Evaluation Metrics for Machine Learning Models

Machine learning practitioners spend much of their time trying different models, different settings, and different parameter values. At the end of that work they still need to answer one question: how well will the chosen model perform on new data it has never seen? Two tools exist to answer that question, cross-validation and a held-out test set. They are the everyday instruments for evaluating and improving learning algorithms, and they are easy to misuse.

The central point of this article is that the way the data is divided determines whether the score you report can be trusted. Two parts of the same dataset can look identical in a spreadsheet, yet one part can be used to make decisions and the other must stay out of them. Keeping that distinction clear is what makes an evaluation honest.

The source makes two claims that work together. First, cross-validation, or the use of a test set, is what allows us to estimate how a machine learning model will perform in the future. Second, if the test set or cross-validation is also used to choose a model or to choose model parameters, the test data gets used up. Once that happens, the same data can no longer give a fair picture of future performance.

The reason is that a selection step is itself a search. Each time you compare candidates on a dataset and keep the winner, you let that dataset influence the final choice. The more candidates you compare, the more likely it is that one of them looks good on that particular data for reasons that will not carry over to new data. If you then measure the winner on the same data, you are measuring a score that was partly shaped by the choice itself. This is why the source describes the resulting estimates as overly optimistic.

To avoid using up the test data, the source recommends splitting the available data into three parts, each with a separate purpose. The training data is used for model building: the model learns its patterns from it. The validation data is used for model and parameter selection: you compare candidate models and settings on it. The test data is used for model evaluation: you measure the final chosen model once, to estimate how it will perform in the future. Keeping these roles separate is what protects the final estimate.

Read this as a division of labor rather than a sequence of copies. The three parts do not overlap, and each one answers a different question. The training part answers what the model should learn. The validation part answers which model or parameter setting to keep. The test part answers how good the kept model really is. Because the test part was never consulted while making choices, its score is not contaminated by those choices.

The three-way split is the simple version. The source points out that each of these splits can be replaced with cross-validation. Cross-validation is therefore not a competitor to the three-set idea. It is a way of carrying out the same roles with a more thorough use of the data, because every part of the data takes a turn serving in the evaluation role rather than being set aside once for a single split.

In the diagram, the data is divided into four slices. In each round, one slice is held out for validation and the others are used for training. The held-out slice changes from round to round, so every slice is used for validation exactly once. The validation results from the rounds are then used to compare candidate models and settings, which is the selection role described above.

The most commonly used arrangement, according to the source, has two layers. One split divides the data into a training set and a test set, and the test set is used for model evaluation. Within the training set, cross-validation is used for model and parameter selection. The outer split protects the final estimate, and the inner cross-validation handles the choices. The test set stays untouched until the very end, while the training set is reused, through cross-validation, to decide which model and settings to keep.