An example on heteroskedastic noise with StudentT likelihood

[IvanDeBoi]

Is there a feature that needs some example code in a notebook?

Hi,
I would like a notbook like this:
https://gpflow.readthedocs.io/en/master/notebooks/advanced/heteroskedastic.html

but with Student-t likelihood as described in http://proceedings.mlr.press/v51/saul16.html.

I can not just change this:

likelihood = gpf.likelihoods.HeteroskedasticTFPConditional( distribution_class=tfp.distributions.Normal, # Gaussian Likelihood scale_transform=tfp.bijectors.Exp(), # Exponential Transform )

into this:

likelihood = gpf.likelihoods.HeteroskedasticTFPConditional( distribution_class=tfp.distributions.StudentT scale_transform=tfp.bijectors.Exp(), # Exponential Transform )

because then I get the following error in the optimization:
missing 1 required positional argument: 'scale'

An example on this would be helpful.

Kind regards,

Ivan

[gustavocmv]

This happens because HeteroskedasticTFPConditional calls the distribution_class as distribution_class(loc, scale), using positional arguments. However, tfp.distributions.StudentT expects signature is tfp.distributions.StudentT(df, loc, scale).

There are some possibilities to work around it. If you want a fixed value for the df parameter, you can just call:

df = 3.0
likelihood = gpf.likelihoods.HeteroskedasticTFPConditional(
    distribution_class=lambda loc, scale: tfp.distributions.StudentT(df=df, loc, scale),
    scale_transform=tfp.bijectors.Exp(), # Exponential Transform
)

If you want to have the df parameter not fixed, I'd suggest subclassing MultiLatentTFPConditional.

[IvanDeBoi]

Great, I thank you very much!