**K-Fold Cross-Validation:**K-fold cross-validation and cross-validation are techniques used in machine learning and statistics to assess the performance of a predictive model and to reduce the risk of overfitting. They both involve splitting a dataset into multiple subsets, training and evaluating the model on different subsets, and then aggregating the results. However, they have some differences in how they achieve this.

- K-fold cross-validation is a technique where the dataset is divided into K equally sized folds or subsets.
- The model is trained and evaluated K times, with each fold serving as the test set once while the remaining K-1 folds are used for training.
- The results from the K iterations are typically averaged to obtain a single performance metric, such as accuracy or mean squared error.
- This technique helps in assessing how well a model generalizes to different subsets of data and reduces the risk of overfitting since the model is evaluated on different data partitions.Example: In 5-fold cross-validation, the dataset is split into 5 subsets, and the model is trained and tested on each subset separately.

**Estimating Prediction Error:**Estimating prediction error and the validation set approach are important concepts in the context of model evaluation and selection in machine learning. They are used to assess how well a predictive model is likely to perform on unseen data. Let’s explore these concepts:

- The prediction error of a machine learning model refers to how well the model’s predictions match the true values in the dataset.
- The primary goal of estimating prediction error is to understand how well the model generalizes to new, unseen data. A model that performs well on the training data but poorly on new data is said to have high prediction error, indicating overfitting.
- There are various techniques to estimate prediction error, including cross-validation, which we discussed earlier, as well as techniques like bootstrapping.
- Common metrics used to measure prediction error include mean squared error (MSE) for regression problems and accuracy, precision, recall, F1-score, etc., for classification problems.