What Is Cross-Validation in Statistics? Definition With Example

Cross validation is an important concept in statistics that is commonly used in the development of models and predictions. It is the process of evaluating the accuracy of a model by splitting the input data into two sets: a training set and a testing set. The model is trained using the training set and then tested using the testing set. This ensures that the model can accurately predict future results as it has been tested on data that has not been used during training. Cross validation is a valuable tool as it reduces overfitting, which can lead to overly optimistic results. It is also useful for selecting parameters for a model, such as the number of neighbors used in k-nearest neighbors algorithm or the complexity of a decision tree. In this blog post, we will discuss what cross validation is and why it is important in the context of statistical modeling. We will also provide an example of cross validation in action and discuss the different types of cross validation techniques.

Why is it important to learn about cross-validation in statistics?

Cross-validation aids statisticians in developing precise predictive models that can be used to develop software and other everyday technology. Accuracy is important for helping create more helpful technology. For instance, the owner of a fresh produce business might hire a statistician to use various software to estimate how much produce will ripen fully or how much will spoil before it can be sold. They can create more accurate budgets and business plans if the software can make accurate predictions.

What is cross-validation in statistics?

Cross-validation is a technique for evaluating a testing model’s reliability. Statisticians typically employ one of several testing models when analyzing data. Cross-validation most often involves models that use data for prediction.

They withhold some of their data and do not test it in order to cross-validate the model they have chosen. The initial data set, also known as the training set, is used by statisticians to train their predictive model. The testing or validation set of data is the reserved set of data. Later, the statisticians can use the testing set in the model and contrast the outcomes with those from their training set. This enables them to evaluate the models’ predictions’ accuracy using various pieces of data. They can also gauge a digital model’s capacity to learn from data.

For statisticians and other professionals who use the tested models, cross-validation has many benefits. The majority of these benefits are related to how cross-validation uses its data to boost predictive accuracy. Some of the top advantages of using cross-validation include:

Tests large and small data sets

Statistics professionals can use cross-validation to test various data set sizes because it has a variety of methods. For instance, the majority of methods can be used to test models with any amount of data, but the k-fold method is particularly good at computing small data sets. This enables statisticians to test their models using any available data.

Uses data efficiently

Data is used in cross-validation to both train and test models. This enables statisticians to create more precise models with the data they already have. When developing and enhancing predictive models, this effectiveness can help save both time and money.

Offers more metrics

The majority of cross-validation techniques include several test phases, each of which provides results. This provides the statistician with numerous opportunities to assess the precision of the predictions made by their models. Having more metrics to examine can assist statisticians in identifying and resolving problems with their model, which can enhance its accuracy.

Types of cross-validation in statistics

Exhaustive cross-validation and non-exhaustive cross-validation are the two types of cross-validation used in statistics. The two types each have their own subtypes. Here are the details of each:

1. Exhaustive cross-validation

The data is split up into all possible combinations of training and testing sets by exhaustive cross-validation. There are multiple primary sub-types of exhaustive cross-validation. Some common methods are:

This sub-type uses that amount of data as its training set after setting a value to p greater than one. All remaining data is its testing set. This process iterates until it uses all possible combinations of data that equal p.

The leave-p-out method, where p = 1, is modified by the LOO CV. This model continues until the statistician has tested each individual data set, one data set at a time. This model’s potential to produce less biased results is a plus.

2. Non-exhaustive cross-validation

Although not in every possible combination, a non-exhaustive cross-validation still divides its data. Instead, most non-exhaustive methods create larger subsets, usually at random. Some of the most common non-exhaustive cross-validation methods include:

The k-fold method divides data into k subsets at random. The remaining subsets work together as the training set, with each subset having an equal number of data sets and rotating as the testing set. This method continues until the statistician tests each subset.

With this technique, the data is randomly split into a training set and a testing set. These two sets are the only ones used in this method to achieve the objectives. The statistician first trains the model before testing it once.

The subsets of the data are randomly divided using the Monte Carlo method, and the process is repeated. All used data is returned to the data set after each testing set phase. Then, the data divides into random subsets again. Because of this, statisticians may use some data more frequently while using other data less frequently or never.

Cross-validation can also have some disadvantages. Knowing them can assist statisticians in anticipating or resolving problems. Some common disadvantages of using cross-validation include:

Takes a lot of time

Most cross-validation methods involve performing many tests. Each of these tests takes time to perform. The exhaustive type of some cross-validation techniques can take a long time to complete. Consider scheduling additional time to complete your tests if you intend to use cross-validation to help you meet your deadline.

Increases computing costs

Computers can help test the models with cross-validation. Using some techniques, such as the LOO CV method, can require a lot of computing power. These computers can be very expensive to buy, set up, and maintain. Some statisticians might have access to the computing power needed. Those who don’t might think twice about starting their project with a larger budget.

Doesnt account for randomization

Randomizing is part of many cross-validation methods. Sometimes, random data sets can be too similar or too different. In some techniques, randomization can mean that not all data collected is used. Any of these circumstances could stop the model from improving in accuracy. Predictive model testers can assess the data sets used to ascertain whether they may have impacted the outcomes of their tests.

Example of cross-validation

Here is an illustration of how the cross-validation procedure might appear: With a set of 10 pieces of data, the k-fold method is used in this illustration. These numbers represent the data:

3, 5, 9, 2, 0, 4, 3, 6, 8, 5

k = 5

Since the method uses equal subsets, k can equal five. Accordingly, there are five equal subsets, each with two data sets. Divide the groups randomly. The five subsets might look like this:

Fold 1: [9, 4]

Fold 2: [5, 3]

Fold 3: [8, 2]

Fold 4: [0, 5]

Fold 5: [6, 3]

You can use these subsets to train many models. You can let each subset alternate as the test set when evaluating the accuracy of a model using all five, as in the following example:

Test one: Practice with folds 1, 2, 3, 4, and 5 before taking the test.

Test two: Practice folds 1, 2, 3, and 5 before taking the fold 4 test.

Train with folds 1, 2, 4, and 5 before taking the third test.

Test four: Practice folds 1, 3, 4, and 5 before taking the fold 2 test.

Test number five: Practice with folds 2, 3, 4, 5, and 1 before the test.

Put the training subsets into each test, then note the outcomes. Then, input the testing subset and record those results. You have a list of your training and test results after completing all five tests. To determine how accurate the model is, you can compare these. Then, you can compile a report of your findings to assist in explaining the model’s accuracy to your coworkers.