Bayesian polynomial neural networks and polynomial neural ordinary differential equations
Fig 6
For the univariate cubic polynomial f(x) = 1 + x + 2x2 + 4x3, a third order Bayesian polynomial neural network was trained with the Laplace approximation, Markov Chain Monte Carlo with the No-U-Turn-Sampler (NUTS) algorithm, and Variational Inference.
For comparision, Bayesian linear regression was also performed on the training data. We repeated the inference methods for 100 distinct datasets and calculated the fraction of the datasets in which the 90% and 95% credible intervals captured the true parameter value. The 90% and 95% confidence intervals for the 90% and 95% coverage fractions are also shown.