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相关概念视频

Standard Deviation01:10

Standard Deviation

15.8K
The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The standard deviation value is small when the data are concentrated close to the mean, exhibiting slight variation or spread. The standard deviation value is never negative, it is either positive or zero. The standard deviation is larger when the data values are more spread out from the mean, which means the data values are exhibiting more variation.
15.8K
Empirical Method to Interpret Standard Deviation01:09

Empirical Method to Interpret Standard Deviation

5.1K
The empirical rule, also known as the three-sigma rule, allows a statistician to interpret the standard deviation in a normally distributed dataset. The rule states that 68% of the data lies within one standard deviation from the mean, 95% lies within two standard deviations from the mean, and 99.7% lies within three standard deviations from the mean. Additionally, this rule is also called the 68-95-99.7 rule.
This rule is used widely in statistics to calculate the proportion of data values...
5.1K
Uniform Distribution01:19

Uniform Distribution

4.8K
The uniform distribution is a continuous probability distribution of events with an equal probability of occurrence. This distribution is rectangular.
Two essential properties of this distribution are
4.8K
Range Rule of Thumb to Interpret Standard Deviation01:13

Range Rule of Thumb to Interpret Standard Deviation

8.9K
The range rule of thumb in statistics helps us calculate a dataset's minimum and maximum values with known standard deviation. This rule is based on the concept that 95% of all values in a dataset lie within two standard deviations from the mean.
For instance, the range rule of thumb can be used to find the tallest and the shortest student in a class, given the mean student height and standard deviation. If the mean student height is 1.6 m and the standard deviation, s is 0.05 m, the height...
8.9K
Calculating Standard Deviation01:08

Calculating Standard Deviation

7.3K
The standard deviation is the most common measure of variation. It is a value that tells us how far a data value is from the mean value in a dataset. Further, the standard deviation is always a positive value or zero.
The standard deviation value is small when all the data is concentrated close to the mean. Here the data exhibits low variation. The standard deviation value is larger when the data values are more spread out from the mean. Here, the data displays high...
7.3K
Chebyshev's Theorem to Interpret Standard Deviation01:15

Chebyshev's Theorem to Interpret Standard Deviation

4.1K
Chebyshev’s theorem, also known as Chebyshev’s Inequality, states that the proportion of values of a dataset for K standard deviation is calculated using the equation:
4.1K

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iSIM-sigma:用于分子相似性的高效标准偏差计算.

Kenneth Lopez Perez, Bill Zhao, Ramon Alain Miranda Quintana

    bioRxiv : the preprint server for biology
    |December 9, 2024
    PubMed
    概括

    计算分子相似度变异在计算上是昂贵的. 本研究介绍了拉塞尔-拉奥和索卡尔-米切纳索引的更快方法,以及大型化学库的准确O (n) 近似.

    科学领域:

    • 化学信息学 化学信息学
    • 计算化学的计算化学
    • 生物信息学是一种生物信息学.

    背景情况:

    • 分子相似度指标对于化学信息学任务至关重要,例如化学空间探索和子集选择.
    • 计算完整相似度矩阵的方差具有二次复杂度 (O(N^2),这对于大型分子库来说是计算不可行的.
    • 现有的方法难以满足现代大规模分子数据集的可扩展性需求.

    研究的目的:

    • 开发计算效率高的方法来计算分子相似性的标准偏差.
    • 在分析大型分子数据集时解决二次复杂性的局限性.
    • 为各种相似度指数提供适用于相似度方差的准确近似值.

    主要方法:

    • 开发了一种具有O(NM^2) 复杂度的替代方法,用于对拉塞尔-拉奥 (RR) 和索卡尔-米切纳 (SM) 相似度指数的精确标准偏差计算.
    • 基于采样代表分子,提出了具有线性复杂度 (O(N)) 的高精度近似.
    • 证明了近似方法对其他相似度指数的适用性,包括Jaccard-Tanimoto (JT).

    主要成果:

    • 拟议的近似方法在使用仅50个样本分子的50,000个分子组中,实现根平均平方误差 (RMSE) 低于0.01.
    • 线性复杂度近似值在估计相似度标准偏差的准确性方面明显优于随机抽样.

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  • O(NM^2) 方法为RR和SM指数提供了准确的计算,为O(N^2) 双向方法提供了更可行的替代方案.

    • 结论:

    • 开发的近似方法提供了一个可扩展和准确的解决方案,用于估计大数据集中的分子相似度变异.
    • 这种方法显著降低了计算负担,使得有效的化学空间探索和子集选择.
    • 该方法的准确性和广泛适用性使其成为现代化学信息学研究的宝贵工具.