Machine Learning
New submissions for Mon, 24 Aug 2026 (showing 1 of 1 entries)
- PX:2607.00001 [pdf]
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Title: Quantifying 2-Component Gaussian Mixture Model Robustness and Visual Diagnostic Efficacy Across Simulated Bimodal Data RegimesSubjects: stat.ME; stat.CO; stat.ML[Submitted on 2026-07-31]
The robustness of Gaussian Mixture Model (GMM) parameter estimation and the efficacy of diagnostic tools are critical concerns when analyzing bimodal data. This study systematically investigated the performance of 2-component GMMs by simulating 54 distinct bimodal datasets, manipulating component separation (0.5 to 3.0 standard deviations), relative mixing proportions (0.5, 0.7, 0.9), and sample sizes (100, 500, 2000). Using the Expectation-Maximization algorithm with multiple initializations, we quantified the bias, Root Mean Squared Error, and precision of estimated means, variances, and mixing coefficients. Our findings indicate that GMM robustness is strongly dependent on component separation, with low separation (≤ 1.0 standard deviations) consistently leading to significant parameter bias, while higher separation (≥ 2.0 standard deviations) substantially improves accuracy. Unbalanced mixing proportions further exacerbated estimation challenges, particularly for minor components. Furthermore, we found that Wasserstein distance provided a more reliable objective indicator of model fit quality than the Kolmogorov-Smirnov statistic, showing a strong positive correlation (r > 0.75) with estimation error. Visual diagnostics, such as the misalignment of fitted GMM modes with empirical data peaks and systematic patterns in residual plots, proved highly informative for identifying suboptimal fits, especially under low component separation. These results offer empirical guidelines for practitioners regarding the reliability of 2-component GMMs and the effective use of diagnosti