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Classifier Pooling for Modern Ordinal Classification

Noam H. Rotenberg, Andreia V. Faria, Brian Caffo

Abstract

Ordinal data is widely prevalent in clinical and other domains, yet there is a lack of both modern, machine-learning based methods and publicly available software to address it. In this paper, we present a model-agnostic method of ordinal classification, which can apply any non-ordinal classification method in an ordinal fashion. We also provide an open-source implementation of these algorithms, in the form of a Python package. We apply these models on multiple real-world datasets to show their performance across domains. We show that they often outperform non-ordinal classification methods, especially when the number of datapoints is relatively small or when there are many classes of outcomes. This work, including the developed software, facilitates the use of modern, more powerful machine learning algorithms to handle ordinal data.

Classifier Pooling for Modern Ordinal Classification

Abstract

Ordinal data is widely prevalent in clinical and other domains, yet there is a lack of both modern, machine-learning based methods and publicly available software to address it. In this paper, we present a model-agnostic method of ordinal classification, which can apply any non-ordinal classification method in an ordinal fashion. We also provide an open-source implementation of these algorithms, in the form of a Python package. We apply these models on multiple real-world datasets to show their performance across domains. We show that they often outperform non-ordinal classification methods, especially when the number of datapoints is relatively small or when there are many classes of outcomes. This work, including the developed software, facilitates the use of modern, more powerful machine learning algorithms to handle ordinal data.
Paper Structure (8 sections, 2 equations, 1 figure, 5 tables, 3 algorithms)

This paper contains 8 sections, 2 equations, 1 figure, 5 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Methods
  3. Model-Agnostic Ordinal Classification Algorithms
  4. Conditional Equivalence for Tree-based Ordinal Classification
  5. Data
  6. Evaluation
  7. Results
  8. Discussion

Figures (1)

  • Figure 1: 1a: Fitting paradigm for thresholded ordinal classification (Algorithm \ref{['alg1:fitting']}), paired with the difference prediction paradigm (fig. 1b; Algorithm \ref{['alg2:DifferenceOrdinalClassifier']}). 1c: Prediction paradigm of tree-based ordinal classification (Algorithm \ref{['alg3:TreeOrdinalClassifier']}). To find $P(Y=i)$, multiply all of the conditional probabilities above the node $Y=i$. Equivalence of this product to $P(Y=i)$ is shown in the Appendix.