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SheffieldML / GPy

Gaussian processes framework in python
BSD 3-Clause "New" or "Revised" License
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Heteroscedastic Regression References #1096

Open Artraxon opened 3 weeks ago

Artraxon commented 3 weeks ago

Hi, I don't know much about the specifics of implementing Gaussian Process Regressions, but I am using the heteroscedastic gaussian process regression with learned variances as shown in this notebook https://github.com/SheffieldML/notebook/blob/master/GPy/heteroscedastic_regression.ipynb .

Does someone have some references on how the heteroscedastic Gaussian Process Regression in this library is implemented (from a mathematical perspective)?

MartinBubel commented 1 week ago

Hi @Artraxon generally in heteroscedastic Gaussian Process regression, the variance is learned as a function of x based on known variances for the training data.

As far as I could check the GPy implementation does not fully account for that atm, I'm afraid. It seems like the variance is fixed for the training data but not learned as a function of the features/inputs (x) for the prediction of new points, as it is said at the bottom of the notebook you commented.

Here is a reference to an implementation from botorch which may be helpful in understanding the implementation.

Does this answer you question?