Gaussian processes for machine learning (GPML) toolbox

The GPML toolbox provides a wide range of functionality for Gaussian process (GP) inference and prediction. GPs are specified by mean and covariance functions; we offer a library of simple mean and covariance functions and mechanisms to compose more complex ones. Several likelihood functions are supported including Gaussian and heavy-tailed for regression as well as others suitable for classification. Finally, a range of inference methods is provided, including exact and variational inference, Expectation Propagation, and Laplace’s method dealing with non-Gaussian likelihoods and FITC for dealing with large regression tasks.

Dynamic learning with the EM algorithm for neural networks

In this paper, we derive an EM algorithm for nonlinear state space models. We use it to estimate jointly the neural network weights, the model uncertainty and the noise in the data. In the E-step we apply a forwardbackward Rauch-Tung-Striebel smoother to compute the network weights. For the M-step, we derive expressions to compute the model uncertainty and the measurement noise. We find that the method is intrinsically very powerful, simple and stable.