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nrontsis / PILCO

Bayesian Reinforcement Learning in Tensorflow
MIT License
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Reference for predicting with uncertain inputs with SMGPR #40

Closed powertj closed 4 years ago

powertj commented 4 years ago

Do you have a reference available for the derivation of prediction with uncertain inputs with a sparse GP? I haven't been able to find one anywhere.

kyr-pol commented 4 years ago

Hey @powertj, I haven't found a reference that shows specifically how to combine both, but in general they are separate procedures. The sparse approximation used here (FITC, Snelson and Ghahramani) is based on inducing points (pseudoinputs for the GP, replacing the real data points). Once you get the approximation to the kernel according to the method for sparse GPs you are using (see par. 2.4, Sparse Approximations using Inducing Inputs, from M. Deisenroth's thesis ), you can continue with the predictions as you would normally.

That is why in our code only the calculate_factorizations function is redefined in SMGPR (performing the kernel computations and inversions), while the predict_given_factorizations (performing the predictions with uncertain inputs) remains the same with MGPR. Hope this helps!