Fisher information and shape-morphing modes for solving the Fokker–Planck equation in higher dimensions

Anderson, William; Farazmand, Mohammad

doi:10.1016/j.amc.2023.128489

Cited by 3 publications

(2 citation statements)

References 40 publications

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“…In the simulated real-world scenario, each vehicle client already independently possesses a portion of the data from the aforementioned four datasets, thus eliminating the need to receive distributed training data. Considering a privacy budget ε 2 [6,8,10,14,16], we evaluated a series of different values. Within this range, a lower privacy budget ε provides stronger privacy protection for the vehicles.…”

Section: Privacy Budgetmentioning

confidence: 99%

“…By pruning unimportant parameters, FFIDS effectively reduces the privacy budget consumption during iterative training while ensuring model accuracy and saving communication costs. Specifically, FFIDS leverages the Fisher Information Matrix [ 14 , 15 ] to evaluate the importance of client model parameters. Parameters with near-zero values that contribute minimally to parameter aggregation on the central server may undergo significant changes under DP noise.…”

Section: Introductionmentioning

confidence: 99%

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Sparsified federated learning with differential privacy for intrusion detection in VANETs based on Fisher Information Matrix

Chen,

Zhao

2024

PLoS ONE

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With the continuous development of vehicular ad hoc networks (VANET) security, using federated learning (FL) to deploy intrusion detection models in VANET has attracted considerable attention. Compared to conventional centralized learning, FL retains local training private data, thus protecting privacy. However, sensitive information about the training data can still be inferred from the shared model parameters in FL. Differential privacy (DP) is sophisticated technique to mitigate such attacks. A key challenge of implementing DP in FL is that non-selectively adding DP noise can adversely affect model accuracy, while having many perturbed parameters also increases privacy budget consumption and communication costs for detection models. To address this challenge, we propose FFIDS, a FL algorithm integrating model parameter pruning with differential privacy. It employs a parameter pruning technique based on the Fisher Information Matrix to reduce the privacy budget consumption per iteration while ensuring no accuracy loss. Specifically, FFIDS evaluates parameter importance and prunes unimportant parameters to generate compact sub-models, while recording the positions of parameters in each sub-model. This not only reduces model size to lower communication costs, but also maintains accuracy stability. DP noise is then added to the sub-models. By not perturbing unimportant parameters, more budget can be reserved to retain important parameters for more iterations. Finally, the server can promptly recover the sub-models using the parameter position information and complete aggregation. Extensive experiments on two public datasets and two F2MD simulation datasets have validated the utility and superior performance of the FFIDS algorithm.

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Section: Privacy Budgetmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sparsified federated learning with differential privacy for intrusion detection in VANETs based on Fisher Information Matrix

Chen,

Zhao

2024

PLoS ONE

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Enforcing conserved quantities in Galerkin truncation and finite volume discretization

Hilliard,

Farazmand

2024

Nonlinear Dyn

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Efficient, multimodal, and derivative-free bayesian inference with Fisher–Rao gradient flows

Chen,

Zhengyu Huang,

Huang

et al. 2024

Inverse Problems

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In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and engineering applications. The computational challenges we address with the proposed methodology are: (i) the need for repeated evaluations of expensive forward models; (ii) the potential existence of multiple modes; and (iii) the fact that gradient of, or adjoint solver for, the forward model might not be feasible.While existing Bayesian inference methods meet some of these challenges individually, we propose a framework that tackles all three systematically. Our approach builds upon the Fisher-Rao gradient flow in probability space, yielding a dynamical system for probability densities that converges towards the target distribution at a uniform exponential rate. This rapid convergence is advantageous for the computational burden outlined in (i). We apply Gaussian mixture approximations with operator splitting techniques to simulate the flow numerically; the resulting approximation can capture multiple modes thus addressing (ii). Furthermore, we employ the Kalman methodology to facilitate a derivative-free update of these Gaussian components and their respective weights, addressing the issue in (iii).The proposed methodology results in an efficient derivative-free posterior approximation method, flexible enough to handle multi-modal distributions: Gaussian Mixture Kalman Inversion (GMKI). The effectiveness of GMKI is demonstrated both theoretically and numerically in several experiments with multimodal target distributions, including proof-of-concept and two-dimensional examples, as well as a large-scale application: recovering the Navier-Stokes initial condition from solution data at positive times.

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Fisher information and shape-morphing modes for solving the Fokker–Planck equation in higher dimensions

Cited by 3 publications

References 40 publications

Sparsified federated learning with differential privacy for intrusion detection in VANETs based on Fisher Information Matrix

Sparsified federated learning with differential privacy for intrusion detection in VANETs based on Fisher Information Matrix

Enforcing conserved quantities in Galerkin truncation and finite volume discretization

Efficient, multimodal, and derivative-free bayesian inference with Fisher–Rao gradient flows

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