# 2.2. Nonnparametric Regression¶

Nonparametric regression is a data-driven alternative to least squares in which the predictor does not take a predetermined form. Kernel regression estimates the response by convolving the data with a kernel function to combine the influence of the individual data points.

## 2.2.1. Nadaraya Watson Regression¶

An example of kernel regression is the Nadaraya-Watson regressor. The Nadaraya-Watson regressor estimates the response \(y\) using a kernel weighted average of the individual datapoints \((x_i, y_i)\):

where \(K(x, x')\) is a kernel function.

The model learned by `NadarayaWatson`

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## 2.2.2. Efficient Leave-one-out Cross-Validation¶

An advantage of the Nadaraya-Watson regressor is that it allows us to perform leave-one-out cross validation in a single evaluation of the regressor. This is useful because often the kernel function \(K(x, x')\) is parameterized by a bandwidth parameter, say \(h\) that controls the width of the kernel. The Nadaraya-Watson regressor can be written as \(\hat{y}(x) = \omega Y\), where:

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Examples