Multiple Polynomial Regression

machine-learning regression statistics

Definition

Multiple Polynomial Regression

Multiple polynomial regression is an extension of polynomial regression to multivariate input features . The model expands the instance space into a higher-dimensional feature space containing all polynomial combinations of the original features up to degree . Formally, the hypothesis is expressed as , where is a basis mapping including all monomial terms such that .

Dimensionality and Overfitting

As the number of features and the degree increase, the dimensionality of the expanded feature space grows combinatorially. This rapid expansion increases the probability of overfitting, necessitating the application of regularisation techniques (e.g., Ridge or Lasso) to ensure the model generalises to unseen data.