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MULTILINEAR TENSOR REGRESSION FOR LONGITUDINAL RELATIONAL DATA.

Peter D Hoff1

  • 1University of Washington.

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This study introduces a multilinear tensor regression model to analyze complex relational data, like social networks. The model captures dependencies between relations over time, revealing patterns such as reciprocity and transitivity in network data.

Keywords:
Array normalBayesian inferenceTucker productevent datainternational relationsnetworkvector autoregression

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Area of Science:

  • Statistics
  • Network Analysis
  • Data Science

Background:

  • Relational data, common in social networks, often exhibits dependencies between different pairs of relations.
  • Understanding these interdependencies is crucial for accurate modeling and analysis of complex systems.

Purpose of the Study:

  • To develop a novel regression model for estimating the effects of dependencies among relations in longitudinal and multivariate relational data.
  • To provide a framework for analyzing data representable as tensors, capturing dynamic network structures.

Main Methods:

  • Development of a general multilinear tensor regression model.
  • Application of a tensor autoregression model, a specialized form, for time-series relational data.
  • Utilizing separable (Kronecker-structured) regression parameters and covariance models.

Main Results:

  • The multilinear tensor regression model effectively estimates dependencies among relations in relational data.
  • Demonstrated ability to represent common network patterns like reciprocity and transitivity in longitudinal multivariate relational data.
  • The tensor autoregression model offers a parsimonious approach to modeling time-varying network relations.

Conclusions:

  • The proposed multilinear tensor regression framework is suitable for analyzing complex relational and network data with temporal dependencies.
  • The model provides insights into the structure and evolution of networks by capturing relational interdependencies.
  • This approach enhances the understanding of dynamic network phenomena like reciprocity and transitivity.