# Kernel Regression

## Definition of Kernel Regression

Kernel Regression: Kernel regression is a type of nonlinear regression that uses a kernel function to calculate the weight of each input data point. This type of regression is often used for time series data, where the input points are close together in time.

## How is Kernel Regression used?

Kernel Regression (KR) is a type of non-parametric regression technique used for predicting the values of unknown variables from known data points. It is a powerful model for predicting continuous or numerical output variables given their relationship to other variables in the dataset. Unlike linear regression, KR does not assume any fixed functional form between the independent and dependent variables, rather it uses kernels (or weight functions) to estimate the response variable’s value based on its proximity to known data points.

To predict a value using KR, first an appropriate kernel is chosen that best describes the relationship between dependent and independent variables. The most commonly used are radial basis function (RBF) and Gaussian kernels, although others such as Laplacian, exponential, polynomial can also be used. The kernel then assigns a weight to each data point in the neighborhood of the unknown variable being estimated. The weights are determined by how close they are to the unknown variable and usually decay with increasing distance from it. Finally, these weights are multiplied with the corresponding values of the known data points to obtain an estimate at that particular location. This gives users more flexibility in modeling complex relationships between different inputs and outputs than linear regression would provide.

Overall, because KR doesn’t require manual feature engineering or assumptions about functional forms of underlying relationships between input and output parameters, it has become increasingly popular for dealing with high-dimensional datasets where simple linear models are inadequate or too restrictive. As such it has become one of the most widely used non-parametric methods for predictive tasks such as forecasting and time series analysis due its ability to capture nonlinear relationships within datasets without overfitting or underfitting training data.