LASSO Regression: A Complete Understanding (2021)

Ajay Ohri
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Introduction

Linear regression and logistic regression are the two frequently used terms when we talk about regression. But there are other types of regression that have their relevance. Lasso regression, Ridge regression, Polynomial regression, Stepwise regression, and Elastic net regression are the other types of regressions. In this blog, we will focus on Lasso regression. The increasing polynomials in the equation made for regression models lead to overfitting. To cope up with overfitting, regularization techniques are utilized.

1. Understanding Lasso Regression

The full form of LASSO is the Least Absolute Shrinkage and Selection Operation. As the name suggests, LASSO uses the “shrinkage” technique in which coefficients are determined, which get shrunk towards the central point as the mean.

The LASSO regression in regularization is based on simple models that posses fewer parameters. We get a better interpretation of the models due to the shrinkage process. The shrinkage process also enables the identification of variables strongly associated with variables corresponding to the target.

2. What is Regularization?

Regularization resolves the overfitting problem, which affects the accuracy level of the model. Regularization is executed by the addition of the “penalty” term to the best-fit equation produced by the trained data. This technique can be effectively used to minimize the number of variables to maintain them in the model. Regularization can cater to various purposes, such as understanding simpler models that include sparse and group structure models.

3. Regularization Techniques

There are two important techniques in the regularization, which are Ridge Regression and Lasso Regression model. Both techniques are utilized to reduce the complexity of the model.  The techniques are similar except in terms of penalty term since the lasso regression uses absolute weighs, whereas ridge regression uses the square of weighs.

4. What is LASSO Regression?

Lasso regression is also called Penalized regression method. This method is usually used in machine learning for the selection of the subset of variables. It provides greater prediction accuracy as compared to other regression models. Lasso Regularization helps to increase model interpretation.

The less important features of a dataset are penalized by the lasso regression. The coefficients of this dataset are made zero leading to their elimination. The dataset with high dimensions and correlation is well suited for lasso regression.

• Lasso Regression Formula:

D= Residual Sum of Squares or Least Squares Lambda * Aggregate of  absolute values of coefficients

Lambda denotes the amount of shrinkage in the lasso regression equation.

The best model is selected in a way to minimize the least-squares.

Penalizing factor is added to form a lasso regression to the least-squares. The selection of the model depends upon its ability to reduce the above loss function to its minimal value.

All the estimated parameters are present in the lasso regression penalty, and the value of lambda lies between zero and infinity which decides the performance of aggressive regularization. Lambda is selected using cross-validation.

The coefficients tend to decrease and gradually become zero when the value of lambda is increased.

5. Lasso Regression V/s Ridge Regression

Lasso regression and Ridge regression both are used for reducing the complexity of the model. Ridge regression is also known as L2 Regularization. But let us understand the difference between ridge and lasso regression:

Ridge regression has an introduction of a small level of bias to get long-term predictions. This amount of bias is known as the Ridge Regression penalty. By the addition of the penalty term, the alteration of the cost function takes place.

As discussed earlier, the penalty term in lasso regression contains the absolute weights. Therefore due to the use of absolute values, the lasso can shrink towards the slope as compared to ridge regression that will shrink near to zero.

Lasso Linear Regression, also known as L1 Regularization, retains one variable, whereas it sets the other correlated variables to zero. This leads to lower accuracy due to the loss of information.

Ridge regression can be significantly termed as the instance of Lasso regression.

Therefore, it can be understood that lasso, as well as ridge regression, have their respective advantages. Lasso eliminates the coefficients (shrinks to zero) with the help of automatic variable selection for the models, whereas ridge is unable to do so.

However, both of the techniques handle overfitting, which is present in the realistic statistical models. The success of these techniques largely depends on the availability of the data for machine learning. Ridge regression is efficient as compared to lasso, but lasso is successful in eliminating the unwanted parameters present in the model.

Conclusion

Regression is a well-known technique that is used in overfitting. These techniques help in machine learning for predicting the output of the data. Lasso regression algorithm is defined as a regularization algorithm that assists in the elimination of irrelevant parameters, thus helping in the concentration of selection and regularizes the models. Lasso models can be evaluated using various metrics such as RMSE and R-Square. Lasso model also consists of Alpha which is a hyper-parameter. This can be tuned using Lasso CV for controlling the regularization.

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