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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...

Confidence Coefficient

Confidence Coefficient

The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under...

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.

Weighted Mean

Weighted Mean

While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...

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.

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...

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An R-Based Landscape Validation of a Competing Risk Model

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Published on: September 16, 2022

Uncertainty-Adjusted Recommendation via Matrix Factorization With Weighted Losses.

Rodrigo Alves, Antoine Ledent, Marius Kloft

IEEE Transactions on Neural Networks and Learning Systems

|July 11, 2023

Summary

This summary is machine-generated.

This study introduces a novel matrix factorization method for recommender systems (RSs) that accounts for rating uncertainty. By weighting uncertain ratings, the approach improves prediction accuracy on noisy datasets.

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Machine Learning Algorithms for Early Detection of Bone Metastases in an Experimental Rat Model

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Published on: August 16, 2020

Area of Science:

Computer Science
Machine Learning

Background:

Recommender systems (RSs) often face noisy user ratings.
Unequal noise levels can stem from user behavior or item divisiveness.
This noise can mislead standard matrix factorization models.

Purpose of the Study:

To develop a nuclear-norm-based matrix factorization method that incorporates rating uncertainty.
To improve the robustness and accuracy of recommender systems by down-weighting noisy ratings.

Main Methods:

A nuclear-norm-based matrix factorization approach was employed.
Side information in the form of rating uncertainty estimates was utilized.
An adjusted trace norm regularizer was introduced to handle weighted loss functions.

Main Results:

The proposed method demonstrated state-of-the-art performance on synthetic and real-world datasets.
Performance improvements were observed across various evaluation metrics.
The effective use of auxiliary uncertainty information was confirmed.

Conclusions:

Incorporating rating uncertainty into matrix factorization significantly enhances recommender system performance.
The adjusted trace norm regularization effectively handles weighted loss, maintaining theoretical guarantees.
This approach offers a robust solution for dealing with noisy data in recommender systems.