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Related Concept Videos

Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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Propagation of Uncertainty from Systematic Error01:10

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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
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Propagation of Uncertainty from Random Error00:59

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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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Uncertainty in Measurement: Accuracy and Precision03:37

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Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value. 
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Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
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Creating Objects and Object Categories for Studying Perception and Perceptual Learning
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Quantifying Epistemic Uncertainty in Multimodal Long-Tailed Classification: A Belief Entropy-Based Evidential Fusion

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  • 1School of Business Administration, Southwestern University of Finance and Economics, Chengdu 611130, China.

Entropy (Basel, Switzerland)
|March 28, 2026
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Summary

This study introduces Uncertainty-Quantified Multimodal Learning for Long-Tailed Classification (UMuLT), a novel framework enhancing deep multimodal learning. UMuLT improves performance on underrepresented classes in long-tailed distributions by addressing modality uncertainty and fairness.

Keywords:
Dempster-Shafer Theorybelief entropylong-tailed classificationmultimodal information fusionuncertainty quantification

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Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Computer Vision

Background:

  • Deep multimodal learning excels across vision, language, and audio.
  • Real-world data often exhibits long-tailed distributions, degrading performance on tail classes.
  • Existing fusion schemes inadequately address modality-specific uncertainty and class-level fairness.

Purpose of the Study:

  • To present a novel framework, Uncertainty-Quantified Multimodal Learning for Long-Tailed Classification (UMuLT), integrating evidential reasoning with deep learning.
  • To tackle information discrepancies and performance degradation in long-tailed multimodal classification.
  • To enhance fairness and accuracy for underrepresented classes.

Main Methods:

  • Developed an uncertainty-gated evidential fusion module to down-weight unreliable modalities.
  • Incorporated an exponential moving average (EMA) fairness regularizer to amplify tail-class gradients.
  • Implemented a two-stage cross-modal consistency regularizer: tail specialization and end-to-end fine-tuning.

Main Results:

  • UMuLT demonstrated consistent gains over strong baselines on multimodal classification benchmarks.
  • Significant improvements were observed in overall metrics, model calibration, and performance on tail subsets.
  • Statistical significance tests confirmed the superiority of the proposed UMuLT framework.

Conclusions:

  • The UMuLT framework effectively addresses modality uncertainty and class imbalance in long-tailed multimodal learning.
  • The proposed methods provide a practical solution for improving fairness and performance on tail classes.
  • UMuLT offers a robust approach for real-world multimodal classification tasks with imbalanced data.