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We developed a convex framework for learning Granger causality networks from categorical time series data using the mixture transition distribution (MTD) model. This approach overcomes traditional MTD limitations, enabling analysis of complex, high-dimensional datasets.

Keywords:
68Q2568R1068U05Granger causalitycategorical dataconvexstructured sparsitytime series

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Area of Science:

  • Statistics
  • Machine Learning
  • Time Series Analysis

Background:

  • Mixture Transition Distribution (MTD) models are used for categorical time series but suffer from non-convexity and local optima.
  • Existing methods struggle with high-dimensional data and identifiability issues.

Purpose of the Study:

  • To present a novel convex formulation for MTD to enable robust Granger causality network inference.
  • To compare the proposed convex MTD with a multi-output logistic autoregressive model (mLTD) for categorical time series.
  • To establish theoretical guarantees for the convex MTD in high-dimensional settings.

Main Methods:

  • Recasting MTD inference as a convex optimization problem.
  • Developing efficient optimization algorithms for the convex MTD formulation.
  • Formulating and comparing a multi-output logistic autoregressive model (mLTD) as a baseline.
  • Establishing identifiability conditions and consistency for MTD and mLTD.

Main Results:

  • The convex MTD formulation successfully addresses traditional limitations, allowing application to high-dimensional data.
  • Comparative experiments on simulated and real data demonstrate the efficacy of the convex MTD.
  • Identifiability conditions for MTD and mLTD were established, and consistency of convex MTD in high dimensions was proven.

Conclusions:

  • The proposed convex MTD framework offers a significant advancement for Granger causality network inference in multivariate categorical time series.
  • This work facilitates modern, regularized inference techniques for MTD models.
  • The study provides a valuable comparison of network inference methods for categorical time series data.