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This study introduces an expectation maximization (EM) algorithm to infer stochastic dynamics from incomplete time-series data. The method effectively restores missing data points and infers network models, even with up to 70% data loss.

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Area of Science:

  • Computational neuroscience
  • Statistical modeling
  • Data analysis

Background:

  • Inferring dynamics from time-series data is crucial but challenging with incomplete datasets.
  • Stochastic dynamics are particularly difficult to model when data points are missing.

Purpose of the Study:

  • To develop a robust method for inferring stochastic dynamics from incomplete time-series data.
  • To accurately restore missing data points and infer underlying network models.

Main Methods:

  • An expectation maximization (EM) algorithm was developed, alternating between data restoration (E-step) and model inference (M-step).
  • A novel stopping criterion based on equal consistency between observed and missing data was implemented.
  • The method was validated using synthetic data from a kinetic Ising model and real neuronal activity data.

Main Results:

  • The EM algorithm successfully restored missing data points and inferred network models from synthetic data.
  • The proposed stopping criterion prevented overfitting and ensured accurate model inference.
  • The method accurately reproduced collective properties of neuronal activity, including correlations and firing statistics, even with 70% missing data.

Conclusions:

  • The developed EM algorithm with a novel stopping criterion is effective for inferring stochastic dynamics from incomplete time-series data.
  • This approach significantly advances the analysis of time-series data in neuroscience and other fields with missing information.