Cross-Validation and The Bootstrap

Cross-validation and bootstrap are two commonly used techniques in statistics and machine learning for assessing the performance of models and estimating parameters. 

Cross-validation is a resampling technique used to evaluate machine learning models on a limited data sample. It involves splitting the dataset into training and validation sets, where the model is trained on the training set and then evaluated on the validation set. This process is repeated multiple times, with different subsets of the data used for training and validation. Common types of cross-validation include k-fold cross-validation, leave-one-out cross-validation, and stratified k-fold cross-validation.

  • K-fold cross-validation: The data is divided into k subsets, and the model is trained and validated k times, with each subset used as the validation data once.
  • Leave-one-out cross-validation (LOOCV): Each observation is used as the validation set once while the rest of the data forms the training set.
  • Stratified k-fold cross-validation: Data is divided into k folds, ensuring that each fold has a similar distribution of the target variable.

Bootstrap is a resampling technique that involves random sampling with replacement from the original dataset to create new samples of the same size. This technique is often used for estimating the sampling distribution of a statistic like mean or variance, or for constructing confidence intervals.

The key steps in bootstrap resampling are:

  • Sample with replacement: Randomly select observations from the original dataset with replacement to create a bootstrap sample of the same size as the original dataset.
  • Calculate statistic: Calculate the statistic of interest (e.g., mean, median, standard deviation) on the bootstrap sample.
  • Repeat: Repeat the above steps a large number of times to create a bootstrap distribution of the statistic.

Bootstrap is particularly useful when the underlying distribution of the data is unknown or when you want to estimate the sampling distribution of a statistic without making strong assumptions about the data.

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