# Machine Learning and Data Analysis Using Posets: A Survey

arXiv: https://arxiv.org/abs/2404.03082 · HTML: https://mlsanity.com/paper/2404.03082/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 318 references that are in the map.
- First posted on arXiv 3 Apr 2024.

## Builds on (most cited first, 30 of 31)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Recurrent Models of Visual Attention](https://mlsanity.com/paper/1406.6247/) (2014)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [Topological Deep Learning: Going Beyond Graph Data](https://mlsanity.com/paper/2206.00606/) (2022)
- [Topological Signal Processing over Simplicial Complexes](https://mlsanity.com/paper/1907.11577/) (2019)
- [Graph-based Semi-supervised Learning: A Comprehensive Review](https://mlsanity.com/paper/2102.13303/) (2021)
- [A General Survey on Attention Mechanisms in Deep Learning](https://mlsanity.com/paper/2203.14263/) (2022)
- [The paradox of the compositionality of natural language: a neural machine translation case study](https://mlsanity.com/paper/2108.05885/) (2021)
- [Compositional Generalization by Learning Analytical Expressions](https://mlsanity.com/paper/2006.10627/) (2020)
- [Semi-Supervised and Unsupervised Deep Visual Learning: A Survey](https://mlsanity.com/paper/2208.11296/) (2022)
- [Topological Deep Learning: A Review of an Emerging Paradigm](https://mlsanity.com/paper/2302.03836/) (2023)
- [Ordering-Based Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/1910.09014/) (2019)
- [Hierarchical Poset Decoding for Compositional Generalization in Language](https://mlsanity.com/paper/2010.07792/) (2020)
- [From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Module](https://mlsanity.com/paper/2305.16174/) (2023)
- [Graph-augmented Learning to Rank for Querying Large-scale Knowledge Graph](https://mlsanity.com/paper/2111.10541/) (2021)
- [RankDNN: Learning to Rank for Few-shot Learning](https://mlsanity.com/paper/2211.15320/) (2022)
- [Learning To Rank Resources with GNN](https://mlsanity.com/paper/2304.07946/) (2023)
- [Introduction to Formal Concept Analysis and Its Applications in Information Retrieval and Related Fields](https://mlsanity.com/paper/1703.02819/) (2017)
- [Joint Modeling of Event Sequence and Time Series with Attentional Twin Recurrent Neural Networks](https://mlsanity.com/paper/1703.08524/) (2017)
- [Depth Functions for Partial Orders with a Descriptive Analysis of Machine Learning Algorithms](https://mlsanity.com/paper/2304.09872/) (2023)
- [Compositional Generalization in Dependency Parsing](https://mlsanity.com/paper/2110.06843/) (2021)
- [Neural-based classification rule learning for sequential data](https://mlsanity.com/paper/2302.11286/) (2023)
- [Deep Unsupervised Similarity Learning using Partially Ordered Sets](https://mlsanity.com/paper/1704.02268/) (2017)
- [MCRapper: Monte-Carlo Rademacher Averages for Poset Families and Approximate Pattern Mining](https://mlsanity.com/paper/2006.09085/) (2020)
- [Ontology Learning Using Formal Concept Analysis and WordNet](https://mlsanity.com/paper/2311.14699/) (2023)
- [Bayesian inference for partial orders from random linear extensions: power relations from 12th Century Royal Acta](https://mlsanity.com/paper/2212.05524/) (2022)
- [Efficient Representation of Multidimensional Data over Hierarchical Domains](https://mlsanity.com/paper/1612.04094/) (2016)
- [Learning Graph Representation via Formal Concept Analysis](https://mlsanity.com/paper/1812.03395/) (2018)
- [Dynamic Programs on Partially Ordered Sets](https://mlsanity.com/paper/2308.02148/) (2023)

## 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.