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Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
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Related Experiment Video

Updated: Dec 4, 2025

Large-Scale Multi-Omics Genome-Wide Association Studies Mo-GWAS: Guidelines for Sample Preparation and Normalization
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Revisiting Internal Covariate Shift for Batch Normalization.

Muhammad Awais, Md Tauhid Bin Iqbal, Sung-Ho Bae

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    |October 23, 2020
    PubMed
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    This summary is machine-generated.

    Batch Normalization (BatchNorm) success is due to reducing internal covariate shift (ICS), not just enabling high learning rates or smoothing optimization. Experiments confirm ICS reduction is key for performance across BatchNorm variants.

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    Area of Science:

    • Deep Learning
    • Machine Learning Optimization

    Background:

    • Batch Normalization (BatchNorm) is widely used in deep learning.
    • Its success is often attributed to reducing internal covariate shift (ICS).
    • Recent studies question the ICS hypothesis, proposing alternative explanations like enabling higher learning rates and smoothing optimization landscapes.

    Purpose of the Study:

    • To empirically validate the importance of ICS reduction for BatchNorm's success.
    • To investigate alternative explanations for BatchNorm's effectiveness.
    • To analyze the role of BatchNorm parameters in performance and ICS.

    Main Methods:

    • Empirical validation of ICS reduction's importance.
    • Demonstration of alternative properties without performance gains.
    • Analysis of BatchNorm parameters and their connection to ICS.
    • Comparison with a novel normalization scheme lacking ICS reduction.

    Main Results:

    • Alternative properties (high learning rates, smoothed landscapes) do not guarantee performance gains without ICS reduction.
    • A normalization scheme with alternative properties but no ICS reduction showed poor performance.
    • All tested BatchNorm variants were found to reduce ICS.
    • BatchNorm parameters' effectiveness was visualized and linked to ICS.

    Conclusions:

    • The primary reason for BatchNorm's success is its ability to reduce internal covariate shift (ICS).
    • Alternative explanations for BatchNorm's effectiveness are insufficient on their own.
    • ICS reduction remains a critical factor for achieving high performance in deep learning models.