L1 and L2 Regularization Techniques to Prevent Overfitting in Machine Learning Models

Exploring L1 and L2 Regularization Techniques to Prevent Overfitting in Machine Learning Models.

[00:07](https://www.youtube.com/watch?v=I08SMeKDbqY&t=7) L1 and L2 regularization techniques manage model complexity.
- L1 regularization, or Lasso, uses the absolute value of coefficients to minimize error and perform feature selection.
- L2 regularization, or Ridge regression, squares the coefficients in the cost function to prevent overfitting while shrinking them.

[00:51](https://www.youtube.com/watch?v=I08SMeKDbqY&t=51) L2 regularization helps prevent overfitting in regression models.
- L2 regularization, or ridge regression, adjusts the cost function by adding a penalty for large weights.
- To combat overfitting, techniques like cross-validation and feature reduction are employed alongside regularization methods.

[01:32](https://www.youtube.com/watch?v=I08SMeKDbqY&t=92) Regularization penalizes complexity to improve model generalization.
- The regularization term adds a penalty to the loss function to prevent overfitting by controlling model complexity.
- Lambda, a hyperparameter, adjusts the penalty; high lambda values increase regularization, while zero makes it equivalent to ordinary least squares.

[02:13](https://www.youtube.com/watch?v=I08SMeKDbqY&t=133) Ridge regression reduces weights but is sensitive to outliers.
- Ridge regularization keeps weights small without driving them to zero, unlike L1 regularization.
- Outliers significantly inflate error due to squaring in ridge regression, impacting overall model robustness.

[02:51](https://www.youtube.com/watch?v=I08SMeKDbqY&t=171) R square measures the closeness of data to a regression line.
- R square, or coefficient of determination, quantifies how much of the variation in the response variable is explained by the linear model.

[03:31](https://www.youtube.com/watch?v=I08SMeKDbqY&t=211) R-squared indicates model quality and data fit.
- A higher R-squared value means a better fit of the model to the data and explains more variability of the response variable.
- The formula R-squared = 1 - (SS regression / SS total) reflects how well independent variables explain the response variable.

[04:08](https://www.youtube.com/watch?v=I08SMeKDbqY&t=248) Adjusted R-squared provides a better model evaluation than R-squared.
- Adding independent variables to a model always increases the R-squared value, even if they are irrelevant.
- Adjusted R-squared penalizes the R-squared value for including non-informative variables, offering a more accurate assessment of model performance.

[04:46](https://www.youtube.com/watch?v=I08SMeKDbqY&t=286) Mean Square Error measures the accuracy of regression predictions.
- MSE quantifies the distance between actual data points and the regression line by squaring the differences.
**L1 and L2 Regularization**
- **L1 Regularization (Lasso)**: Utilizes the absolute value of coefficients in its cost function, which can lead to some coefficients becoming exactly zero, effectively excluding certain features from the model. This method helps in feature selection and managing overfitting.

- **L2 Regularization (Ridge)**: Incorporates the square of coefficients in its cost function. It penalizes larger coefficients but does not eliminate them, thus ensuring that all features remain in the model while preventing overfitting.
- **Overfitting Mitigation**: Both regularization techniques aim to address the issue of overfitting by balancing model complexity and performance on unseen data through methods like cross-validation and feature reduction.

**Understanding R-Squared**

- **Definition**: R-squared, or the coefficient of determination, measures how well the independent variables explain the variability of the dependent variable in a regression model, usually expressed as a percentage ranging from 0% to 100%.

- **Limitations**: A significant issue with R-squared is that it can falsely indicate a better model fit simply by adding more independent variables, regardless of their relevance or impact. This can lead to misleading conclusions about model performance.

- **Adjusted R-Squared**: To overcome the limitations of R-squared, adjusted R-squared is used. This metric accounts for the number of predictors in the model, providing a more accurate measure of model quality by penalizing the inclusion of non-informative variables.

**Mean Square Error (MSE)**

- **Definition**: Mean Square Error quantifies how close the predicted values are to the actual values by averaging the squares of the differences between them. It serves as a key metric for evaluating the performance of regression models.

- **Calculation**: MSE is calculated by taking the average of the squared differences between the true values and the predicted values. This formulation emphasizes larger errors due to the squaring of the differences.

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