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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.

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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...

Classification of Systems-II

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Classification of Systems-I

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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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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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Related Experiment Video

Updated: Oct 7, 2025

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Published on: September 7, 2019

Active Classification With Uncertainty Comparison Queries.

Zhenghang Cui^1,2, Issei Sato^1,3

¹The University of Tokyo, Tokyo 13-0033, Japan.

Neural Computation

|January 11, 2022

Summary

This summary is machine-generated.

This study introduces a novel uncertainty-based pairwise comparison oracle to improve interactive learning for binary classifiers. This method efficiently determines classification thresholds, overcoming limitations of existing approaches for noisy feedback and limited labeling budgets.

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Area of Science:

Machine Learning
Computational Statistics
Pattern Recognition

Background:

Interactive learning for binary classifiers often uses noisy pairwise comparison feedback.
Existing methods rely on positivity comparison oracles and explicit labeling oracles, which have limitations.
Current approaches require sorting for label inference and struggle with noisy feedback, leading to inefficiencies.

Purpose of the Study:

To develop a more efficient method for interactively learning binary classifiers with noisy pairwise feedback.
To address the limitations of existing oracles in determining classification thresholds and handling insufficient labeling budgets.
To introduce a new pairwise comparison oracle that leverages uncertainty information.

Main Methods:

Proposed a novel pairwise comparison oracle that provides feedback on data point uncertainty.
Developed an efficient adaptive labeling algorithm to utilize the proposed uncertainty oracle.
Addressed scenarios with limited labeling budgets relative to dataset size.

Main Results:

The proposed uncertainty-based oracle efficiently acquires information about the classification threshold.
The adaptive labeling algorithm effectively utilizes the new oracle, improving upon existing methods.
Theoretical and empirical validation confirms the feasibility and performance of the proposed oracle and algorithm.

Conclusions:

The novel uncertainty-based pairwise comparison oracle offers a more efficient approach to interactive binary classifier learning.
The proposed adaptive labeling algorithm effectively handles noisy feedback and limited budgets.
This work advances the field of active learning by providing a more robust and efficient framework.