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Machine Learning

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California University of Management and Sciences

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Running head: MACHINE LEARNING 1

Machine Learning

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MACHINE LEARNING 2

Lasso and Ridge Regression

Lasso and ridge regression techniques are used in the machine learning algorithm. The

primary difference between the two techniques is that they use different penalty functions in their

computations. Ridge regression is viewed as a regularized linear regression model. In ridge

regression, the regression coefficients are shrunk by imposing a penalty on their size. One of the

assumptions in ridge regression is that predictors are standardized, and the response is centered.

Rodriguez (2013) notes that the ridge coefficients minimize a penalized residual sum of squares.

As a result, weights tend to have smaller absolute values that are evenly distributed. Moreover,

they tend to be close to zero. Although the ridge regression technique enforces the β coefficients

to be lower, it does not enforce coefficients to be zero. Therefore, the technique does not

eliminate irrelevant features but minimizes their impact on a trained model. GeeksforGeeks.org

(2020) notes that the technique leads to both low bias and low variance.

Lasso is the Least Absolute Shrinkage and Selection Operator. Unlike ridge regression,

Lasso penalizes the sum of coefficients absolute values. Further, Lasso differs from ridge

regression in that there is no closed-form expression to compute β (Rodriguez, 2013). The Lasso

technique is also capable of performing the variable selection. Rodriguez (2013) highlights that

as λ increases, a higher number of coefficients are set to zero. In turn, fewer variables are

selected. Indeed, it is a significant advantage in machine learning when fewer features are

included in the model than the initial ones. Lasso tends to have a competitive advantage over the

ridge regression technique due to its prediction error and interpretation ability.

Nonetheless, Lasso is faced with some limitations. GeeksforGeeks.org (2020) explains that

it struggles with some types of data, especially when the number of predictors (p) is greater than

the number of observations (n). In such a case, the technique can select most n predictors as non-

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Running head: MACHINE LEARNING 1 Machine Learning Student’s Name Institution Affiliation MACHINE LEARNING 2 Lasso and Ridge Regression Lasso and ridge regression techniques are used in the machine learning algorithm. The primary difference between the two techniques is that they use different penalty functions in their computations. Ridge regression is viewed as a regularized linear regression model. In ridge regression, the regression coefficients are shrunk by imposing a penalty on their size. One of the assumptions in ridge regression is that predictors are standardized, and the response is centered. Rodriguez (2013) notes that the ridge coefficients minimize a penalized residual sum of squares. As a result, weights tend to have smaller absolute values that are evenly distributed. Moreover, they tend to be close to zero. Although the ridge regression technique enforces the β coefficients to be lower, it does not enforce coefficients to be zero. Therefore, the technique does not eliminate irrelevant features but minimizes their impact on a trained model. GeeksforGeeks.org (2020) notes that the technique leads to both low bias and low variance. Lasso is the Least Absolute Shrinkage and Selection Operator. Unlike ridge regression, Lasso penalizes the sum of coefficients absolute values. Further, Lasso differs from ridge regression in that there is no closed-form expression to compute β (Rodriguez, 2013). The Lasso technique is also capable of performing the variable ...
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Tags: machine learning Linear Regression Model optimization algorithm penalty functions interpretation ability