The EM algorithm and the Laplace Approximation

The Laplace approximation calls for the computation of second derivatives at the likelihood maximum. When the maximum is found by the EM algorithm, there is a convenient way to compute these derivatives. The likelihood gradient can be obtained from the EMauxiliary, while the Hessian can be obtained from this gradient with the Pearlmutter trick. Let X denote the observed data, H some hidden variables and Θ the model parameters. P (X, Θ) P (X, H, Θ) dH (2) has a more complex form.