Regressors

Regressors are models or algorithms used to predict a continuous target variable from input features. In statistics and machine learning, regression aims to estimate a function f such that y is approximately f(x). A regressor differs from a classifier, which predicts discrete class labels.

Common regressor families range from simple to complex. Linear regression and ordinary least squares model a linear relationship between inputs and the target. Regularized variants include ridge (L2), lasso (L1), and elastic net, which penalize model complexity. Polynomial regression extends linear models with nonlinear feature transformations. Nonparametric and instance-based regressors include k-nearest neighbors, decision trees, random forests, and gradient boosting methods. Support vector regression and neural network-based regressors are also widely used, especially for capturing nonlinear patterns.

Training a regressor typically involves selecting parameters to minimize a loss function on training data, commonly mean squared error or mean absolute error. Regularization helps prevent overfitting by constraining model complexity. Some regressors require feature scaling or normalization, while others are largely scale-invariant.

Model evaluation usually employs cross-validation and metrics such as root mean squared error (RMSE), mean absolute error (MAE), and the coefficient of determination (R^2). Regressors are used in forecasting, economics, environmental modeling, engineering, and other domains where the goal is to predict a continuous outcome. Limitations include sensitivity to outliers for certain models and the challenge of extrapolating beyond observed data.