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Propagation of Uncertainty from Random Error00:59

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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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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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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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The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
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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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Estimation with Uncertainty via Conditional Generative Adversarial Networks.

Minhyeok Lee1, Junhee Seok2

  • 1School of Electrical & Electronics Engineering, Chung-Ang University, Seoul 06974, Korea.

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|September 28, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a novel probabilistic neural network for accurate predictions and uncertainty estimation, outperforming traditional models, especially with noisy data. This advancement is crucial for applications like medical diagnosis and financial forecasting.

Keywords:
adversarial learningdeep learninggenerative adversarial networkportfolio managementprobability estimationrisk estimation

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Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Deep Learning

Background:

  • Conventional Artificial Neural Networks (ANNs) provide deterministic point estimates, limiting their use in fields requiring prediction uncertainty.
  • Applications in medical diagnosis, law, and finance necessitate understanding prediction confidence alongside the prediction itself.

Purpose of the Study:

  • To propose a novel predictive probabilistic neural network model.
  • To address the limitations of deterministic ANNs by incorporating uncertainty estimation.
  • To enhance the robustness and applicability of neural networks in critical decision-making domains.

Main Methods:

  • A predictive probabilistic neural network model is proposed, adapting conditional Generative Adversarial Networks (cGANs) by reversing input/output.
  • Adversarial training is employed to enhance model robustness against noisy data.
  • Entropy and relative entropy are introduced for uncertainty measurement in regression and classification tasks, respectively.

Main Results:

  • The proposed framework demonstrates superior estimation performance, particularly on noisy datasets.
  • The model effectively estimates the uncertainty associated with its predictions.
  • Successful application demonstrated on stock market data and an image classification task.

Conclusions:

  • The developed probabilistic neural network offers a robust alternative to conventional ANNs for tasks requiring uncertainty quantification.
  • The framework provides a reliable method for estimating prediction uncertainty, enhancing decision-making in complex and noisy environments.
  • This approach advances the practical application of neural networks in sensitive fields like finance and healthcare.