Quantification via Gaussian Latent Space Representations

2025-01-23

AI Summary

This paper addresses quantification—the task of directly estimating the class prior distribution over an unlabeled sample set, rather than performing instance-wise classification. Conventional methods rely on explicit classifiers and often assume prior probability shift, limiting their robustness and flexibility. To overcome these limitations, we propose the first end-to-end neural framework based on Gaussian latent-space representations: inputs (bags of instances) are mapped to Gaussian distributions in a learned latent space, and a differentiable mapping is established between class proportions and Gaussian parameters (mean and covariance). Our approach eliminates classifier cascades and introduces a quantification-specific loss for joint optimization. It requires no pre-trained classifier or post-hoc calibration. Extensive experiments on standard benchmarks demonstrate significant improvements over classical quantification methods and state-of-the-art deep learning baselines, achieving new SOTA performance. The code is publicly available.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Computer Vision: Representation Learning for Vision

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Quantification, or prevalence estimation, is the task of predicting the prevalence of each class within an unknown bag of examples. Most existing quantification methods in the literature rely on prior probability shift assumptions to create a quantification model that uses the predictions of an underlying classifier to make optimal prevalence estimates. In this work, we present an end-to-end neural network that uses Gaussian distributions in latent spaces to obtain invariant representations of bags of examples. This approach addresses the quantification problem using deep learning, enabling the optimization of specific loss functions relevant to the problem and avoiding the need for an intermediate classifier, tackling the quantification problem as a direct optimization problem. Our method achieves state-of-the-art results, both against traditional quantification methods and other deep learning approaches for quantification. The code needed to reproduce all our experiments is publicly available at https://github.com/AICGijon/gmnet.

Problem

• Deep Learning
• Quantification
• Frequency Estimation

Innovation

• Gaussian Integration
• Quantization Optimization
• Deep Learning