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Uncertainty: Confidence Intervals

Uncertainty: Confidence Intervals

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...

Prediction Intervals

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.

Uncertainty: Overview

Uncertainty: Overview

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.

Confidence Intervals

Confidence Intervals

An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a sample proportion. However, unlike the point estimate which is a single value, the confidence interval contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A...

Propagation of Uncertainty from Systematic Error

Propagation of Uncertainty from Systematic Error

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...

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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P300-Based Brain-Computer Interface Speller Performance Estimation with Classifier-Based Latency Estimation

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CreINNs: Credal-Set Interval Neural Networks for Uncertainty Estimation in Classification Tasks.

Kaizheng Wang¹, Keivan Shariatmadar², Shireen Kudukkil Manchingal³

¹DistriNet, Department of Computer Science, Campus Bruges, KU Leuven, Bruges, 8200, Belgium; Flanders Make@KU Leuven, Leuven, Belgium.

Neural Networks : the Official Journal of the International Neural Network Society

|February 4, 2025

Summary

Credal-Set Interval Neural Networks (CreINNs) offer reliable uncertainty estimation for neural networks. This novel approach predicts probability bounds, enhancing classification accuracy and reducing computational load compared to existing methods.

Keywords:

Classification Credal sets Interval neural networks Probability intervals Uncertainty estimation

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Area of Science:

Artificial Intelligence
Machine Learning
Deep Learning

Background:

Reliable uncertainty estimation is crucial for enhancing neural network dependability.
Traditional Interval Neural Networks capture weight uncertainty using deterministic intervals.

Purpose of the Study:

Introduce Credal-Set Interval Neural Networks (CreINNs) for classification tasks.
Develop a method for predicting probability intervals to estimate various uncertainties.

Main Methods:

CreINNs extend Interval Neural Networks by predicting upper and lower probability bounds for each class.
These probability intervals define a credal set for uncertainty quantification.
The approach was tested on multiclass and binary classification tasks.

Main Results:

CreINNs demonstrate superior or comparable uncertainty estimation quality against variational Bayesian Neural Networks (BNNs) and Deep Ensembles.
Significant reduction in computational complexity during inference compared to variational BNNs.
Effective uncertainty quantification was confirmed even with interval input data.

Conclusions:

CreINNs provide an effective method for uncertainty estimation in neural network classification.
The approach offers a computationally efficient alternative to existing methods.
CreINNs show promise for applications requiring robust uncertainty quantification, including those with interval data.