get_most_significant_input_dimensions() for GPy.GPCoregionalizedRegression?

[gehbiszumeis]

I have trained successfully a multi-output Gaussian Process model using an GPy.models.GPCoregionalizedRegression model. The model has ~25 inputs and 6 outputs.

The underlying kernel is an GPy.util.multioutput.ICM kernel consisting of an RationalQuadratic kernel GPy.kern.RatQuad and the GPy.kern.Coregionalize Kernel.

I am now interested in the feature importance on each individual output. The RatQuad kernel provides an ARD=True (Automatic Relevance Determination) keyword, which allows to get the feature importance of its output for a single output model (which is also exploited by the get_most_significant_input_dimension() method of the GPy model).

However, calling the get_most_significant_input_dimension() method on the GPy.models.GPCoregionalizedRegression model gives me a list of indices I assume to be the most significant inputs somehow for all outputs.

How can I calculate/obtain the lengthscale values or most significant features for each individual output of the model? Thanks!

[gehbiszumeis]

Actually my question didn't make too much sense. After rethinking it, it cannot work with this kind of model, as the ICM is set up such, that all outputs are determined by the same, shared underlying "latent" Gaussian Process. Thus, calling get_most_significant_input_dimension() on a GPy.models.GPCoregionalizationRegression model can only give you one set of input dimensions significant to all outputs together.

Using the GPy.utils.multioutput.LCM model helps out and allows to call the get_most_significant_input_dimension() method for each output individually, as it provides latent GPs for each individual output

See here for more details