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When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
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Partial Information Rate Decomposition.

Luca Faes1,2, Laura Sparacino1, Gorana Mijatovic2

  • 1University of Palermo, Department of Engineering, Palermo, Italy.

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This summary is machine-generated.

This study introduces partial information rate decomposition (PIRD) to accurately analyze complex interactions in dynamic networks. PIRD offers a more complete depiction of high-order effects in time series data.

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Area of Science:

  • Information theory
  • Network science
  • Time series analysis

Background:

  • Partial information decomposition (PID) is used to study high-order interactions in networks.
  • Existing PID methods struggle with dynamic networks and time series data, leading to incomplete analyses.
  • There is a need for a method that accurately captures temporal statistical structures in dynamic systems.

Purpose of the Study:

  • To introduce a novel framework, partial information rate decomposition (PIRD), for analyzing dynamic networks.
  • To overcome limitations of traditional PID in depicting high-order effects in time series.
  • To provide a principled method for quantifying dynamic information sharing in complex systems.

Main Methods:

  • Formalized PIRD using lattice theory to decompose dynamically shared information between source and target processes.
  • Implemented PIRD for Gaussian processes via spectral expansion of information rates.
  • Validated the PIRD framework in simulated network systems.

Main Results:

  • PIRD provides a more complete and less misleading depiction of high-order effects in dynamic networks compared to traditional PID.
  • The spectral expansion method effectively implements PIRD for Gaussian processes.
  • The framework successfully analyzed time series data from large-scale climate oscillations.

Conclusions:

  • PIRD is a powerful new framework for understanding complex information flow in dynamic systems.
  • The method accurately captures temporal statistical structures, improving analysis of multivariate time series.
  • PIRD has practical applications in fields like climate science and network analysis.