Скачать или смотреть Lasso Regression in Machine Learning

1. **Linear Regression Background**: Linear regression is a fundamental supervised learning algorithm used for modeling the relationship between a dependent variable and one or more independent variables. The model assumes a linear relationship between the independent variables and the dependent variable.

2. **Regularization**: Regularization is a technique used to prevent overfitting by adding a penalty term to the loss function. It discourages overly complex models by penalizing large coefficients. There are two commonly used types of regularization in linear regression: L1 regularization (Lasso) and L2 regularization (Ridge).

3. **Lasso Regression (L1 Regularization)**:
In Lasso regression, the penalty term added to the loss function is the sum of the absolute values of the coefficients multiplied by a regularization parameter (λ).
The L1 penalty encourages sparsity by shrinking some coefficients to exactly zero. This means that some features are completely ignored in the model, effectively performing feature selection.
The objective function of Lasso regression is the sum of the squared differences between the observed and predicted values (ordinary least squares) plus the sum of the absolute values of the coefficients multiplied by the regularization parameter:
```
Loss = OLS Loss + λ * Σ|βi|
```
where βi represents the coefficients, and λ controls the strength of the regularization.
By tuning the regularization parameter λ, you can control the amount of shrinkage applied to the coefficients. A larger λ results in more shrinkage and more coefficients being pushed to zero.

4. **Advantages of Lasso Regression**:
Feature Selection: Lasso regression automatically selects a subset of relevant features by setting some coefficients to zero. This can improve model interpretability and reduce overfitting, especially in high-dimensional datasets with many irrelevant features.
Handles Multicollinearity: Lasso can handle multicollinearity (high correlation between independent variables) by selecting one of the correlated variables and setting the coefficients of others to zero.
Simplicity: Lasso produces simpler models with fewer features, making them easier to understand and interpret.

5. **Disadvantages of Lasso Regression**:
It tends to arbitrarily select one variable from a group of correlated variables and shrink the others to zero. This can lead to instability and inconsistency in variable selection.
If the number of predictors (features) is larger than the number of observations, Lasso may select at most n features (where n is the number of observations), making the model underdetermined.
Choosing the optimal regularization parameter (λ) can be challenging and may require cross-validation.

Overall, Lasso regression is a powerful technique for feature selection and regularization in linear regression models, particularly when dealing with high-dimensional data or when interpretability is important. It strikes a balance between model simplicity and predictive accuracy by penalizing the absolute size of the coefficients.
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