Accuracy

Accuracy is measured as the closeness of a value to a desired value.

One example of accuracy measurement is the distance of values in relation to the mean of a probability density function:

Use Cases

For more details on true/false positives/negatives see: Confusion Matrix.

Binary Classification

A binary classification has only two classes. In this case, accuracy is calculated as the number of true results divided by the number of all results expressed as follows:

$\\A=\frac{TP+TN}{TP+TN+FP+FN} \\\\\mathrm{\textup{where:}} \\\\A\,\,\,\,\,\,\,\,\,\mathrm{\textup{accuracy}} \\TP\,\,\,\,\mathrm{\textup{number of true positive results}} \\TN\,\,\,\,\mathrm{\textup{number of true negative results}} \\FP\,\,\,\,\mathrm{\textup{number of false positive results}} \\FN\,\,\,\mathrm{\textup{number of false negative results}}$

Multiclass Classification

A multiclass classification has more than two classes. In this case, accuracy is calculated as the number of true results divided by the number of all results expressed as follows:

$\\A=\frac{T}{R} \\\\\mathrm{\textup{where:}} \\\\A\,\,\,\,\mathrm{\textup{accuracy}} \\T\,\,\,\,\mathrm{\textup{number of true results}} \\R\,\,\,\,\mathrm{\textup{number of all results}}$

The Accuracy Paradox

The accuracy paradox can occur when a model with high accuracy has low predictive value. For example, a model trained to predict financial fraud using training data with a very high proportion of non-fraud examples might have high accuracy in training results, but not be good at identifying fraud in real world predictions. In these cases, measures of Precision and Recall are better indicators of actual prediction accuracy.

Black Box Models and Inaccurate Results

Black Box refers to systems and Machine Learning models, such as Deep Learning Artificial Neural Networks, that can produce results not traceable through modeling processes.

Black Box model inaccurate results can be caused by factors such as:

insufficient model training data
malicious prediction data manipulation
edge cases in prediction inputs

An example is an image recognition model that produces an inaccurate classification due to a small object in front of an actual target object.

For an in-depth analysis related to computer vision, see: Analysis of Explainers of Black Box Deep Neural Networks for Computer Vision: A Survey