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The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
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An Experimental Platform to Study the Closed-loop Performance of Brain-machine Interfaces
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Block models and personalized PageRank.

Isabel M Kloumann1, Johan Ugander2, Jon Kleinberg3

  • 1Center for Applied Mathematics, Cornell University, Ithaca, NY 14853.

Proceedings of the National Academy of Sciences of the United States of America
|December 22, 2016
PubMed
Summary
This summary is machine-generated.

We found that personalized PageRank, a common node ranking method, is theoretically optimal for community detection in stochastic block models. This provides a formal basis for its effectiveness in seed set expansion and network analysis.

Keywords:
PageRankseed set expansionstochastic block models

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Area of Science:

  • Network analysis
  • Machine learning
  • Graph theory

Background:

  • Node importance ranking is crucial in network analysis.
  • Seed set expansion aims to identify community members from a known subset.
  • Existing methods like personalized PageRank lack a direct theoretical link to the seed set objective.

Purpose of the Study:

  • Develop a principled framework for evaluating node ranking methods.
  • Analyze seed set expansion within the stochastic block model.
  • Provide a formal motivation for the success of personalized PageRank.

Main Methods:

  • Studied seed set expansion applied to the stochastic block model.
  • Derived the optimal gradient for separating landing probabilities in stochastic block models.
  • Analyzed the asymptotic equivalence of the derived gradient to personalized PageRank.

Main Results:

  • The optimal gradient is asymptotically equivalent to personalized PageRank under specific parameter choices.
  • This equivalence formally motivates the use of personalized PageRank for seed set expansion.
  • Advanced methods incorporating higher moments of landing probabilities showed improved performance.

Conclusions:

  • Personalized PageRank has a strong theoretical foundation for node ranking and community detection.
  • The derived framework provides a basis for developing more advanced and effective ranking techniques.
  • New methods demonstrate competitive performance against established techniques like belief propagation.