Online Performance Estimation with Unlabeled Data: A Bayesian Application of the Hui-Walter Paradigm

TL;DR

This paper bridges the gap in machine learning practices by adapting the Hui-Walter paradigm, a method traditionally applied in epidemiology and medicine, to the field of machine learning, and is able to estimate unknown parameters through Gibbs sampling, eliminating the need for ground-truth or labeled data.

Abstract

In the industrial practice of machine learning and statistical modeling, practitioners often work under the assumption of accessible, static, labeled data for evaluation and training. However, this assumption often deviates from reality, where data may be private, encrypted, difficult-to-measure, or unlabeled. In this paper, we bridge this gap by adapting the Hui-Walter paradigm, a method traditionally applied in epidemiology and medicine, to the field of machine learning. This approach enables us to estimate key performance metrics such as false positive rate, false negative rate, and priors in scenarios where no ground truth is available. We further extend this paradigm for handling online data, opening up new possibilities for dynamic data environments. Our methodology involves partitioning data into latent classes to simulate multiple data populations (if natural populations are unavailable) and independently training models to replicate multiple tests. By cross-tabulating binary outcomes across multiple categorizers and multiple populations, we are able to estimate unknown parameters through Gibbs sampling, eliminating the need for ground-truth or labeled data. This paper showcases the potential of our methodology to transform machine learning practices by allowing for accurate model assessment under dynamic and uncertain data conditions.

Figures (6)

• Figure 1: Two tests on one population.
• Figure 2: Hui-Walter assumptions with a $2 \times 2 \times 2$ contingency table. Variables $X_{1,1}, X_{2,1}, X_{3,1}$ and $X_{4,1}$ are cell frequency counts from a product-multinomial distribution. This setup is the minimum number of populations and classifiers required for the Hui-Walter method. However, this framework supports $n$ populations and $m$ classifiers.
• Figure 3: Comparison of scaled features from the Wisconsin Breast Cancer Data Set distributions with and without latent classes. The top panel displays the distributions of five scaled features—Compactness Mean, Radius Mean, Smoothness Mean, Texture Mean, and Texture SE—segmented by latent profile classes. Individual data points are color-coded by class, with means, standard deviations, and 95% confidence intervals indicated. The bottom panel shows the same features aggregated without class separation, illustrating the overall distributions of the Latent Classes.
• Figure 4: The two-dimensional t-SNE visualization of the training data from the Wisconsin breast cancer data set shows the viability of reducing the data space into Latent Classes. The high-dimensional feature space reduces to two dimensions using t-distributed Stochastic Neighbor Emulation (t-SNE)tsne with two components. Each point represents a single patient sample: benign cases are depicted as green squares and malignant cases are represented as red circles. This embedding reveals distinct clustering of benign and malignant samples, indicating that the selected features capture intrinsic differences between the two classes and suggest potential separability in the reduced dimensional space.
• Figure 5: A pairwise scatter plot matrix of selected morphological features from the Wisconsin Breast data set demonstrates the effectiveness of a two-class Latent Class Analysis (LCA) model. Plotted features are Radius Mean, Texture Mean, Smoothness Mean, Compactness Mean, and Texture SE, with data points colored by their assigned latent class. The distinct groupings in the plots indicate that the LCA effectively captures latent patterns in the data.