How does bayesopt fit a Gaussian process regression model to noisy data?

Hi,

I am using bayesopt to optimise a non-deterministic objective function. I have set the ‘IsObjectiveDeterministic’ input argument to ‘false’, to reflect the stochastic nature of my objective function. My objective function features different levels of noise, depending on the input that is applied to the model.

My question is, does the Gaussian process regression model used in bayesopt assume a constant variance on the noise applied to objective function, or does the GPR model use a non-identically distributed noise for different data points in the observed data? If the latter case is true, how is the noise estimated for different inputs?

Many thanks

Answer 1

[Don Mathis]

bayesopt uses fitrgp to fit the GP models, which assumes constant noise everywhere.

https://www.mathworks.com/help/stats/bayesian-optimization-algorithm.html

[James Finley]

Hi Don,

Many thanks for your response, you have have answered my question. I was also wondering how fitrgp estimates the variance for the noise in a non-determinisitc system?

Thank you

[Don Mathis]

That's part of the Gaussian Process learning algorithm, described here https://www.mathworks.com/help/stats/gaussian-process-regression-models.html

Answer 2

[Resul Al]

Hi Don,

Is there a way to make fitrgp to estimate heteroscedastic noise, i.e noise variance is not constant everywhere?

Thank you.

[Don Mathis]

fitrgp provides no built-in way to do that. It may be possible to do it with a custom kernel function, but I'm not sure.