K-Fold Cross Validation on Diabetes dataset

1. Model Training (Pre k-fold):
   • A polynomial regression model of degree 2 was trained on the entire dataset.
   • The Mean Squared Error (MSE) was calculated on the entire dataset to obtain a pre k-fold error estimate of 0.326
2. Cross-validation (Post k-fold):
   • K-fold cross-validation with = 5k was applied to the entire dataset to obtain a more robust estimate of the model’s performance.
   • The average MSE across the 5 folds was calculated to obtain a post k-fold error estimate of 0.364

Results and Discussion:

• The pre k-fold error was lower compared to the post k-fold error (0.326 vs 0.364). This suggests that the model may have initially overfit to the specific structure of the entire dataset.
• The post k-fold error, which is higher, indicates a more realistic estimate of the model’s performance across different subsets of the data. This suggests that the model’s performance has some variance across different subsets of the data.
• K-fold cross-validation provides a more robust and conservative estimate of the model’s performance, which is crucial for understanding the model’s generalisation ability.

The increase in error from pre k-fold to post k-fold does not necessarily indicate that k-fold cross-validation is not good for this data. Instead, it provides a more realistic estimate of the model’s performance across different subsets of the data. Here are a few points to consider:

1. Overfitting:
   • Without cross-validation, the model might be overfitting to the specific structure of the entire dataset. The lower error in the pre k-fold scenario might be because the model has learned the noise in the data rather than the underlying pattern.
2. Robustness:
   • Cross-validation provides a more robust estimate of the model’s performance. It does this by training and evaluating the model on different subsets of the data, which gives a better understanding of how the model performs across a variety of data scenarios.
3. Variance:
   • The higher error in the post k-fold scenario suggests that the model’s performance has some variance across different subsets of the data. This is valuable information as it indicates that the model’s performance is not consistent across the dataset.
4. Generalisation:
   • Cross-validation helps to assess the model’s ability to generalize to unseen data, which is crucial for building models that perform well in real-world scenarios.
5. Better Model Selection:
   • Cross-validation can be particularly useful in model selection, where different models or hyper parameters are being compared. It provides a more reliable basis for choosing the model that is likely to perform best on unseen data.

Conclusion: The analysis illustrates the importance of cross-validation in providing a more reliable estimate of model performance. Although the post k-fold error was higher, it offers a more realistic insight into how well the model may perform across various data scenarios, thus underscoring the value of cross-validation in model evaluation and selection.