MLJan 24, 2014
The EM algorithm and the Laplace Approximation
arXiv:1401.6276v1
Originality Synthesis-oriented
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This provides a computational improvement for statistical inference in models using EM, but it is incremental as it builds on existing methods.
The paper tackles the problem of efficiently computing second derivatives for the Laplace approximation when using the EM algorithm, by deriving the likelihood gradient from the EM-auxiliary and the Hessian via the Pearlmutter trick.
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 EM-auxiliary, while the Hessian can be obtained from this gradient with the Pearlmutter trick.