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相关概念视频

Uncertainty: Overview00:59

Uncertainty: Overview

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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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Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

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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

Propagation of Uncertainty from Random Error

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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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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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Uncertainty in Measurement: Accuracy and Precision03:37

Uncertainty in Measurement: Accuracy and Precision

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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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Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
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机器学习潜力的空间解决不确定性

Esther Heid1, Johannes Schörghuber1, Ralf Wanzenböck1

  • 1Institute of Materials Chemistry, TU Wien, A-1060 Vienna, Austria.

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此摘要是机器生成的。

本研究引入了一种新的方法,通过聚合认识不确定性来准确估计机器学习潜力的错误. 这使得原子模拟的有效主动学习成为可能,改善了数据集组成.

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科学领域:

  • 计算化学计算化学
  • 材料科学 材料科学 材料科学
  • 机器学习 机器学习

背景情况:

  • 机器学习潜力 (MLP) 对于原子模拟至关重要,以较低的计算成本提供接近初始精度.
  • 提高MLP的准确性需要仔细的数据集组成,可靠地识别预测错误是一个关键的挑战.
  • 目前用于MLP的不确定性估计技术在将不确定性与实际模型错误相关联方面取得了有限的成功.

研究的目的:

  • 开发一种用于将不确定性估计与机器学习潜力的模型错误相关的多功能方法.
  • 为了能够可靠地识别错误预测的数据集扩展配置.
  • 设计一个积极的学习框架,利用准确的不确定性量化来有效地生成模拟数据.

主要方法:

  • 研究了在机器学习潜力中的认识不确定性和模型错误之间的相关性.
  • 开发了一种方法来汇总对原子组的认识不确定性,以改善与模型错误的相关性.
  • 实施了一个主动学习框架,利用局部不确定性估计来指导初始计算的配置选择.

主要成果:

  • 证明,虽然单独的认识不确定性与模型错误没有相关性,但其对原子组的聚合产生了强烈的相关性.
  • 展示了提出的方法准确地估计了全球 (每个结构) 和本地 (每个原子) 的预测错误.
  • 成功应用了主动学习框架,以高效地生成用于低数据模式下液态水模拟的数据.

结论:

  • 开发的方法提供了一种可靠的方法,通过利用聚合的认识体系不确定性来估计机器学习潜力的预测错误.
  • 这种方法有助于设计有效的积极学习策略,大大提高了生成高质量的模拟数据的效率.
  • 这些发现为在各种科学领域进行更准确,更高效的原子模拟铺平了道路.