Regression analysis is a fundamental concept in machine learning. It's used to predict outcomes based on input variables. Here are some of the most common types of regression in machine learning:
1. Linear Regression
Linear regression is the most basic form of regression analysis. It assumes a linear relationship between the input variables (X) and the single output variable (Y).
- Form: Y = mX + c
- Where:
- Y is the predicted value of the dependent variable.
- m is the slope of the line.
- c is the y-intercept.
2. Logistic Regression
Logistic regression is used for binary classification problems. It predicts the probability of an event occurring based on one or more features.
- Form: P(Y=1) = 1 / (1 + e^-(b0 + b1X1 + b2X2 + ... + bnXn))
- Where:
- P(Y=1) is the probability of the event occurring.
- e is the base of the natural logarithm.
- b0, b1, b2, ..., bn are the coefficients.
3. Polynomial Regression
Polynomial regression is a form of linear regression where the relationship between the input and output variables is modeled as a polynomial.
- Form: Y = b0 + b1X + b2X^2 + ... + bnX^n
- Where:
- Y is the predicted value of the dependent variable.
- b0, b1, b2, ..., bn are the coefficients.
4. Ridge Regression
Ridge regression is a type of linear regression that adds a penalty to the size of the coefficients to prevent overfitting.
- Form: Y = (X^T X)^(-1) X^T y - λ(X^T X)^(-1) X^T u
- Where:
- Y is the predicted value of the dependent variable.
- λ is the regularization parameter.
- u is the vector of coefficients.
5. Lasso Regression
Lasso regression is similar to ridge regression but uses a different penalty term. It can also perform feature selection by shrinking some coefficients to zero.
- Form: Y = (X^T X)^(-1) X^T y - λ(X^T X)^(-1) X^T u
- Where:
- Y is the predicted value of the dependent variable.
- λ is the regularization parameter.
- u is the vector of coefficients.
For more information on regression analysis, check out our Machine Learning Tutorial.