Cluster Prediction for Opinion Dynamics From Partial Observations

Ze-hong, Zhang; Lu, Fei

doi:10.1109/tsipn.2020.3046992

Cited by 2 publications

(2 citation statements)

References 36 publications

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“…A desirable extension is to the case of partial observations of a subset of particles or macroscopic observations of the population density, which is a practical concern when the system is large with millions of particles in high dimension. Since it is an ill-posed inverse problem to recover the missing trajectories of unobserved particles [54], a new formulation based on the corresponding mean field equations [27,28,43] is under investigation.…”

Section: (M)mentioning

confidence: 99%

Learning Interaction Kernels in Stochastic Systems of Interacting Particles from Multiple Trajectories

Maggioni

Tang

2021

Found Comput Math

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We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel, which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of the positions of the particles, in either continuous or discrete time, along multiple independent trajectories. We introduce a nonparametric inference approach to this inverse problem, based on a regularized maximum likelihood estimator constrained to suitable hypothesis spaces adaptive to data. We show that a coercivity condition enables us to control the condition number of this problem and prove the consistency of our estimator, and that in fact it converges at a near-optimal learning rate, equal to the min–max rate of one-dimensional nonparametric regression. In particular, this rate is independent of the dimension of the state space, which is typically very high. We also analyze the discretization errors in the case of discrete-time observations, showing that it is of order 1/2 in terms of the time spacings between observations. This term, when large, dominates the sampling error and the approximation error, preventing convergence of the estimator. Finally, we exhibit an efficient parallel algorithm to construct the estimator from data, and we demonstrate the effectiveness of our algorithm with numerical tests on prototype systems including stochastic opinion dynamics and a Lennard-Jones model.

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Section: (M)mentioning

confidence: 99%

Learning Interaction Kernels in Stochastic Systems of Interacting Particles from Multiple Trajectories

Maggioni

Tang

2021

Found Comput Math

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“…Recently, many researchers have explored dynamic calibration methods [ 38 , 39 , 40 , 41 , 42 , 43 , 44 ]. However, few have aimed at the field of opinion dynamics [ 45 ]. Thus, combining the advantages of the theoretical model and data-driven method to predict public opinion is a direction for future opinion dynamics research [ 46 ], and one way to achieve this is to introduce a data assimilation method.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Parameter Calibration Framework for Opinion Dynamics Models

Zhu

Yao

Tang

et al. 2022

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In the past decade, various opinion dynamics models have been built to depict the evolutionary mechanism of opinions and use them to predict trends in public opinion. However, model-based predictions alone cannot eliminate the deviation caused by unforeseeable external factors, nor can they reduce the impact of the accumulated random error over time. To solve this problem, we propose a dynamic framework that combines a genetic algorithm and a particle filter algorithm to dynamically calibrate the parameters of the opinion dynamics model. First, we design a fitness function in accordance with public opinion and search for a set of model parameters that best match the initial observation. Second, with successive observations, we tracked the state of the opinion dynamic system by the average distribution of particles. We tested the framework by using several typical opinion dynamics models. The results demonstrate that the proposed method can dynamically calibrate the parameters of the opinion dynamics model to predict public opinion more accurately.

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Cluster Prediction for Opinion Dynamics From Partial Observations

Cited by 2 publications

References 36 publications

Learning Interaction Kernels in Stochastic Systems of Interacting Particles from Multiple Trajectories

Learning Interaction Kernels in Stochastic Systems of Interacting Particles from Multiple Trajectories

Dynamic Parameter Calibration Framework for Opinion Dynamics Models

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