Problems interpreting a Gaussian Process Model.

I have a dataset consisting on a 1000 by 22 matrix (21 features + the label).

That set is normalized (except the label) and introduced into the Regression Learner application of Matlab. The chosen model is “Gaussian Process Regression – Exponential GPR”.

The model is trained and the solution works well for the application, but this is where my doubts start.

I save the model and check its parameters, finding two kernel parameters with two different values, predictor locations (all with very low values ~10^-15), alpha values…

How do I make sense of all of that?

My objective is to see a value or values for each feature, so I can say determine the importance of each feature when calculating the final result. Something along the lines of “if the value of feature_1 increases, the final result decreases a little, but if the value of feature_2 increases, the final result increases significantly”.

Answer 1

[Ayush Anand]

Hi Andrés,

I understand you have some data having certain number of features and you are fitting a Gaussian process regression model on it in the Regression Learner application. You want to approximate the feature importance for each of the features.

The model parameters like alpha values, predictor locations and kernel parameters are a part of the Gaussian Process Regression model and are important for training the model. However, they don’t provide a direct measure of feature importance as would be the case with, say, coefficients for a linear regression model. For a Gaussian process regression model, there are a few workarounds you can try to estimate the feature importance, like Feature Shuffling or drawing Partial Dependence Plots.

The following answers explain these methods in detail:

1. https://www.mathworks.com/matlabcentral/answers/1625860-predictor-importance-for-a-gpr-model?s_tid=answers_rc1-1_p1_Topic
2. https://www.mathworks.com/matlabcentral/answers/2017351-importance-of-predictors-within-an-optimizable-gpr-model

I hope this helps!