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Related Concept Videos

Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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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.
William S. Gosset (1876–1937) of the...
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Estimating Population Mean with Known Standard Deviation01:16

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To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate +...
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Estimating Population Standard Deviation01:26

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When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
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Regression Toward the Mean01:52

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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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Central Limit Theorem01:14

Central Limit Theorem

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The central limit theorem, abbreviated as clt, is one of the most powerful and useful ideas in all of statistics. The central limit theorem for sample means says that if you repeatedly draw samples of a given size and calculate their means, and create a histogram of those means, then the resulting histogram will tend to have an approximate normal bell shape. In other words, as sample sizes increase, the distribution of means follows the normal distribution more closely.
The sample size, n, that...
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Distributions to Estimate Population Parameter01:26

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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms
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Effective and Efficient Batch Normalization Using a Few Uncorrelated Data for Statistics Estimation.

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    Summary
    This summary is machine-generated.

    Researchers developed efficient methods to speed up deep neural network training by reducing the cost of batch normalization (BN). These techniques use minimal data for normalization, achieving significant training speedups without accuracy loss.

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    Area of Science:

    • Artificial Intelligence
    • Machine Learning
    • Computer Vision

    Background:

    • Deep neural networks (DNNs) are crucial in modern AI.
    • Batch Normalization (BN) is vital for DNN training but computationally expensive.
    • Current BN methods hinder training speed due to parallelization challenges.

    Purpose of the Study:

    • To propose a cost-effective methodology for batch normalization in DNNs.
    • To enhance training speed without compromising model accuracy or convergence.
    • To address the computational burden of BN in deep learning.

    Main Methods:

    • Developed techniques using minimal sampled or generated data for mean and variance estimation.
    • Introduced batch sampling (BS) and feature sampling (FS) for uncorrelated data.
    • Proposed virtual data set normalization (VDN) for synthetic data generation.
    • Designed multiway strategies to balance normalization effectiveness and execution efficiency.

    Main Results:

    • Achieved practical 1.98x BN layer acceleration and 23.2% overall training speedup on GPUs.
    • Demonstrated negligible loss in model accuracy and convergence rate.
    • Showcased effective solutions for the 'micro-BN' problem with tiny batch sizes.
    • Validated methods across various DNN models without specialized libraries.

    Conclusions:

    • The proposed methods offer a promising solution for efficient DNN training.
    • Significant speedups are achievable with minimal impact on performance.
    • These techniques are effective even in challenging scenarios like small batch sizes.