## Cross-validation

Cross-validation is a statistical technique used to estimate the accuracy of machine learning models. It is often used in settings where the goal is prediction, and one wants to estimate how accurately a model will perform in practice. In cross-validation, a dataset is divided into a training set and a test set.

### Holdout method

The holdout method is the simplest way to do cross-validation. You randomly split the dataset into a training set and a test set. You train on the training set and evaluate on the test set. The advantage of this method is that it is computationally fast. The disadvantage is that it can have high variance, meaning that the results you get from different splits of the data can vary greatly.

Other cross-validation methods include:

-K-fold cross-validation: Split the dataset into K folds (typically K=10). For each fold, train on K-1 folds and test on the remaining fold. This gives you K results. Average them together to get a final estimate.

-Leave-one-out cross-validation: This is similar to k-fold cross validation, except you only use one fold for testing and all other folds for training (i.e., you train on N-1 data points and test on the remaining one). This obviously requires more computational effort than k-fold cross validation, but can sometimes give more accurate results.

-Stratified k-fold cross validation: This method is used when your data are not evenly distributed across classes (e.g., if you have many more positive examples than negative examples). In stratified k-fold cross validation, you split the data such that each fold contains a roughly equal percentage of each class.

### k-fold cross-validation

k-fold cross-validation is a model validation technique for assessing how the results of a statistical analysis will generalize to an independent data set. The data set is divided into k subsets, and the holdout method is repeated k times. Each time, one of the k subsets is used as the test set and the other k-1 subsets are put together as a training set. Then the average over all k trials is computed.

The advantage of this method is that all observations are used for both training and validation, and each observation is used for validation exactly once. The disadvantage of this method is that the training set size is reduced by a factor of 1/k.

Other cross-validation techniques include:

-Leave-one-out cross-validation: This technique consists of using all but one observation from the data set to train the model, and then using only that one remaining observation to validate it. This process is repeated until every observation in the data set has been used to validate the model at least once. The advantage of this technique over k-fold cross-validation is that it makes use of all available data for both training and validation, so no data goes unused. The disadvantage of this technique is that it can be computationally expensive if you have a largedata set.

-Holdout cross-validation: This technique consists of randomly splitting your data set into a training set and a validation set, then training your model on the training set and evaluating it on the validation set. The advantage of this technique over k-fold crossValidationis that you can use a larger proportionof your data for training, since you don’t have to split it up into multiple folds. The disadvantageis that if you split your data randomly, there’s a chancethat your trainingand validate sets might not be representativeof the overallpopulation, which could lead to inaccurate results.

### Leave-one-out cross-validation

Leave-one-out cross-validation (LOOcv) is a type of cross-validation. It is also known as the leave-one-sample-out cross-validation.

LOOcv works by splitting the data set into two sets: a training set and a test set. The training set contains all of the data except for one sample, which is reserved for testing. The model is then fit on the training set and tested on the test set. This process is repeated until each sample in the data set has been used as a test set.

The advantage of LOOcv is that it is very efficient; all of the data are used to train the model and all of the data are used to test the model. The disadvantage of LOOcv is that it can be quite sensitive to outliers; if there are any outliers in the data, they will be magnified when LOOcv is used.

### Bootstrap

Bootstrap is a resampling technique used to estimate statistics when data are limited or unavailable. The bootstrap was introduced by Efron (1979) as a computer-based method for estimating the standard error of a statistic. In simple terms, the bootstrap can be thought of as a method for generating new data from existing data. Although the bootstrap is usually applied to estimate measures of variability (e.g., standard error,confidence intervals), it can be used to estimate any statistic.

The basic idea behind the bootstrap is to randomly select observations with replacement from the original sample. This generates a new sample that can be used to estimate the statistic of interest. The process is repeated a number of times (e.g., 100) to generate a distribution of estimates. The Bootstrap distribution can then be used to compute measures such as bias, variance and confidence intervals.

## Which of the following is not a cross validation technique?

There are several cross validation techniques that are commonly used, but not all of them are created equal. Some of the most popular cross validation techniques include the holdout method, k-fold cross validation, and leave-one-out cross validation.

### Random sampling

Cross validation is a model validation technique that is used to assess the performance of a machine learning model on a new data set. There are several different types of cross validation, but the most common is k-fold cross validation. In k-fold cross validation, the data set is divided into k subsets, and the model is trained and evaluated k times, each time using a different subset as the test set. The final performance score is then averaged over all k runs.

Other cross validation techniques include leave-one-out cross validation and bootstrap cross validation.

### Monte Carlo simulation

Monte Carlo simulation is a cross validation technique used to generate new points in a space by randomly sampling from a probability distribution. This technique can be used to generate new data points for a regression or classification model, or to generate new points in a space for clustering.

### Cross-validation

Cross-validation is a statistical method used to estimate the performance of machine learning models. It is often used in conjunction with other techniques such as data partitioning and bootstrapping. Cross-validation is a Generalization of the Validation Set Approach.

There are several types of cross-validation, including:

-k-fold cross-validation

-Leave-one-out cross-validation

-Holdout method

### None of the above

None of the above