What is kernel regression?

Kernel regression is a non-parametric technique used to estimate the conditional expectation of a random variable given some independent variables. It aims to approximate the relationship between the input variables and the output variable without assuming a specific functional form.

In kernel regression, a weighted average of the target variable is computed using a kernel function. The kernel function assigns weights to the data points based on their proximity to the point at which the prediction is being made. Common kernel functions include Gaussian, linear, and polynomial kernels.

Kernel regression is particularly useful when the relationship between the input and output variables is non-linear and is often used in cases where traditional parametric regression techniques may not be appropriate. It is also capable of capturing complex patterns in the data and can be more flexible than linear regression models.

However, kernel regression can be computationally intensive and may require tuning of hyperparameters, such as the kernel bandwidth or the type of kernel function used. Additionally, it may not perform well in high-dimensional data or with large datasets due to the computational complexity involved. Despite these limitations, kernel regression remains a powerful tool for modeling non-linear relationships in data.