StudentTProcessModel.exp_model_variance() needs to be computed in every time step because it contains the observation-dependent scaling factor. Currently it's coded so that the routine calls the GaussianProcessModel.exp_model_variance(). While this makes sense theoretically, it is unfortunate, because it is practical only when the model uses RBF-Gauss, which is inexpensive. If we are using RBF-Student however, we need to use large amounts of MC samples to get good approximations to the RBF-Student expectations. Calling this in every time step is insane!
This is a results of a deeper problem. In a broader sense, all the necessary kernel expectations should be pre-computed and saved along with weights as member variables (as done in bq_weights()) so they can be accessed by integral_variance() and exp_model_variance(). This can be done because they only depend on unit sigma-points.
Re-computation of EMV was implemented mainly because at one time I experimented with Bayesian online kernel parameter estimation technique in MarginalInference. It might still be useful for estimation of Bayes-Sard transform parameters.
💡 Use np.random.seed(0) for repeatable results.
💡 RBF-Student expectations could be jitted.
StudentTProcessModel.exp_model_variance()needs to be computed in every time step because it contains the observation-dependent scaling factor. Currently it's coded so that the routine calls theGaussianProcessModel.exp_model_variance(). While this makes sense theoretically, it is unfortunate, because it is practical only when the model uses RBF-Gauss, which is inexpensive. If we are using RBF-Student however, we need to use large amounts of MC samples to get good approximations to the RBF-Student expectations. Calling this in every time step is insane!This is a results of a deeper problem. In a broader sense, all the necessary kernel expectations should be pre-computed and saved along with weights as member variables (as done in
bq_weights()) so they can be accessed byintegral_variance()andexp_model_variance(). This can be done because they only depend on unit sigma-points.Re-computation of EMV was implemented mainly because at one time I experimented with Bayesian online kernel parameter estimation technique in
MarginalInference. It might still be useful for estimation of Bayes-Sard transform parameters.💡 Use
np.random.seed(0)for repeatable results. 💡 RBF-Student expectations could be jitted.