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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.

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...

Propagation of Uncertainty from Random Error

Propagation of Uncertainty from Random Error

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...

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...

Interpretation of Confidence Intervals

Interpretation of Confidence Intervals

A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...

Uncertainty in Measurement: Accuracy and Precision

Uncertainty in Measurement: Accuracy and Precision

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.

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Related Experiment Video

Updated: May 9, 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

FedSI: Federated Subnetwork Inference for Efficient Uncertainty Quantification.

Hui Chen, Hengyu Liu, Zhangkai Wu

IEEE Transactions on Neural Networks and Learning Systems

|May 6, 2025

Summary

This summary is machine-generated.

FedSI introduces a novel Bayesian deep neural network framework for personalized federated learning. This method efficiently quantifies uncertainty in federated learning, outperforming existing approaches in heterogeneous data scenarios.

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Area of Science:

Artificial Intelligence
Machine Learning
Computer Science

Background:

Personalized federated learning (PFL) addresses data heterogeneity but struggles with efficient uncertainty quantification.
Existing Bayesian deep neural networks (DNNs) for PFL face challenges with model complexity and high computational costs.

Purpose of the Study:

To introduce FedSI, a novel Bayesian DNN-based subnetwork inference (SI) PFL framework.
To enable efficient and scalable systematic uncertainty quantification in PFL.

Main Methods:

FedSI utilizes a client-specific subnetwork inference mechanism.
It incorporates Bayesian methods to effectively manage systematic uncertainties by inferring parameters with large variance.
Network parameters with low variance are fixed as deterministic.

Main Results:

FedSI demonstrates a simple and scalable approach to PFL.
The framework achieves fast and scalable inference while preserving systematic uncertainties.
Experiments show FedSI outperforms existing Bayesian and non-Bayesian federated learning baselines on heterogeneous datasets.

Conclusions:

FedSI offers an effective solution for uncertainty quantification in heterogeneous PFL.
The proposed framework balances efficiency, scalability, and accuracy in personalized federated learning.