously Trained Distributed Topographic Maps [0.0]
  We present an algorithm that uses $N$ autonomous units to generate a feature map by distributed training. Unit autonomy is achieved by sparse interaction in time & space through the combination of a distributed search, and a cascade-driven weight updating scheme.
  arXiv  Detail & Related papers  (2023-01-20T01:15:56Z)
• Space-Time Graph Neural Networks [104.55175325870195]
  We introduce space-time graph neural network (ST-GNN) to jointly process the underlying space-time topology of time-varying network data. Our analysis shows that small variations in the network topology and time evolution of a system does not significantly affect the performance of ST-GNNs.
  arXiv  Detail & Related papers  (2021-10-06T16:08:44Z)
• 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)
• Stability to Deformations of Manifold Filters and Manifold Neural Networks [89.53585099149973]
  The paper defines and studies manifold (M) convolutional filters and neural networks (NNs) The main technical contribution of the paper is to analyze the stability of manifold filters and MNNs to smooth deformations of the manifold.
  arXiv  Detail & Related papers  (2021-06-07T15:41:03Z)
• 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.