# BasisFunction Argument in fitrgp function for fitting Gaussian process regression model in matlab

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Shiqun Qiguan on 15 Jun 2022
Hi everyone,
Does someone know that, What is the meaning of BasisFunction Argument in fitrgp function for fitting Gaussian process regression model in matlab? And in which cases should I use constant linear or pureQuadratic?
Thanks a lot

Atharva on 4 Sep 2023
Hey Shiqun,
In MATLAB's fitrgp function for fitting a Gaussian process regression (GPR) model, the BasisFunction argument specifies the type of basis functions used to model the relationship between the input features and the target variable. Basis functions are mathematical functions that transform the input features to a different space, which can help capture complex relationships in the data.
The BasisFunction argument in fitrgp can take one of the following values:
1. 'constant': This option uses a constant basis function, which essentially means that the GPR model only considers a constant mean value for the predictions. In other words, the GPR model assumes that the mean of the target variable is constant across all input points. Use this option when you have reason to believe that the target variable does not depend on the input features, and you want a simple, constant prediction.
2. 'linear': This option uses linear basis functions. Linear basis functions allow the GPR model to capture linear relationships between the input features and the target variable. Use this option when you suspect that the relationship between the input features and the target variable is approximately linear.
3. 'pureQuadratic': This option uses pure quadratic basis functions. Pure quadratic basis functions allow the GPR model to capture quadratic relationships between the input features and the target variable. Use this option when you suspect that the relationship between the input features and the target variable is quadratic in nature.
I hope this helps!
Mahmoud ELKAFAFY on 1 Mar 2024
Hello, But, what does it mean if I set up the basis function to the option 'none'?