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A Rigorous Information-Theoretic Definition of Redundancy and Relevancy in Feature Selection Based on (Partial) Information Decomposition

arXiv 2105.04187 ↗First posted 10 May 2021cs.IT cs.LG math.ITcited by 25

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Abstract (arXiv)

Selecting a minimal feature set that is maximally informative about a target variable is a central task in machine learning and statistics. Information theory provides a powerful framework for formulating feature selection algorithms -- yet, a rigorous, information-theoretic definition of feature relevancy, which accounts for feature interactions such as redundant and synergistic contributions, is still missing. We argue that this lack is inherent to classical information theory which does not provide measures to decompose the information a set of variables provides about a target into unique, redundant, and synergistic contributions. Such a decomposition has been introduced only recently by the partial information decomposition (PID) framework. Using PID, we clarify why feature selection is a conceptually difficult problem when approached using information theory and provide a novel definition of feature relevancy and redundancy in PID terms. From this definition, we show that the conditional mutual information (CMI) maximizes relevancy while minimizing redundancy and propose an iterative, CMI-based algorithm for practical feature selection. We demonstrate the power of our CMI-based algorithm in comparison to the unconditional mutual information on benchmark examples and provide corresponding PID estimates to highlight how PID allows to quantify information contribution of features and their interactions in feature-selection problems.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). Builds on 6 of its 85 references that are in the map. First posted on arXiv 10 May 2021.

Builds on

6 of 85 references.

References · 6

  1. 2017Estimating Mutual Information for Discrete-Continuous Mixturescited by 34
  2. 2020Bits and Pieces: Understanding Information Decomposition from Part-whole Relationships and Formal Logiccited by 15
  3. 2014JIDT: An information-theoretic toolkit for studying the dynamics of complex systemscited by 11
  4. 2019Large-scale directed network inference with multivariate transfer entropy and hierarchical statistical testingcited by 7
  5. 2015Optimal model-free prediction from multivariate time seriescited by 6
  6. 2018BROJA-2PID: A robust estimator for bivariate partial information decompositioncited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 2; 2023: 2; 2024: 8; 2025: 5; 2026: 7.

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  1. 2023Quantifying & Modeling Multimodal Interactions: An Information Decomposition Frameworkcited by 81
  2. 2025I2MoE: Interpretable Multimodal Interaction-aware Mixture-of-Expertscited by 29
  3. 2024Quantifying Knowledge Distillation Using Partial Information Decompositioncited by 12
  4. 2023Demystifying Local and Global Fairness Trade-offs in Federated Learning Using Partial Information Decompositioncited by 10
  5. 2025MMQ: Multimodal Mixture-of-Quantization Tokenization for Semantic ID Generation and User Behavioral Adaptationcited by 10
  6. 2022Synergistic information supports modality integration and flexible learning in neural networks solving multiple taskscited by 7
  7. 2022Ultra-marginal Feature Importance: Learning from Data with Causal Guaranteescited by 6
  8. 2024Towards Formalizing Spuriousness of Biased Datasets Using Partial Information Decompositioncited by 6
  9. 2024TERC: A Transfer Entropy Redundancy Criterion for State Variable Selection in Reinforcement Learningcited by 3
  10. 2024Partial Information Decomposition for Data Interpretability and Feature Selectioncited by 3
  11. 2024A Unified View of Group Fairness Tradeoffs Using Partial Information Decompositioncited by 3
  12. 2024Feature Selection for Network Intrusion Detectioncited by 3
13 more
  1. 2025Learning Invariant Graph Representations Through Redundant Informationcited by 1
  2. 2026Feature-level Interaction Explanations in Multimodal Transformerscited by 1
  3. 2021Interaction-Aware Sensitivity Analysis for Aerodynamic Optimization Results using Information Theorycited by 0
  4. 2024Study Features via Exploring Distribution Structurecited by 0
  5. 2024Foundations of Multisensory Artificial Intelligencecited by 0
  6. 2025Redundancy as a Structural Information Principle for Learning and Generalizationcited by 0
  7. 2025Video and Language Alignment in 2D Systems for 3D Multi-object Scenes with Multi-Information Derivative-Free Controlcited by 0
  8. 2026M-IDoL: Information Decomposition for Modality-Specific and Diverse Representation Learning in Medical Foundation Modelcited by 0
  9. 2026Self-Captioning Multimodal Interaction Tuning: Amplifying Exploitable Redundancies for Robust Vision Language Modelscited by 0
  10. 2026Does Role Specialization Matter for Explanation Faithfulness in Mixture-of-Experts?cited by 0
  11. 2026Partial Information Decomposition as a Multi-Contrast 3D MRI Selection Strategy for Resource-Constrained Deep Neural Network Training in Brain Tumor Segmentationcited by 0
  12. 2026When Does Synergy Help Active Feature Acquisition? A PID-Based Studycited by 0
  13. 2026Interpreting Reasoning of Large Language Models via Partial Information Decompositioncited by 0