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Knowledge Propagation over Conditional Independence Graphs

Urszula Chajewska, Harsh Shrivastava

TL;DR

This work proposes algorithms for performing knowledge propagation over the conditional Independence graphs and demonstrates that their techniques improve upon the state-of-the-art on the publicly available Cora and PubMed datasets.

Abstract

Conditional Independence (CI) graph is a special type of a Probabilistic Graphical Model (PGM) where the feature connections are modeled using an undirected graph and the edge weights show the partial correlation strength between the features. Since the CI graphs capture direct dependence between features, they have been garnering increasing interest within the research community for gaining insights into the systems from various domains, in particular discovering the domain topology. In this work, we propose algorithms for performing knowledge propagation over the CI graphs. Our experiments demonstrate that our techniques improve upon the state-of-the-art on the publicly available Cora and PubMed datasets.

Knowledge Propagation over Conditional Independence Graphs

TL;DR

This work proposes algorithms for performing knowledge propagation over the conditional Independence graphs and demonstrates that their techniques improve upon the state-of-the-art on the publicly available Cora and PubMed datasets.

Abstract

Conditional Independence (CI) graph is a special type of a Probabilistic Graphical Model (PGM) where the feature connections are modeled using an undirected graph and the edge weights show the partial correlation strength between the features. Since the CI graphs capture direct dependence between features, they have been garnering increasing interest within the research community for gaining insights into the systems from various domains, in particular discovering the domain topology. In this work, we propose algorithms for performing knowledge propagation over the CI graphs. Our experiments demonstrate that our techniques improve upon the state-of-the-art on the publicly available Cora and PubMed datasets.
Paper Structure (16 sections, 11 equations, 4 figures, 1 table, 2 algorithms)

This paper contains 16 sections, 11 equations, 4 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background and Related work
  3. Obtaining Conditional Independence Graphs
  4. Knowledge Propagation in Graphs
  5. Preprocessing the data
  6. Knowledge Propagation over CI graphs
  7. Transition probability matrix
  8. Iterative approach
  9. Analytical solution
  10. Deep learning approach
  11. Experiments
  12. Datasets
  13. Algorithms used in experiments
  14. Prediction accuracy
  15. Additional experiments
  16. ...and 1 more sections

Figures (4)

  • Figure 1: Graph Recovery approaches. Methods used to recover Conditional Independence graphs, borrowed from shrivastava2023methods. Please refer to this survey for details. The algorithms (leaf nodes) listed here are representative of the sub-category and the list is not exhaustive.
  • Figure 2: iterative-posneg on CORA: The graph shows the accuracy on the Cora validation dataset as a function of the number of missing attributes. The range varies from 1 node with a missing attribute to 225 nodes (75% of all nodes). The method used is the iterative solution consisting of both positive and negative transition matrices with KL-divergence as the regularization mechanism. Results are averaged over 50 runs and the mean accuracy is reported.
  • Figure 3: iterative-pos on CORA with different regularization options: We restrict the associated CI graph recovered for the CORA data to only the positive partial correlations. The plot shows the accuracy on the Cora validation dataset as a function of the number of missing attributes ranging from 1 node with a missing attribute to 150 nodes (50% of all nodes). The three curves show the results of applying three regularization options: KL-divergence, Wasserstein's distance and no regularization mechanism. Results are averaged over 50 runs and the mean accuracy is reported.
  • Figure 4: iterative-pos on CORA with different confidence bands: The accuracy is calculated on the Cora validation dataset as a function of the number of missing attributes, ranging from 1 node with a missing attribute to 225 nodes (75% of all nodes). The method used is the iterative solution with positive transition matrix and KL regularization mechanism. Results averaged over 50 runs.