What are training set, validation set and test set?

这三个名词在机器学习领域的文章中极其常见，但很多人对他们的概念并不是特别清楚，尤其是后两个经常被人混用。Ripley, B.D（1996）在他的经典专著Pattern Recognition and Neural Networks中给出了这三个词的定义。



Training set: A set of examples used for learning, which is to fit the parameters [i.e., weights] of the classifier.



Validation set: A set of examples used to tune the parameters [i.e., architecture, not weights] of a classifier, for example to choose the number of hidden units in a neural network.



Test set: A set of examples used only to assess the performance [generalization] of a fully specified classifier.

显然，training set是用来训练模型或确定模型参数的，如ANN中权值等； validation set是用来做模型选择（model selection），即做模型的最终优化及确定的，如ANN的结构；而 test set则纯粹是为了测试已经训练好的模型的推广能力。当然，test set这并不能保证模型的正确性，他只是说相似的数据用此模型会得出相似的结果。



但实际应用中，一般只将数据集分成两类，即training set 和test set，大多数文章并不涉及validation set。 Ripley还谈到了Why separate test and validation sets?

1. The error rate estimate of the final model on validation data will be biased (smaller than the true error rate) since the validation set is used to select the final model.

2. After assessing the final model with the test set, YOU MUST NOT tune the model any further.

It is rarely useful to have a NN simply memorize a set of data, since memorization can be done much more efficiently by numerous algorithms for table look-up. Typically, you want the NN to be able to perform accurately on new data, that is, to generalize. There
seems to be no term in the NN literature for the set of all cases that you want to be able to generalize to. Statisticians call this set the "population". Tsypkin (1971) called it the "grand truth distribution," but this term has never caught on. Neither is
there a consistent term in the NN literature for the set of cases that are available for training and evaluating an NN. Statisticians call this set the "sample". The sample is usually a subset of the population. (Neurobiologists mean something entirely different
by "population," apparently some collection of neurons, but I have never found out the exact meaning. I am going to continue to use "population" in the statistical sense until NN researchers reach a consensus on some other terms for "population" and "sample";
I suspect this will never happen.) In NN methodology, the sample is often subdivided into "training", "validation", and "test" sets.

The distinctions among these subsets are crucial, but the terms "validation" and "test" sets are often confused. Bishop (1995), an indispensable reference on neural networks, provides the following explanation (p. 372): 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.



And there is no book in the NN literature more authoritative than Ripley (1996), from which the following definitions are taken (p.354):

Training set: A set of examples used for learning that is to fit the parameters [i.e., weights] of the classifier.

Validation set: A set of examples used to tune the parameters [i.e., architecture, not weights] of a classifier, for example to choose the number of hidden units in a neural network.

Test set: A set of examples used only to assess the performance [generalization] of a fully-specified classifier.

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. The crucial point is that a test set, by the standard
definition in the NN literature, is never used to choose among two or more networks, so that the error on the test set provides an unbiased estimate of the generalization error (assuming that the test set is representative of the population, etc.). Any data
set that is used to choose the best of two or more networks is, by definition, a validation set, and the error of the chosen network on the validation set is optimistically biased. There is a problem with the usual distinction between training and validation
sets. Some training approaches, such as early stopping, require a validation set, so in a sense, the validation set is used for training. Other approaches, such as maximum likelihood, do not inherently require a validation set. So the "training" set for maximum
likelihood might encompass both the "training" and "validation" sets for early stopping. Greg Heath has suggested the term "design" set be used for cases that are used solely to adjust the weights in a network, while "training" set be used to encompass both
design and validation sets. There is considerable merit to this suggestion, but it has not yet been widely adopted.



参考：

http://www.cppblog.com/guijie/archive/2008/07/29/57407.html

http://www.faqs.org/faqs/ai-faq/neural-nets/part1/