K-Fold Cross-Validation is a widely utilized method for estimating test errors in machine learning and statistics. The fundamental idea behind it is to randomly divide the dataset into K equal-sized parts or folds. One of these folds, denoted as “part K,” is set aside as a validation set, while the model is trained on the remaining K-1 folds (combined). Predictions are then generated for the left-out Kth fold. This process is iteratively repeated for each fold, where K can take values from 1 to the total number of folds, typically denoted as “n.” Finally, the results from each iteration are combined to obtain an overall estimate of the model’s performance.
It’s important to note that since each training set consists of only (K-1)/K of the original data, the estimates of prediction error may be biased upward. This bias tends to be minimized when K is equal to n, the total number of data points, but such an estimate can have high variance.
Bootstrapping, on the other hand, is a resampling technique used in statistics to estimate the sampling distribution of a statistic. It achieves this by repeatedly drawing random samples, with replacement, from the original dataset. This method is particularly useful when the population distribution is unknown or challenging to model.For example, consider a dataset containing products for hair of 60 types of hair . The bootstrapping process involves creating multiple bootstrap samples, each of the same size as the original dataset . The following steps are taken:
Randomly select data points from the original dataset with replacement to form each bootstrap sample.Calculate the desired statistic for each of these bootstrap samples. In our example, we compute the mean for each bootstrap sample.
Repeat the resampling process and statistic calculation a large number of times to generate a distribution of the statistic. This distribution represents the variability of the statistic under different random samples.The resulting bootstrap distribution can then be used to estimate confidence intervals or assess the variability of the statistic. For instance, one might compute a at most 95% confidence interval for the mean exam score based on the bootstrap distribution.