how to create equation from gaussian trained model from regression learner?

But, then it give me larger error while I'm creating equation from this. As I have a different flow chart of equation. Is it possible to make equation using regression learner. I'm creating model gaussian regression matern 5/2 GPR. How can I get the equation from the this trained model. I'm selecting pressure, temperature, humidity as input and trying to get some output. The y estimated values from the trainedmodel is fitting good. But, Now I want to make equation from this model and how can I make that?

I'm also attaching the input trained data file and test data file.

I want to find coefficient for gaussian equation.

Is there any code or function to calculated the gaussian coefficients?

[Nathan Williams]

Also would like to know this

Answer 1

[Saarthak Gupta]

Hi Nilanshu,

Looks like you are trying to obtain a closed-form expression for the Gaussian Process Regression model trained on your dataset.

Unlike other regression models such as Linear and Nonlinear, Gaussian process regression (GPR) models are nonparametric kernel-based probabilistic models. In GPR models, an instance of the response y can be modelled as:

where f(x)~GP(0,k(x,x′)), that is f(x) are from a zero mean GP with covariance function, k(x,x′). h(x) are a set of basis functions that transform the original feature vector x in Rd into a new feature vector h(x) in Rp. β is a p-by-1 vector of basis function coefficients.

Note: The ’fitrgp’ function is used to fit a GPR model. The function estimates the covariance function, noise variance and the coefficient vector of fixed-basis functions. These properties can be accessed from the ‘RegressionGP’ object which is returned by the function.

Since the model is probabilistic, the response cannot be captured in a closed form expression. Instead, we give the probability density of a response at a new point , given y, X (training data) as:

The expected value of ynew can then be given as:

However, it is recommended that you use the built-in routines for prediction.

Please refer to the following MATLAB documentation for further reference:

• Gaussian Process Regression Models: https://www.mathworks.com/help/stats/gaussian-process-regression-models.html
• Exact GPR Method: https://www.mathworks.com/help/stats/exact-gpr-method.html
• RegressionGP: https://www.mathworks.com/help/stats/regressiongp.html
• fitrgp: https://www.mathworks.com/help/stats/fitrgp.html