Validation for Machine Learning with Python

The k-fold cross-validation procedure is used to estimate the performance of machine learning models when making predictions on data not used during training.

This procedure can be used both when optimizing the hyperparameters of a model on a dataset, and when comparing and selecting a model for the dataset. When the same cross-validation procedure and dataset are used to both tune and select a model, it is likely to lead to an optimistically biased evaluation of the model performance.

One approach to overcoming this bias is to nest the hyperparameter optimization procedure under the model selection procedure. This is called double cross-validation or nested cross-validation and is the preferred way to evaluate and compare tuned machine learning models.

In this tutorial, you will discover nested cross-validation for evaluating tuned machine learning models.

After completing this tutorial, you will know:

  • Hyperparameter optimization can overfit a dataset and provide an optimistic evaluation of a model that should not be used for model selection.
  • Nested cross-validation provides a way to reduce the bias in combined hyperparameter tuning and model selection.
  • How to implement nested cross-validation for evaluating tuned machine learning algorithms in scikit-learn.

Let’s get started.

Nested Cross-Validation for Machine Learning with PythonNested Cross-Validation for Machine Learning with Python

Tutorial Overview

This tutorial is divided into three parts; they are:

  1. Combined Hyperparameter Tuning and Model Selection
  2. What Is Nested Cross-Validation
  3. Nested Cross-Validation With Scikit-Learn

Combined Hyperparameter Tuning and Model Selection

It is common to evaluate machine learning models on a dataset using k-fold cross-validation.

The k-fold cross-validation procedure divides a limited dataset into k non-overlapping folds. Each of the k folds is given an opportunity to be used as a held back test set whilst all other folds collectively are used as a training dataset. A total of k models are fit and evaluated on the k holdout test sets and the mean performance is reported.

For more on the k-fold cross-validation procedure, see the tutorial:

The procedure provides an estimate of the model performance on the dataset when making a prediction on data not used during training. It is less biased than some other techniques, such as a single train-test split for small- to modestly-sized dataset. Common values for k are k=3, k=5, and k=10.

Each machine learning algorithm includes one or more hyperparameters that allow the algorithm behavior to be tailored to a specific dataset. The trouble is, there is rarely if ever good heuristics on how to configure the model hyperparameters for a dataset. Instead, an optimization procedure is used to discover a set of hyperparameters that perform well or best on the dataset. Common examples of optimization algorithms include grid search and random search, and each distinct set of model hyperparameters are typically evaluated using k-fold cross-validation.

This highlights that the k-fold cross-validation procedure is used both in the selection of model hyperparameters to configure each model and in the selection of configured models.

The k-fold cross-validation procedure is an effective approach for estimating the performance of a model. Nevertheless, a limitation of the procedure is that if it is used multiple times with the same algorithm, it can lead to overfitting.

Each time a model with different model hyperparameters is evaluated on a dataset, it provides information about the dataset. Specifically, an often noisy model performance score. This knowledge about the model on the dataset can be exploited in the model configuration procedure to find the best performing configuration for the dataset. The k-fold cross-validation procedure attempts to reduce this effect, yet it cannot be removed completely, and some form of hill-climbing or overfitting of the model hyperparameters to the dataset will be performed. This is the normal case for hyperparameter optimization.

The problem is that if this score alone is used to then select a model, or the same dataset is used to evaluate the tuned models, then the selection process will be biased by this inadvertent overfitting. The result is an overly optimistic estimate of model performance that does not generalize to new data.

A procedure is required that allows both the models to select well-performing hyperparameters for the dataset and select among a collection of well-configured models on a dataset.

One approach to this problem is called nested cross-validation.

What Is Nested Cross-Validation

Nested cross-validation is an approach to model hyperparameter optimization and model selection that attempts to overcome the problem of overfitting the training dataset.

In order to overcome the bias in performance evaluation, model selection should be viewed as an integral part of the model fitting procedure, and should be conducted independently in each trial in order to prevent selection bias and because it reflects best practice in operational use.

— On Over-fitting in Model Selection and Subsequent Selection Bias in Performance Evaluation, 2010.

The procedure involves treating model hyperparameter optimization as part of the model itself and evaluating it within the broader k-fold cross-validation procedure for evaluating models for comparison and selection.

As such, the k-fold cross-validation procedure for model hyperparameter optimization is nested inside the k-fold cross-validation procedure for model selection. The use of two cross-validation loops also leads the procedure to be called “double cross-validation.”

Typically, the k-fold cross-validation procedure involves fitting a model on all folds but one and evaluating the fit model on the holdout fold. Let’s refer to the aggregate of folds used to train the model as the “train dataset” and the held-out fold as the “test dataset.”

Each training dataset is then provided to a hyperparameter optimized procedure, such as grid search or random search, that finds an optimal set of hyperparameters for the model. The evaluation of each set of hyperparameters is performed using k-fold cross-validation that splits up the provided train dataset into k folds, not the original dataset.

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Validation for Machine Learning with Python
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