When the activation function of a network is analytic (e.g., sigmoid

Neural Information Processing Systems http://nips.cc/

Its derivation, based on Lu et al.[54] is as follows. For the HMC baseline, we use the default implementation of NUTS in Pyro. In Table 7, we present the detailed, non-averaged results to complement Table 4. In both cases, we observe that the performance of the refined posterior approaches HMC's. C.2 Textclassification We further validate the proposed method on text classification problems.

Markov chain Monte Carlo (MCMC) is an inference mechanism that approximates a target probability distribution by a sequence of states (a.k.a.

Table evaluated hyperparameters Dataset Nd GPR |M| - - q() - - free-form Boston 506 13 3.049 Concrete 1030 8 4.864 Ener 768 8 0.441 WineRed1599 11 0.640 Yacht308 6 0.353

Further,the presence of multiple modes can affect the interpretability of kernel hyperparameters.