Jove
Visualize
联系我们
JoVE
x logofacebook logolinkedin logoyoutube logo
关于 JoVE
概览领导团队博客JoVE 帮助中心
作者
出版流程编辑委员会范围与政策同行评审常见问题投稿
图书馆员
用户评价订阅访问资源图书馆顾问委员会常见问题
研究
JoVE JournalMethods CollectionsJoVE Encyclopedia of Experiments存档
教育
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab Manual教师资源中心教师网站
使用条款与条件
隐私政策
政策

相关概念视频

Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

1.7K
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...
1.7K
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

1.3K
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...
1.3K
Uncertainty: Overview00:59

Uncertainty: Overview

1.6K
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.
1.6K
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

10.1K
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...
10.1K
Propagation of Action Potentials01:23

Propagation of Action Potentials

8.9K
The propagation of an action potential refers to the process by which a nerve impulse, or "action potential," travels along a neuron.
Neurons (nerve cells) have a resting membrane potential, with a slightly negative charge inside compared to outside. This is maintained by ion channels, such as sodium (Na+) and potassium (K+) channels, which control the flow of ions. When a stimulus, like a touch or a signal from another neuron, triggers the neuron, sodium channels open, allowing sodium ions to...
8.9K
Uncertainty in Measurement: Accuracy and Precision03:37

Uncertainty in Measurement: Accuracy and Precision

99.7K
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. 
99.7K

您也可能阅读

相关文章

通过共同作者、期刊和引用图与本文相关的文章。

排序
Same author

Tensor approximation of functional differential equations.

Physical review. E·2024
查看所有相关文章

相关实验视频

在feed-forward神经网络模型中不确定性传播

Jeremy Diamzon1, Daniele Venturi1

  • 1Department of Applied Mathematics, UC Santa Cruz, Santa Cruz, CA, 95064, USA.

Neural networks : the official journal of the International Neural Network Society
|October 11, 2025
PubMed
概括

新的方法准确地预测神经网络输出不确定性. 线性化漏洞的 ReLU 激活函数提供了精确的统计结果,即使有显著的输入扰动,通过模拟验证.

科学领域:

  • 人工智能的人工智能
  • 机器学习 机器学习
  • 计算数学 计算数学 计算数学

背景情况:

  • 输入前传神经网络 (FNN) 容易受到输入不确定性的影响.
  • 量化FNN的输出不确定性,特别是与诸如漏洞ReLU之类的非线性激活函数,仍然具有挑战性.
  • 现有的方法在显著的输入扰动下,往往在分析处理性和准确性方面扎.

研究的目的:

  • 开发新型的不确定性传播方法,以FNN泄漏ReLU激活.
  • 为概率密度函数 (PDF) 和FNN输出的统计时刻推导分析表达式.
  • 提出可处理的替代模型,以近似网络输出的联合PDF.

主要方法:

  • 对输出PDF和考虑到输入矢量扰动的统计时刻的分析表达式的导出.
  • 针对漏洞的 ReLU 激活函数,应用了一种特定的线性化技术.
  • 为近似输出PDF开发高斯铜替代模型.
  • 在复杂的FNN模型上通过蒙特卡洛模拟和错误分析进行验证.

主要成果:

  • 为输出不确定性和统计时刻获得了准确的分析表达式.
  • 一个关键的发现是线性泄漏ReLU方法的准确性,即使对于大输入扰动.
关键词:
多项可行性网络 (MLP) 的网络.神经网络模型的可靠性 神经网络模型的可靠性不确定性量化不确定性的量化.

相关实验视频

  • 建议的高斯偶模型为输出PDF提供了分析可处理的近似值.
  • 理论预测与蒙特卡洛模拟结果非常一致.

    • 结论:

    • 开发的方法提供了准确和分析可处理的方式,可以通过有漏洞的ReLU激活的FNNs传播输入不确定性.
    • 线性化技术对于处理显著的输入扰动是有效的,简化了不确定性量化.
    • 这项研究为理解和管理复杂神经网络模型中的不确定性提供了有价值的工具.