1. Training Data Set

A training data set is a data set of examples used during the learning process and is used to fit the parameters (e.g., weights) of, for example, a classifier.^[1][2]

For classification tasks, a supervised learning algorithm looks at the training data set to determine, or learn, the optimal combinations of variables that will generate a good predictive model.^[3] The goal is to produce a trained (fitted) model that generalizes well to new, unknown data.^[4] The fitted model is evaluated using “new” examples from the held-out datasets (validation and test datasets) to estimate the model’s accuracy in classifying new data.^[5] To reduce the risk of issues such as over-fitting, the examples in the validation and test datasets should not be used to train the model.^[5]

Most approaches that search through training data for empirical relationships tend to overfit the data, meaning that they can identify and exploit apparent relationships in the training data that do not hold in general.

2. Validation Data Set

A validation data set is a data-set of examples used to tune the hyperparameters (i.e. the architecture) of a classifier. It is sometimes also called the development set or the "dev set".^[6] An example of a hyperparameter for artificial neural networks includes the number of hidden units in each layer.^[1][2] It, as well as the testing set (as mentioned above), should follow the same probability distribution as the training data set.

In order to avoid overfitting, when any classification parameter needs to be adjusted, it is necessary to have a validation data set in addition to the training and test datasets. For example, if the most suitable classifier for the problem is sought, the training data set is used to train the different candidate classifiers, the validation data set is used to compare their performances and decide which one to take and, finally, the test data set is used to obtain the performance characteristics such as accuracy, sensitivity, specificity, F-measure, and so on. The validation data set functions as a hybrid: it is training data used for testing, but neither as part of the low-level training nor as part of the final testing.

The basic process of using a validation data set for model selection (as part of training data set, validation data set, and test data set) is:^[2][7]

Since our goal is to find the network having the best performance on new data, the simplest approach to the comparison of different networks is to evaluate the error function using data which is independent of that used for training. Various networks are trained by minimization of an appropriate error function defined with respect to a training data set. The performance of the networks is then compared by evaluating the error function using an independent validation set, and the network having the smallest error with respect to the validation set is selected. This approach is called the hold out method. Since this procedure can itself lead to some overfitting to the validation set, the performance of the selected network should be confirmed by measuring its performance on a third independent set of data called a test set.

An application of this process is in early stopping, where the candidate models are successive iterations of the same network, and training stops when the error on the validation set grows, choosing the previous model (the one with minimum error).

3. Test Data Set

A test data set is a data set that is independent of the training data set, but that follows the same probability distribution as the training data set. If a model fit to the training data set also fits the test data set well, minimal overfitting has taken place (see figure below). A better fitting of the training data set as opposed to the test data set usually points to over-fitting.

A test set is therefore a set of examples used only to assess the performance (i.e. generalization) of a fully specified classifier.^[1][2] To do this, the final model is used to predict classifications of examples in the test set. Those predictions are compared to the examples' true classifications to assess the model's accuracy.^[3]

In a scenario where both validation and test datasets are used, the test data set is typically used to assess the final model that is selected during the validation process. In the case where the original data set is partitioned into two subsets (training and test datasets), the test data set might assess the model only once (e.g., in the holdout method).^[8] Note that some sources advise against such a method.^[4] However, when using a method such as cross-validation, two partitions can be sufficient and effective since results are averaged after repeated rounds of model training and testing to help reduce bias and variability.^[4][5]

4. Confusion in Terminology

Testing is trying something to find out about it ("To put to the proof; to prove the truth, genuineness, or quality of by experiment" according to the Collaborative International Dictionary of English) and to validate is to prove that something is valid ("To confirm; to render valid" Collaborative International Dictionary of English). With this perspective, the most common use of the terms test set and validation set is the one here described. However, in both industry and academia, they are sometimes used interchanged, by considering that the internal process is testing different models to improve (test set as a development set) and the final model is the one that needs to be validated before real use with an unseen data (validation set). "The literature on machine learning often reverses the meaning of 'validation' and 'test' sets. This is the most blatant example of the terminological confusion that pervades artificial intelligence research.^[9] Nevertheless, the important concept that must be kept is that the final set, whether called test or validation, should only be used in the final experiment.

5. Cross-validation

In order to get more stable results and use all valuable data for training, a data set can be repeatedly split into several training and a validation datasets. This is known as cross-validation. To validate the model performance, an additional test data set held out from cross-validation is normally used.

The content is sourced from: https://handwiki.org/wiki/Training,_validation,_and_test_sets