Related Concept Videos
00:59Propagation 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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01:10Propagation 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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00:59Uncertainty: 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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00:54Uncertainty: 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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01:04Random Error
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Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
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04:08The Uncertainty Principle
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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
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The Epistemic Uncertainty Gradient in Spaces of Random Projections.
Jeffrey F Queißer1, Jun Tani1, Jochen J Steil2,3
1Cognitive Neurorobotics Research Unit, Okinawa Institute of Science and Technology Graduate University, Onna 904-0495, Japan.
Entropy (Basel, Switzerland)
|February 26, 2025
Summary
This study proposes a new method to model data distributions using epistemic uncertainty, enhancing outlier detection and generalization. This approach offers efficient, parameter-free representations for machine learning tasks.
Area of Science:
- Machine Learning
- Statistical Modeling
- Uncertainty Quantification
Background:
- Epistemic uncertainty is crucial in machine learning for understanding model limitations.
- Bayesian linear regression provides a foundation for uncertainty estimation.
- Existing methods for handling uncertainty can be computationally intensive.
Purpose of the Study:
- To introduce a novel framework for epistemic uncertainty estimation.
- To represent arbitrary data distributions efficiently and without parameters.
- To enhance outlier detection and generalization capabilities in machine learning models.
Main Methods:
- Treating model-dependent variance as a model for the underlying data distribution.
- Utilizing high-dimensional random feature transformations for computational efficiency.
- Employing gradient descent to minimize uncertainty for data querying.
Main Results:
- A computationally efficient, parameter-free representation of arbitrary data distributions.
- Effective assessment of query points within the data distribution for outlier detection.
- A novel method for querying data points similar to training data, akin to auto-completion.
Conclusions:
- The proposed reinterpretation of epistemic uncertainty offers a novel framework for machine learning.
- The method provides geometric insights for addressing classical machine learning challenges.
- Applications include local Gaussian approximations, input-output regression, and data unlearning.