Confirmation Bias in Gaussian Mixture Models

2024-08-19

arXiv.org

AI Summary

This work exposes a confirmation bias induced by Gaussian Mixture Models (GMMs) on pure noise data: both K-means and the EM algorithm systematically produce spurious clusters strongly correlated with initial assumptions—even in the absence of underlying structure—posing severe risks to low-SNR scientific imaging, such as cryo-electron microscopy. We formally prove that this bias arises intrinsically from algorithmic estimation: estimators theoretically expected to be unbiased exhibit persistent positive bias in practice. Closed-form expressions for this bias are derived under both finite- and infinite-sample regimes, rigorously quantifying its monotonic dependence on the number of assumed components and noise variance. By integrating asymptotic analysis with probabilistic modeling, we elucidate the failure mechanism of classical clustering methods under high noise and provide critical methodological guidance for ensuring robust, reliable scientific discovery.

Technology Category

• Machine Learning: Clustering
• Reasoning under Uncertainty: Graphical Models
• Computer Vision: Bias, Fairness & Privacy

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Social Networks and Social Media: Fairness and bias in social network and social media analysis

Abstract

Confirmation bias, the tendency to interpret information in a way that aligns with one's preconceptions, can profoundly impact scientific research, leading to conclusions that reflect the researcher's hypotheses even when the observational data do not support them. This issue is especially critical in scientific fields involving highly noisy observations, such as cryo-electron microscopy. This study investigates confirmation bias in Gaussian mixture models. We consider the following experiment: A team of scientists assumes they are analyzing data drawn from a Gaussian mixture model with known signals (hypotheses) as centroids. However, in reality, the observations consist entirely of noise without any informative structure. The researchers use a single iteration of the K-means or expectation-maximization algorithms, two popular algorithms to estimate the centroids. Despite the observations being pure noise, we show that these algorithms yield biased estimates that resemble the initial hypotheses, contradicting the unbiased expectation that averaging these noise observations would converge to zero. Namely, the algorithms generate estimates that mirror the postulated model, although the hypotheses (the presumed centroids of the Gaussian mixture) are not evident in the observations. Specifically, among other results, we prove a positive correlation between the estimates produced by the algorithms and the corresponding hypotheses. We also derive explicit closed-form expressions of the estimates for a finite and infinite number of hypotheses. This study underscores the risks of confirmation bias in low signal-to-noise environments, provides insights into potential pitfalls in scientific methodologies, and highlights the importance of prudent data interpretation.

Problem

• Investigating confirmation bias in Gaussian mixture models with noisy data
• Analyzing biased centroid estimates from K-means and EM algorithms on pure noise
• Demonstrating algorithm outputs correlate with initial hypotheses despite no signal

Innovation

• Analyzing Gaussian mixture models with K-means and EM algorithms
• Deriving closed-form expressions for finite and infinite hypotheses
• Proving positive correlation between estimates and initial hypotheses