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Machine Learning and Data Analysis Using Posets: A Survey

arXiv 2404.03082 ↗First posted 3 Apr 2024cs.LGcited by 0

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Abstract (arXiv)

Partially ordered sets (posets) are discrete mathematical structures that formalize the notion of comparison without forcing every pair of objects to be comparable. This makes them a natural representation for the many machine learning and data-analysis settings in which objects are related by dominance, containment, priority, or refinement relations rather than by a single scalar score. Over the past two decades, a substantial and fragmented literature has connected posets and lattice theory to ranking, clustering, formal concept analysis, multidimensional and multi-criteria data analysis, structured and safe learning, graph and topological deep learning, and explainable artificial intelligence, spanning a wide range of application domains. Despite this activity, the field has lacked (i) an organizing taxonomy that relates these disparate strands of work, and (ii) an up-to-date account extending through 2025--2026 that incorporates recent developments in poset-structured learning methods, including poset-structured safety layers for reinforcement learning, poset-valued neural pooling operators, functor-calculus approaches to multiparameter persistent homology. This survey addresses both gaps. We propose a four-axis taxonomy of poset-based methods (representation, learning paradigm, data modality, and task), provide a comprehensive and comparative review of representative models and algorithms organized along this taxonomy, curate an extensive collection of datasets, software packages, and algorithmic resources, and close with a critical discussion of open theoretical and practical problems -- including model depth and expressivity, scalability--fidelity trade-offs, heterogeneity of order-structured data, and dynamicity of posets over time -- that we argue define a research agenda for the next generation of order-aware machine learning.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 31 of its 318 references that are in the map. First posted on arXiv 3 Apr 2024.

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31 of 318 references.

References · 31

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19 more
  1. 2019Ordering-Based Causal Structure Learning in the Presence of Latent Variablescited by 26
  2. 2020Hierarchical Poset Decoding for Compositional Generalization in Languagecited by 26
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