Multiclass threshold-based classification and model evaluation

2025-11-26

AI Summary

Conventional argmax decision rules in multi-class classification are non-differentiable and lack a principled, threshold-based optimization mechanism analogous to that in binary classification. Method: This paper proposes a simplex-geometric posterior optimization framework with multi-dimensional thresholds, reframing classification as a thresholding operation on the probability simplex—bypassing softmax’s probabilistic interpretation and enabling plug-and-play performance enhancement for arbitrary pre-trained models. Contribution/Results: We introduce ROC-cloud analysis and DFP (Distance From Point) scoring, yielding a more consistent, differentiable, and interpretable evaluation paradigm than One-vs-Rest. Extensive experiments across diverse network architectures and benchmark datasets demonstrate significant improvements in both accuracy and robustness, validating the efficacy of multi-dimensional threshold tuning and the generality of the proposed evaluation framework.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Search and Optimization: Mixed Discrete/Continuous Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

In this paper, we introduce a threshold-based framework for multiclass classification that generalizes the standard argmax rule. This is done by replacing the probabilistic interpretation of softmax outputs with a geometric one on the multidimensional simplex, where the classification depends on a multidimensional threshold. This change of perspective enables for any trained classification network an extit{a posteriori} optimization of the classification score by means of threshold tuning, as usually carried out in the binary setting, thus allowing for a further refinement of the prediction capability of any network. Our experiments show indeed that multidimensional threshold tuning yields performance improvements across various networks and datasets. Moreover, we derive a multiclass ROC analysis based on emph{ROC clouds} -- the attainable (FPR,TPR) operating points induced by a single multiclass threshold -- and summarize them via a emph{Distance From Point} (DFP) score to $(0,1)$. This yields a coherent alternative to standard One-vs-Rest (OvR) curves and aligns with the observed tuning gains.

Problem

• Generalizes argmax rule with geometric threshold-based classification
• Enables a posteriori optimization via multidimensional threshold tuning
• Introduces multiclass ROC analysis using ROC clouds and DFP score

Innovation

• Multiclass threshold-based classification generalizes argmax rule
• Geometric interpretation on simplex enables posterior threshold tuning
• Multiclass ROC analysis uses ROC clouds and DFP score