# Test set

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A test set is a set of data used in various areas of information science to assess the strength and utility of a predictive relationship. Test sets are used in artificial intelligence, machine learning, genetic programming and statistics. In all these fields, a test set has much the same role.

## Rationale

Regression analysis was one of the earliest such approaches to be developed. The data used to construct or discover a predictive relationship are called the training data set. Most approaches that search through training data for empirical relationships tend to overfit the data, meaning that they can identify apparent relationships in the training data that do not hold in general. A test set is a set of data that is independent of the training data, but that follows the same probability distribution as the training data. If a model fit to the training set also fits the test set well, minimal overfitting has taken place. If the model fits the training set much better than it fits the test set, overfitting is likely the cause.

In order to avoid overfitting, when any classification parameter needs to be adjusted, it is necessary to have a validation set in addition to the training and test sets. For example if the most suitable classifier for the problem is sought, the training set is used to train the candidate algorithms, the validation set is used to compare their performances and decide which one to take, and finally, the test set is used to obtain the performance characteristics such as accuracy, sensitivity, specificity, F-measure and so on. Another example of parameter adjustment is hierarchical classification (sometimes referred to as instance space decomposition [1]), which splits a complete multi-class problem into a set of smaller classiﬁcation problems. It serves for learning more accurate concepts due to simpler classiﬁcation boundaries in subtasks and individual feature selection procedures for subtasks. When doing classiﬁcation decomposition, the central choice is the order of combination of smaller classiﬁcation steps, called the classiﬁcation path. Depending on the application, it can be derived from the confusion matrix and, uncovering the reasons for typical errors and finding ways to prevent the system make those in the future. For example,[2] on the validation set one can see which classes are most frequently mutually confused by the system and then the instance space decomposition is done as follows: firstly, the classification is done among well recognizable classes, and the difficult to separate classes are treated as a single joint class, and finally, as a second classification step the joint class is classified into the two initially mutually confused classes.

## References

1. ^ Cohen S, Rokach L., Maimon O. Decision-tree instance-space decomposition with grouped gain-ratio In J. Information Sciences, vol. 177, issue 17, pp. 3592–3612. Elsevier. 2007.
2. ^ Sidorova, J., Badia, T. "ESEDA: tool for enhanced speech emotion detection and analysis". The 4th International Conference on Automated Solutions for Cross Media Content and Multi-Channel Distribution (AXMEDIS 2008). Florence, November, 17-19, pp. 257–260. IEEE press.

## Example

A training set (left) and a test set (right) from the same statistical population are shown as blue points. Two predictive models are fit to the training data. Both fitted models are plotted with both the training and test sets. In the training set, the MSE of the fit shown in orange is 4 whereas the MSE for the fit shown in green is 9. In the test set, the MSE for the fit shown in orange is 15 and the MSE for the fit shown in green is 13. The orange curve severely overfits the training data, since its MSE increases by almost a factor of four when comparing the test set to the training set. The green curve overfits the training data much less, as its MSE increases by less than a factor of 2.