الملخص
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Uncertainty estimation in machine learning typically decomposes uncertainty into aleatoric uncertainty (AU) and epistemic uncertainty (EU) using the standard information-theoretic framework. However, in practice, two critical issues arise: entanglement (AU and EU are highly correlated) and epistemic collapse (EU magnitude shrinks with increasing model capacity). We analyze this framework on a functional level and discover that significant portions of the assumed AU, EU range are infeasible in finite settings, and cannot be attained with any class probabilities. We characterize how this infeasible region scales with the number of classes and Monte Carlo samples $N$ (e.g., from ensembles with $N$ members), revealing it is bounded by $\text{AU} \leq \log(2)/N$. Crucially, the infeasible region's boundary helps explain epistemic collapse: when model confidence is high, $\text{AU} > \text{EU}$ is guaranteed by this fundamental structural limitation. Our findings show that increasing ensemble size mitigates epistemic collapse by reducing the infeasible area. Lastly, we caution against interpreting AU and EU as independent quantities in low AU regimes, since we show they are coupled when $\text{AU} \leq \log(2)/N$.
الكلمات المفتاحية
الموضوع
بيانات النشر
- المجلة
- غير متاح
- وصول مفتوح
- وصول مفتوح أخضر
اقتبس هذه المقالة
APA 7
Christensen, J. L., Baumgartner, C. F., Hannemose, M. R., Dahl, A. B., & Dahl, V. A. (2026). الحدود البنيوية لتحلل عدم اليقين المعلوماتي-النظري. https://omanscience.com/ar/articles/structural-limits-of-the-information-theoretic-uncertainty-decomposition
MLA 9
Christensen, Jakob Lønborg, et al. "الحدود البنيوية لتحلل عدم اليقين المعلوماتي-النظري." https://omanscience.com/ar/articles/structural-limits-of-the-information-theoretic-uncertainty-decomposition.
شيكاغو (المؤلف–التاريخ)
Christensen, Jakob Lønborg, Christian F. Baumgartner, Morten Rieger Hannemose, Anders Bjorholm Dahl, and Vedrana Andersen Dahl. 2026. "الحدود البنيوية لتحلل عدم اليقين المعلوماتي-النظري." https://omanscience.com/ar/articles/structural-limits-of-the-information-theoretic-uncertainty-decomposition.
هارفارد
Christensen, J. L., Baumgartner, C. F., Hannemose, M. R., Dahl, A. B. and Dahl, V. A. (2026) 'الحدود البنيوية لتحلل عدم اليقين المعلوماتي-النظري', Available at: https://omanscience.com/ar/articles/structural-limits-of-the-information-theoretic-uncertainty-decomposition.
فانكوفر
Christensen JL, Baumgartner CF, Hannemose MR, Dahl AB, Dahl VA. الحدود البنيوية لتحلل عدم اليقين المعلوماتي-النظري. https://omanscience.com/ar/articles/structural-limits-of-the-information-theoretic-uncertainty-decomposition
IEEE
J. L. Christensen, C. F. Baumgartner, M. R. Hannemose, A. B. Dahl, and V. A. Dahl, "الحدود البنيوية لتحلل عدم اليقين المعلوماتي-النظري," https://omanscience.com/ar/articles/structural-limits-of-the-information-theoretic-uncertainty-decomposition.