# Probabilistic Multi-Dimensional Classification

arXiv: https://arxiv.org/abs/2306.06517 · HTML: https://mlsanity.com/paper/2306.06517/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 76 references that are in the map.
- First posted on arXiv 10 Jun 2023.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [MUFASA: Multimodal Fusion Architecture Search for Electronic Health Records](https://mlsanity.com/paper/2102.02340/) (2021)
- [The Bayesian Structural EM Algorithm](https://mlsanity.com/paper/1301.7373/) (2013)
- [Classifier Chains: A Review and Perspectives](https://mlsanity.com/paper/1912.13405/) (2019)
- [On the Bayes-optimality of F-measure maximizers](https://mlsanity.com/paper/1310.4849/) (2013)
- [Multi-label classification: do Hamming loss and subset accuracy really conflict with each other?](https://mlsanity.com/paper/2011.07805/) (2020)
- [Properties of Bayesian Belief Network Learning Algorithms](https://mlsanity.com/paper/1302.6792/) (2013)
- [Bayesian Network Structure Learning with Integer Programming: Polytopes, Facets, and Complexity](https://mlsanity.com/paper/1605.04071/) (2016)
- [Entropy-based Pruning for Learning Bayesian Networks using BIC](https://mlsanity.com/paper/1707.06194/) (2017)
- [Learning Bayesian Networks with Incomplete Data by Augmentation](https://mlsanity.com/paper/1608.07734/) (2016)
- [Exact Inference in Networks with Discrete Children of Continuous Parents](https://mlsanity.com/paper/1301.2289/) (2013)

## Abstract (arXiv)

Multi-dimensional classification (MDC) can be employed in a range of applications where one needs to predict multiple class variables for each given instance. Many existing MDC methods suffer from at least one of inaccuracy, scalability, limited use to certain types of data, hardness of interpretation or lack of probabilistic (uncertainty) estimations. This paper is an attempt to address all these disadvantages simultaneously. We propose a formal framework for probabilistic MDC in which learning an optimal multi-dimensional classifier can be decomposed, without loss of generality, into learning a set of (smaller) single-variable multi-class probabilistic classifiers and a directed acyclic graph. Current and future developments of both probabilistic classification and graphical model learning can directly enhance our framework, which is flexible and provably optimal. A collection of experiments is conducted to highlight the usefulness of this MDC framework.